Modal Parts

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 pW 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 pW then o exists, o has a part o’ such that Necessarily, o’ exists iff pW.

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 pW. 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.

10 Replies to “Modal Parts”

  1. Brian,
    Two questions. (1) You work to get your modal parts doctrine into a form which is neutral between “modal realists” (in quotation marks because some, like Al Plantinga, think this label is misleading and that actualists are the true modal realists — see his “Modal Realism and Modal Reductionism”) and actualists. But you don’t similarly work to get your motivations and/or arguments for modal parts into a form which actualists can understand. But for the life of me I can’t see how to separate some of your motivations from modal realism. For example, what’s an actualist to make of the claim that an actual lump of clay or an actual statue is a fusion of modal parts? Is it the sum of this actual thing and those haecceities? The sum of a bunch of haecceities? The haecceity of a sum? Similarly, the argument from contingent intrinsics seems to have no appeal to an actualist as an argument for your actualism/realism -neutral form of the doctrine of modal parts. (See Plantinga and van Inwagen on transworld identity. They don’t hold what Lewis is arguing against, namely that Humphrey, he himself, has 10 fingers “here” and 12 fingers “there” — there is only one Humphrey on there view, and he is only really “here” — there is no “there” in any sense that could raise Lewis’ problem. But it is true that Humphrey has (had, anyway) 10 fingers, though he might have had 12.)

    (2) The only argument you give that seems to me to even intelligible to an actualist is your vagueness argument. But, I don’t see the force of that argument. Mind you, I haven’t read Sider on temporal parts. But, going just by your summary:

    “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 pW. 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.”

    So? Why suppose that there must be any such principle? Why not just let the objects/haecceities dictate matters here? I think that the assumption that there must be a principle, as opposed to just a bunch of irreducible modal facts about parts, is of a piece with what Plantinga calls “modal reductionism” in his argument that Lewis is not truly a modal realist. So I can see reasons for dissenting from this argument too (possibly these reasons make more sense from an actualist point of view).

  2. Yep, most objects have parts that don’t (actually) exist. That’s odd. Though temporal parts theory has a similar consequence – most objects have parts that don’t (now) exist.

    I agree that it isn’t clear the arguments generalise if you’re not a modal realist. That’s definitely something to be taken into account here.

    I wouldn’t try explaining what modal parts are in terms of haecceities. Rather, I’d do something like what Yablo does and have individuals ‘built up’ out of their modal properties. So the statue is the matter there plus the modal property ‘can survive replacement of some matter’ etc., and the lump of clay is the matter plus the modal property ‘can survive being squished’ etc. These are fairly ugly objects, since they are so heterogenous, and that I think detracts from the quality of the solution to the paradoxes. But I don’t think it destroys it.

    The response to the vagueness argument is I think an important one. People have made similar responses to Ted’s arguments for temporal parts – it might be that some things just are extended for a certain temporal duration and others aren’t, an that’s all there is to it. (‘Brutalism’ I think is the preferred name for this view, since facts about temporal duration are brute facts.)

    Interestingly, the two people who have made this objection to Ted (Ned Markosian and Trenton Merricks) are both presentists, which matches up with your idea that this objection works better on an actualist metaphysics. I think it’s an important objection either way though.

    I worry that the vagueness argument for modal parts will end up collapsing at every point when spelled out. Even if it does, that would be interesting, because it might tell us something about the (quite important I think) vagueness argument for temporal parts.

  3. It’s cheating to put in the qualifiers “now” and “actually”. It’s a consequence of the position (as stated) that most objects have parts that don’t exist, simpliciter. It’s not a consequence of temporal-parts theory (as usually understood) that most objects have parts that don’t exist, simpliciter. (I’m assuming that quantifiers in the definition are unrestricted.)

  4. It’s cheating iff you believe in eternalism but not any kind of modal realism. Personally, I’m inclined to think that some kind of modal realism, probably what Stalnaker calls moderate modal realism, is true, so these modal parts do exist, they are just abstracta. If you don’t believe in possible worlds at all, then perhaps this is a disanalogy.

    Or perhaps it isn’t. What’s the logical form of “Most objects have parts that don’t exist.” I think there are three quantifiers as in:

    (Most x)(Some y:Part-of(y,x))~(Some z)(y=z)

    That’s clearly false. But now I think my original statement of the doctrine of modal parts will be false too. What I should have said is:

    For any class of worlds W, let pW 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 pW then o exists, o might have had a part o’ such that Necessarily, o’ exists iff pW.

  5. Right: adding an extra operator avoids the problem. Of course a presentist temporal-parts theorist should do the same thing.

  6. Brian,

    Could you clarify the last? First, the case for extending a potential o’ within pW doesn’t demonstrate an actual or required o’ within pW. Nor is it accurate to claim an o’ that existed in the past as a part of o Necessarily continues in the same state of relation with o in the present. If the relation between o and o’ has a past perfective connective, there’s not really a case for extending the relation to imply the existance of o in the present must also imply the existance of o’ as well… Probably I’m just not catching the relations.

    It reads a lot like classic topology. There is a map such that… &etc. Is that the source of the connectives?

  7. brian,

    if modal parts are parts i might have had, there seems a pretty uncontroversial way to read that.

    possibly p is a part of x iff there is a world at which p is a part of x

    On counterpart theory, thats going to come out that x has a counterpart that has p as a part.

    This is reminding me of the modal properties stuff. There’s one way of reading the claim that x is possibly F thats really controversial – x has the property of being-possibly-F. On a different reading, it turns out that the truth conditions for the claim that x is possibly F just involve x being F at some possible world. E.g. we can call the de re fact that our world could have been smaller a modal property if we want, but all that boils down to is our world having a counterpart that is smaller.



  8. Rich, that would be an uncontroversial statement of the modal parts doctrine if it were uncontroversial that possible worlds exist. But that isn’t uncontroversial. Nor is counterpart theory. I’m trying to find a statement of the modal parts theory that an actualist, and an anti-counterparter, can accept. (By ‘accept’ I mean accept as coherent, not accept as true. The first stage is just to convince actualists that there is an interesting debate here.)

  9. ok, so possible worlds and counterpart theory are controversial. Im just concerned that anyone (actualist or non-actualist), (counterparter or anti-counterparter), (fictionalist or realist), is going to think that there is a really uncontroversial statement of the doctrine of modal parts – viz. the one i listed. Fair enough, this is going to depend on whether we are playing ball with possible worlds semantics, and that is controversial. (Actually, its going to be controversial whether we should be realists (as opposed to error-theorists or fictionalist or agnostics)). Rightly or wrongly, people tend to talk about possible worlds first and worry about their status later. And if they are the rules of the game, then the thesis that we have modal parts has a (pretty much) uncontroverisal reading. Maybe…

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