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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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Now suppose O is a world-bound object—a strange object that has no modal properties because it is not modally (or world-ally) extended; it is just a world-chunk. It exists in only one possible world, and no other.30 And suppose O is composed of (world-bound) parts O1, …, On. If mereological essentialism was false, then O would exist in a world without O1, …, On. Yet in every world in which O exists (just the one!), O is composed of all and only its parts O1, …, On. So, again, mereological essentialism is never false; so it is true.

So either way—whether we are considering trans-world fusions, or world-bound fusions— ME is true if a modal parts theory is.

It may help to think of the temporal analog. Instead of mereological essentialism, let us consider mereological eternalism—the view that that for any composite object, O, O is composed of (all and only) its parts O1, …, On, at every time O exists. The endurantist typically rejects this view because while they accept that ordinary objects are wholly located at particular times, they (typically) disagree that an object has all of its (spatial) parts at every time it exists. That is, the endurantist thinks that objects in fact gain and lose parts over time, thus mereological eternalism is false. But the temporal parts theorist would technically accept mereological eternalism (so defined) for reasons similar to why the modal parts theorist accepts mereological essentialism. According to temporal parts theory, an ordinary object, O, is a trans-temporal object, with parts O1, …, On at different times. Some of O’s temporal parts will qualitatively differ in some of their respective (spatial) parts.

This is analogous to an object that has no temporal properties because it is not temporally-extended (it is just a timeslice), which is analogous to an object that has no spatial properties because it is not spatially-extended (it is just a spacepoint). See footnote 29.

But O itself is the mereological fusion of all of its temporal parts. But then O doesn’t (wholly) exist at any one time—by hypothesis, O’s temporal parts are scattered across different times. If mereological eternalism was false, then O would (wholly) exist at a time without O1, …, On. Yet at every time in which O (wholly) exists (none!), O is composed of all and only its parts O1, …, On. So mereological eternalism is never false; so it is true. Now suppose O is a temporally-bound object—a strange object that has no temporal properties because it is not temporally extended; it is just an instantaneous time-slice. It exists at only one time, and no other. And suppose O is composed of (temporally bound) parts O1, …, On. If mereological eternalism was false, then O would exist at a time without O1, …, On. Yet at every time in which O exists (just the one!), O is composed of all and only its parts O1, …, On. So, again, mereological eternalism is never false; so it is true.

The difference in the underlying metaphysics of ordinary objects between the modal parts theorist and (a certain kind of) non-modal parts theorist is analogous to the difference in the metaphysics of ordinary objects as understood by the perdurantist and endurantist, respectively. An endurantist believes that ordinary objects are wholly present wherever and whenever they are located. A perdurantist (or temporal parts theorist) believes that ordinary objects are never wholly located at (in) a particular time (assuming that no ordinary object is instantaneous). What the endurantist considers the whole object, the perdurantist will argue, is really just a time-slice of a much larger object composed of various temporal parts. Similarly, an ordinary object is not wholly located in one world, according to the modal parts theorist. What many of us consider to be the whole object, the modal parts theorist will insist, is really just a world-chunk of a much larger object composed of various world parts. So the modal parts theorist and the non-modal parts theorist differ greatly as to what they think ordinary objects are, and this difference will factor into our understanding of the connection between mereological essentialism and modal parts theory.

A modal parts theorist will assent to “my cat has all of his parts in every possible world in which he exists.” For this is vacuously true on a modal parts view since cats—having a rich modal profile—don’t (wholly) exist in any one world. Yet it is still the case that my cat can lose (spatial and temporal) parts, since all that this means (on the modal parts view) is that my cat (a trans-world object) has world parts that qualitatively differ (in their spatial and temporal parts).

So according to modal parts theory, ME is true and yet ordinary objects possibly gain and lose parts. How is this even coherent? It seems flat-out contradictory.

On the one hand we have the statement “a trans-world object has all of its parts in every possible world in which it exists.” On the other hand we have the statement “a trans-world object possibly gains and loses some of its parts.” I have been arguing that a modal parts theorist will assent to both of these. The key to avoiding contradiction is to pay close attention to what is exactly meant by ‘parts’ in each statement. In the first case, a modal parts theorist will insist that we are specifically attending to a trans-world object’s world parts. But if so, then she can easily grant that a trans-world object has all of these necessarily (for there is no world where it lacks them). In the second case, however, what is generally meant is that an object possibly gains or loses its spatial and temporal parts (but not world parts). Given what the modal part theorist says that it is for an object to possibly gain and lose (spatial or temporal!) parts—i.e., that the object has world parts that qualitatively differ (in their spatial or temporal parts)—this is no problem. Disambiguating what is meant by ‘parts’ in each case, the modal parts theorist will insist, shows how she can consistently grant that objects possibly gain and lose (spatial and temporal) parts, but also how objects have their (world) parts in every world in which that object exists (none).

