A problem of the many

Assume compositional universalism, the doctrine that any bunch of non-overlapping objects have a whole which they wholly compose. Unger's problem of the many is that there seem to be too many people who think my thoughts. After all, if I think my thoughts, so does the guy composed of the same parts as I have, plus one additional particle near me, as does the guy composed of the same as I have, minus one flake of skin. There are solutions to this problem, however. For instance, it might be that for some reason only one of the composites is a person—maybe a person has to be maximal in some way, including all the parts. Or maybe persons are souls, or matter connected with a soul (and there is a metaphysical fact as to which particles are connected to a soul).

The only consistently unrestricted universalism that has any hope of truth, however, is what one might call modal universalism. I will give the four-dimensionalist version, but a three-dimensionalist version is just as easy. Modal universalism says that for any function f from worlds to sets of objects, such that all the f(w) are non-overlapping, and such that for at least one w the set f(w) is non-empty, there is an object O_f such that:

1. For all w, O_f exists at w if and only if f(w) is non-empty.
2. For all w, if f(w) is non-empty, then O_f is composed precisely of the members of f(w) at w.

(For the three-dimensionalist version, replace worlds with world-time pairs.) Bald claim: Anything more restrictive than modal universalism will either not yield all the objects of common sense, such as organisms and artefacts, or else will be ad hoc.

Modal universalism, however, gives a particularly serious problem of the many. Here is a rough-and-ready thesis:

3. Whether x is a person in the actual world thinking about p depends only on what x is up to at w and at worlds sufficiently close to the actual world.

To make this precise, one would need an account of categorical properties to spell out the "is up to".

Anyway, for any at all reasonable story about what "sufficiently close" means, according to modal universalism, there will be infinitely many entities that are composed of the same parts as I am in all the sufficient close worlds, but that differ in some odd way in the further worlds. (There is a being that has the same parts as me in all sufficiently close worlds, but in all further worlds is composed of number seven, assuming the number seven is an object.) By (3), they will be thinking about the same thing as I am. And hence we get too many thinkers thinking my thoughts. Moreover, to make things worse, if there are no empty worlds, some of these thinkers will be necessary beings (e.g., the Pruss/Number-7 being of my previous paranthetical remark).

Now something like a maximality condition, or bringing in souls, may help with Unger's original problem. But there would still be this version to tackle.

Maybe introducing some story about naturalness will help. Maybe only the more natural entities think, and an entity that is composed of the same parts as I at all close worlds and of the number seven at all other worlds isn't natural. However, at some distant worlds, there will be multiple, equally natural (at least if natural is linked with simplicity of law and that sort of thing), choices for f(w), even if we constrain that f(w) = { me } at all close worlds. Unless, of course, naturalness is some kind of metaphysical primitive, having nothing much to do with simplicity of law and so on. So that's a way out, but I doubt it will appeal to many modal universalists.

Let me end with a note about a different topic. I suspect that the only ontology that will support a psychological theory of personal identity will be a universalist one. Thus, this might yield an argument against psychological theories of personal identity.

[Minor errors fixed.]