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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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Composition as Identity, Mereological Essentialism and

Modal Parts

1. Introduction

There are many arguments against composition as identity.1 One of the more prominent of

these maintains that composition as identity (CAI) entails mereological essentialism (ME).

Composition as Identity (CAI): for any a composite object, O, is (collectively)

identical to its parts, O1, O2, …, On.2

Mereological Essentialism (ME): for any composite object, O, O is composed of (all and only) its parts O1, …, On, in every possible world in which O exists.3 But ME is prima facie outrageous. You do not, after all, think that you would have ceased to exist if you had lost one skin cell. Or that cutting your hair or growing a mustache or taking a shower would result in the destruction of one person—you!—or the (ex nihilo) creation of another. What goes for you goes for any ordinary object whatsoever—they can all survive the loss (or replacement or addition) of parts. But if so, then ME is false. And so is any view that entails ME. So much the worse for CAI, then, if CAI entails ME.4 Appeal to the entailment of CAI to ME, and to the purported falsity of ME, abounds in the metaphysical literature. Van Inwagen (1981, 1990), for example, thinks that the choice is between mereological essentialism and denying the existence of composite objects. Famously, he embraces the latter, but he does so by disjunctive syllogism, relying on the supposed falsity of ME.5 Cameron See Merricks (1999), Van Inwagen (1990), Sider (2007), Cameron (this volume), etc., e.g.

O is not identical to each of O1, O2,..., On, but is collectively identical to them in the way that some students collectively surround a building. Also, the identity here is strict identity, not merely analogical, or one that disobeys the Indiscernibility of Identicals, contra Lewis (1991) and Baxter (1999), respectively.

Definition borrowed from Merricks (1999).

This argument is given by Merricks (1999).

To be a bit more careful: Van Inwagen thinks that a commitment to universal composition (universalism) carries with it a commitment to something like mereological essentialism; he doesn’t specifically talk about CAI. But since a (this volume) relies on the supposed absurdity of ME as one reason to reject CAI. Van Cleve (1985), while not concerned with composition, argues that trouble abounds for (a certain kind of) bundle theory of properties because it entails mereological essentialism, and ME is clearly false. And so on.

My aim in the following paper is not todeny the claim that CAI entails ME; indeed, as I will explain in the next section, I think this claim is true.6 Rather, I aim to show how mereological essentialism—contrary to popular intuition—may in fact be true. I will do this by outlining a view of ordinary objects that embraces modal parts, the possible world analog of temporal parts. This view maintains that individuals are stretched out across possible worlds in the way that a temporal parts theorist maintains we are stretched out over time.7 Such a view of objects, I argue, renders mereological essentialism both intuitive and compelling. If I am right about this, then any arguments which have heretofore relied on the falsity of mereological essentialism must now be reconsidered.

Moreover, embracing rather than rejecting mereological essentialism undermines the argument against CAI given above, as well as others that are similar in spirit. While I think that adopting modal parts is advantageous in its own right8, a coupling of this view with CAI fortifies CAI against (certain) opponents. I will conclude by considering some objections.

commitment to universal composition is assumed by my account of CAI (defended in Wallace 2011), his argument will apply to CAI. The important point is that mereological essentialism is often seen as a reason to reject certain other views, including CAI.

If this claim is understood in the way Merricks intends. See discussion, end of section 3.

See Weatherson, “Stages, Worms, Slices and Lumps” (ms) http://brian.weatherson.org/swsl.pdf. A view that accepts modal parts is what Weatherson calls a “lump theory”. To my knowledge, Weatherson is one of the more recent discussions of modal parts (as I describe the view here), although his interest in the view is primarily an exploration of logical space. Weatherson attributes modal parts (or lumps) to Kaplan (1979), which is a paper that was first presented in

1967. McDaniel (2004)) discusses a kind of modal parts theory, but it is different than the one I propose here, and he does not defend the view as plausible. L. A. Paul (2002) defends a view of objects as mereological sums of properties, including modal poperties, in which case objects may be said to have modal parts. So while the idea of modal parts in general is not novel, the particular theory described here, and how it is used as a way to make mereological essentialism plausible, and its application to puzzles of constitution and composition, is. Moreover, as far as I am aware, no one has proposed modal parts (so understood in this paper) as a competitive view, worth taking seriously, as I suggest in this paper.

Defense of this claim will be left for another time. But see Wallace (ms) for an independent argument for modal parts.

–  –  –





Here are two quick arguments for why we should think CAI is true (these are not intended

to be decisive; I am merely providing initial, intuitive motivations for the view):

–  –  –

However, there are several arguments against CAI, all similar in spirit, each of which seemingly renders moot the above arguments. Trenton Merricks (1999), for example, argues against CAI as follows:13

–  –  –

I mentioned at the outset why (2) is seemingly true—we think that many ordinary objects could lose (and gain) parts and still survive, which violates ME. But let us focus on (1).

