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«There are many arguments against composition as identity.1 One of the more prominent of these maintains that composition as identity (CAI) entails ...»

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do so by having different parts at different times (worlds).” So we will be committed to spatial, temporal, and modal parts; we will be committed to the idea that objects are spatially, temporally, and modally extended. 19 A temporal parts theorist defends the view that individuals are trans-time fusions—stretched out in time (and space) the way that ordinary folk believe a road is stretched out (only) in space.20 Ordinary objects—such as cars and cats and running shoes—are spatiotemporal worms, or mereological sums of time slices of three-dimensional objects.21 One of the benefits touted for temporal parts is that we can wriggle out of notorious metaphysical puzzles.22 Consider change over time: When you were five years old you were 3’ tall, not 5’4; now you are 5’4, not 3’. We would like to think that you remain the same object over time despite minor changes (a growth spurt, say). But you at five years old had the property being 3’ (and not 5’4). You at thirty-seven have the property being 5’4 (and not 3’). But then by the Indiscernibility of Idenitcals, you at five is not identical to you at thirty-six. So, contrary to our intuitions, you do not survive over time or over change.

But temporal parts to the rescue. The idea of ‘you at five’ and ‘you at thirty-seven’, a temporal parts theorist argues, is strictly speaking a mis-description of the facts. Objects aren’t wholly present at a time. Rather, they are extended across time (and space). So one temporal part of you is 3’ and another temporal part of you is 5’3. But this is no more of a contradiction than the fact It is possible to commit to modal parts without committing to spatial or temporal parts. For this reason, and following Weatherson (ms), I will refrain from calling a modal parts theory ‘five-dimensionalism.’ However, since the view I am defending here is the modal analog of views that endorse spatial and temporal extension, and it is (to my mind) conceptually easier to consider a position that maintains symmetry with respect to its view on space, time and worlds, I will only focus on a modal parts theory that embraces spatial, temporal, and modal parts. But variations of my view are theoretically available.

I am admittedly being a bit sloppy. There are various kinds of temporal parts theories, and not all of them agree on the picture I am painting here. Yet since I am only using temporal parts as a springboard to make a modal parts view coherent, broad strokes should be fine for now.

Sider (1997), (2001), Heller (1993), Lewis (1986), etc.

In fact, this is one of the leading reasons Sider is convinced that the view is true.

that a spatial part of you is on the ground (your foot, for example) and another spatial part of you is not (your head, let’s hope). The temporal parts theorist insists that what it is for an object to change over time is analogous to change over space. A spatially extended object changes over space iff there is one spatial part of that object that is qualitatively distinct from another spatial part. A temporally extended object changes over time iff there is one temporal part of that object that is qualitatively distinct from another temporal part of that object. Change over time, then, “is difference between successive temporal parts.”23 One may object that on a temporal parts picture, ordinary objects do not strictly speaking gain and lose parts. Since objects on this view are trans-temporal fusions, the object itself—the fusion— has all of its parts all of the time; it doesn’t gain and lose parts at all. So it seems that all of our ordinary statements about change will turn out false.24 But the temporal parts theorist insists that the metaphysical facts are different than we may have initially supposed. Let’s take my desk as an example. According to a temporal parts theorist, my desk is a trans-temporal object that has a temporal part, tp1, that is composed of molecules m1, …mn. My desk has another temporal part, tp2, however, that is composed of molecules m1, …,mn, mn+1. To say that my desk gained a part, then, is just to say that my desk has two temporal parts, tp1 and tp2, which differ in their mis, such that tp2 has all of the parts tp1 has, plus one. So, the temporal parts theorist will insist, it is not the case that our statements about ordinary objects concerning change are flat-out false. Rather, what makes these statements true is different than we may have pre-theoretically thought. In this way, we have a view of objects that captures our intuitions about my desk: my desk does gain and lose parts over time and still remains the same object. It’s just that 23Sider (1997), (2001), (2007).

See Hinchliff (1996), e.g.

the metaphysical facts grounding what it is for something to change, or gain and lose parts, are slightly different than we may have first supposed.

I intend for a modal parts view to be very similar, with the difference being that the relevant parts under consideration are modal (or world-al), as well as temporal. According to this view, individuals are not only trans-time, but also trans-world.25 What makes it the case that my desk could have had one more (spatial) part than it actually does is that in some other possible world, a (world) part of my desk (the part that is in another possible world) has one more (spatial) part than another (world) part (the part of it that is in the actual world) does.26 The definition of modal parts may be given as an analog of the definition of temporal parts.





Sider (2001) gives the following mereological definition of a temporal part: x is an instantaneous temporal part of y at an instant t =df (i) x exists at, but only at, t, (ii) x is part of y at t; and (iii) x overlaps at t everything that is part of y at t.27A parallel (initial) definition of modal part is: x is a world-bound modal part of y at a world w =df (i) x exists at, but only at, w, (ii) x is part of y at w; and (iii) x overlaps at w everything that is part of y at w.28 This definition may ultimately need some tweaking, but let us begin with it.