One might quickly object, however, that the way in which modal parts theory embraces ME is a cheat, and furthermore belies the seeming boldness of my claim that modal parts makes mereological essentialism intuitive. For ME simply follows trivially from modal parts, and trivial truths are rarely metaphysically significant. Moreover, if ME as originally defined is circumvented in this tricky manner by the modal parts theorist, then it is implausible to think that a modal parts theorist would accept the definition of ME given at the outset of this paper. Indeed, shouldn’t she rather define mereological essentialism as follows?

–  –  –

Since the modal parts theorist cashes out modal differences by qualitative differences in modal parts, these qualitative differences are generated by differences in spatio-temporal parts. Conversely, the modal parts theorist cashes out modal sameness by qualitative identity of modal parts, which is generated by sameness of spatio-temporal parts. So MEmp accurately captures how the modal parts theorist should think of mereological essentialism, not ME.

It’s true that interpreting ‘mereological essentialism’ as MEmp rather than ME falsifies my earlier claim that modal parts “makes good sense of mereological essentialism.” For a modal parts theorist will reject MEmp, making no good sense of it at all. But this is why we must remind ourselves of why we are concerned with mereological essentialism in the first place. I proposed modal parts as a way for the composition as identity theorist to circumvent arguments (a la Merricks) that rely on modal intuitions. If we reinterpret what it is that grounds the modal truths—if it is the fact that we have qualitatively distinct modal parts that makes it the case that certain things are possible or impossible for us—then the modal arguments against CAI fail to gain traction. This is because a modal parts theory accounts for what it is for an object to gain and lose parts. What matters is that they can account for our modal profiles, not how they understand ‘mereological essentialism’. Put another way, the sense of ‘mereological essentialism’ that is seemingly so devastating for CAI is whatever sense it is that entails that ordinary objects cannot gain and lose parts—that is, that ordinary objects are composed of modal parts, each of which is composed of (all and only) the same spatiotemporal parts. But a CAI theorist who accepts modal parts is not committed to this.

Let’s suppose a CAI theorist adopts modal parts (CAI +MP). Then she will claim that ordinary objects are mereological sums of spatial, temporal, and world parts. Moreover, each transworld sum is (collectively) identical to (all and only) its spatial, temporal, and world parts. Any difference in any of these parts will result in a distinct object. Suppose you have a lump of clay that comes into existence at the same time as a statue, such that the lump constitutes the statue. We have a lump and a statue that have completely overlapping spatial and temporal parts. Are the lump and the statue nonetheless distinct objects? According to CAI +MP, yes if they differ in their modal parts; no if they don’t. If you have the intuition that most of us have, the lump of clay can be squished and still survive, but the statue cannot. But, according to modal parts theory, this just means that the (trans-world) lump of clay has modal parts that the (trans-world) statue does not.

Some of their world parts overlap, but their distinctness is determined by the world parts that don’t.

Does this mean that CAI is false? No. Because CAI claims that any object—in this case the transworld lump or trans-world statue—is identical to all of its respective parts. This is still the case;

given CAI+MP, the relevant trans-world objects are identical to all of their respective parts, which include the modal ones.

Let’s change the case to one of composition, not constitution.31 Suppose we have some Lego blocks that compose a Lego house. If CAI is true, does that mean the blocks are identical to the house? Not if they differ in any of their spatial, temporal or world parts. Does this mean that CAI is false? No, because again, according to CAI, a whole is (collectively) identical to all of its parts.

Traditionally, the difference between composition and constitution is that the former is a many-one relation whereas the latter is one-one. I do not think that there is a metaphysically important difference here, and I certainly do not think that a CAI theorist should think so. But I’ll leave this discussion for another time.

According to CAI + MP, this includes modal parts (assuming the object in question is modally extended).

So how, exactly, does CAI + MP get us out of the modal objections presented in section 2?

As explained above, ME is true if CAI + MP is. If it is protested that once CAI + MP is on the

table, we mean by ‘mereological essentialism’ MEmp, then premise (2) will have to be changed to:

MEmp is false. But if so, then premise (1) must claim that CAI entails MEmp, on pain of invalidity.

But CAI + MP does not entail MEmp, so CAI does not either. In this way, a CAI +MP theorist can reject MEmp, accept ME, and yet avoid the modal objections given at the outset of this paper.

4. Objections, Replies Let me take a moment to address a few objections, beginning with modal parts, and ending with some considerations about modal parts with CAI.

One of the more controversial assumptions I began with in order to get the modal parts view going was a commitment to modal realism—i.e., that there are concrete possible worlds.

Indeed, I have talked of possible worlds and world parts as if these were uncontroversial entities.

But very few of us are modal realists. So why should anyone take modal parts seriously?

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