Merricks argues:

“…suppose that O, the object composed of O1 …On, is identical with O1...On. From this, the fact that O1...On are identical with Ol...On in every possible world, and the indiscernibility of identicals it follows that O is identical with Ol...On in every possible world). Therefore, if composition as identity is true, there is no world in which O exists but is not composed of Argument given in Wallace (2011).

Universalism claims that any two objects whatsoever compose a mereological sum.

If there are not finitely many things in the universe, then if CAI is false and universalism is true, then there are uncountably many things in the universe. This (some may argue) is absurd, or (at the very least) unnecessarily unparsimonious. Thanks to Aaron Cotnoir and Donald Baxter for bringing this to my attention.

Some philosophers may wish to pin the reductio on universalism, not CAI. Fair enough. But my aim here is to give some initially plausibility for CAI, not a conclusive argument. So more carefully, if one accepts universalism, then there is motivation to accept CAI, on pain of the absurd consequence that there is a priori an odd number of things in the universe (if the universe has finitely many objects).

Where CAI and ME are defined as they are above, p. 1.

O1...On. So composition as identity implies that O—and, of course, every other composite object—must, in every world in which it exists, be composed of the parts that actually compose it. Composition as identity entails mereological essentialism.” [1999:192-1] If CAI is true, then any composite object is (collectively) identical to its parts. But then by the Indiscernibility of Identicals, there is no world where the composite object exists and its (actual) parts do not. This is pretty convincing. If you disagree, and think (1) is false14, then CAI is safe.15 So I will assume (1) in what follows.

One way to put Merricks’ argument in connection with the above arguments for CAI is with a Moorean spin: we are more assured of ME's falsehood than we are that CO-LOCATION or ODD THINGS are good (enough) reasons for CAI. So CAI is false.

A slightly different line of reasoning is the following: CAI is a thesis that (can be) motivated by thinking about the relation that a mereological sum has to its parts (as evidenced by ODD THINGS). But mereological sums have their parts essentially, while ordinary objects do not. So it cannot be that the relation a mereological sum holds to its parts is the same relation that I hold to my parts, since I can lose my parts but a mereological sum cannot. Assuming that the CAI theorist is endorsing a single relation (viz., identity) that is had by both mereological sums and ordinary objects, this is doomed from the start since these are clearly different relations.

Finally, another argument against CAI: ordinary objects might have a very special relationship with their parts, but they aren’t identical to them. For arrangement matters. I cannot be identical to my parts because if all of my parts were arranged haphazardly, I could not survive. So CAI must be false.16 One way would be to deny the Indiscernibility of Identicals, as Donald Baxter (1999) does. Also, if one maintains a weaker form of composition as identity, a la Lewis (1991), then one could maintain that one of the (few) differences between composition and identity would be that the latter obeys the Indiscernibility of Identicals while the former does not. But these options do not assume the version of CAI I am defending here, so let us leave them aside for now.

From Merricks’ argument, at least.

See Cameron (this volume), e.g.

All of the above arguments are similar in spirit, for they all rely on modal intuitions: I could lose some parts and survive, I could not have my parts haphazardly re-arranged and survive, etc. Our intuitions about the modal profiles of ordinary objects (seemingly) direct us to conclude that CAI is false, regardless of any arguments (such as CO-LOCATION and ODD THINGS) to the contrary.

In the next section, I aim to show how these modal intuitions can be respected and yet this is no threat to CAI. I propose that this can be accomplished if we accept a particular view of ordinary objects—one that maintains that they are modally extended.

–  –  –

Most of us think that ordinary objects have spatial parts.17 You have your hand and head as parts, for example. This page has a top half and a bottom half, etc. Some of us think that in addition to these spatial parts, objects also have temporal parts—instantaneous time slices of a temporally extended whole.18 Yet it is theoretically available to think that you have more than just spatial and temporal parts; you may also think that you have modal or world parts. Let me take the following section to describe (at least one kind of) modal parts view, and to explain how such a view makes good sense of mereological essentialism. Then I will explain how such a view can be beneficial to CAI.

For expository purposes, let us allow the modal parts theorist two assumptions for now (which we may later choose to drop): let us be realists about times and realists about possible worlds.

We will assume that there are times other than the present, and we will assume that there are possible worlds other than the actual world. Following Weatherson (ms), let us also characterize the modal parts theorist as someone who thinks that “objects which exist at more than one time (world) Some don’t. See Van Inwagen (1990), Unger (1979), Sider (forthcoming), e.g.

See Sider (2001), Lewis (1986), Heller (1993), et. al.



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