One initial worry for the temporal parts theorist is that she will not be able to account for the fact that we think that objects gain and lose parts over time. For if an ordinary object just is a I mean by ‘trans-world’ in ‘trans-world individual’ something similar to ‘trans-continental’ in ‘trans-continental country’—I am talking about an individual (country) that is stretched out across worlds (continents), yet is not wholly located in one world (continent). I do not mean it (as it is sometimes used) to indicate an individual that is wholly located in more than one world.

Even Lewis himself countenances such trans-world individuals (because he accepts universalism). But he denies that they are metaphysically relevant. See Lewis (1986).

Sider (2001: 59). Sider gives an atemporal mereological definition of ‘temporal part’ for the benefit of the threedimensionalist a page later. Similarly, one may give an a-world-al mereological definition of ‘modal part’ for the benefit of the modal equivalent of the three-dimensionalist—i.e., those who think that objects can exist in more than one world and are wholly located wherever they exist.

I’m assuming that the modal equivalent of instantaneous is world-bound.

trans-time fusion, then it has all of its parts all of the time, and so—in a certain sense—it (the fusion) doesn’t lose parts at all. But the strategy invoked is to recast our talk of temporal change into differences between successive temporal parts. Similarly, the modal parts theorist faces an initial, parallel worry: we think that objects can gain and lose parts. We think that, even if my desk is composed of parts p1, …, pn, in the actual world, it could have been composed of parts p1, …, pn, pn+1 instead; we think that it is made out of parts p1, …, pn, pn+1 in some other possible world. According to the modal parts theorist, talk about differences of individuals (or counterparts) in distinct possible worlds will be cashed out in terms of differences between modal parts of trans-world (and transspatio-temporal) individuals. An individual, then, has (at least) one (world) part in one world and another (world) part in another world.29 Any differences between these parts will ground the modal facts about these individuals.

Let’s take my desk as an example again. My desk (a trans-world object) has a world part, wp1, let’s say, that is in the actual world, and which is composed of wood molecules m1, …mn. My desk has another world part, wp2, however, that is in another possible world, where it is composed of wood molecules m1, …,mn, mn+1. To say that my desk could have gained a (spatial) part, then, is just to say that my desk—the lumpy, trans-world object—has (at least) two world parts, wp1 and wp2, which differ in their mis, such that wp2 has all of the parts wp1 has, plus one. Analogous to the move the temporal parts theorist makes to account for change, the modal parts theorist maintains that it is not that our statements about the persistence conditions of ordinary objects are flat-out false.

Rather, what makes these statements true is different than we might have (pre-theoretically) thought. In this way, the modal parts theorist endorses a view of objects that captures our intuitions about my I suppose there could be strange individuals that have only one modal part, just like there may be strange individuals that have just one (instantaneous) temporal part, just like there may be strange non-extended objects that have only one spatial part, etc. But let’s leave these weird objects aside for now; objects with no modal parts would be extremely fragile beings!

desk: my desk could gain and lose parts and still remain the same object. It’s just that the metaphysical facts grounding what it is for something to possibly gain parts are slightly different than we may have first supposed.

But wait. At the start of this paper I had said that a commitment to modal parts would make mereological essentialism plausible. Yet I have just said that a modal parts theorist will gloss our talk of what is possible and impossible for ordinary objects by talk of differences in world parts— analogous to how a temporal parts theorist glosses our talk of change over time by talk of differences in temporal parts—thereby honoring our ordinary intuitions that ordinary objects possibly gain and lose parts—i.e., honoring our intuition that objects do not have their parts essentially. If a modal parts theorist can capture the intuition that ordinary objects possibly gain and lose parts, then how is it that a commitment to modal parts is not only consistent with mereological essentialism but, in addition, makes ME intuitive?

Just because a modal parts theorist grants that it’s possible for ordinary objects to gain and lose (spatial and temporal) parts, this does not contradict her commitment to mereological essentialism as it was defined above. Recall that ME maintains that any composite object O, is composed of (all and only) its parts O1, …, On, in every possible world in which O exists. But this is going to turn out trivially true on a modal parts picture, since she maintains that ordinary objects are trans-world fusions—not world-bound objects that exist in only one world. And this, she will insist, is going to make all of the difference in our understanding of what mereological essentialism is.

Suppose O is any ordinary object you please: a car, a cat, a running shoe, etc. According a modal parts theory, O is a lumpy, trans-world object, with parts O1, …, On in different possible worlds. Some of O’s world parts will have qualitatively different spatial and temporal parts. But O itself is the mereological fusion of all of these world (and spatial and temporal) parts. But then O doesn’t (wholly) exist in any one world—by hypothesis, O’s parts O1, …, On are scattered across different possible worlds. If mereological essentialism was false, then O would (wholly) exist in a world without O1, …, On. Yet in every world in which O (wholly) exists (none of them!), O is composed of all and only its parts O1, …, On. So mereological essentialism is never false; so it is true.



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