Philosophical Studies

, Volume 159, Issue 1, pp 1–20

Modal Mereology and Modal Supervenience

Authors

    • Department of PhilosophyUniversity of Minnesota
Article

DOI: 10.1007/s11098-010-9681-2

Cite this article as:
Walsh, S.D. Philos Stud (2012) 159: 1. doi:10.1007/s11098-010-9681-2
  • 120 Views

Abstract

David Lewis insists that restrictivist composition must be motivated by and occur due to some intuitive desiderata for a relation R among parts that compose wholes, and insists that a restrictivist’s relation R must be vague. Peter van Inwagen agrees. In this paper, I argue that restrictivists need not use such examples of relation R as a criterion for composition, and any restrictivist should reject a number of related mereological theses. This paper critiques Lewis and van Inwagen (and others) on their respective mereological metaphysics, and offers a Golden Mean between their two opposite extremes. I argue for a novel account of mereology I call Modal Mereology that is an alternative to Classical Mereology. A modal mereologist can be a universalist about the possible composition of wholes from parts and a restrictivist about the actual composition of wholes from parts. I argue that puzzles facing Modal Mereology (e.g., puzzles concerning Cambridge changes and the Problem of the Many, and how to demarcate the actual from the possible) are also faced in similar forms by classical universalists. On my account, restricted composition is rather motivated by and occurs due to a possible whole’s instantiating an actual type. Universalists commonly believe in such types and defend their existence from objections and puzzles. The Modal Mereological restrictivist can similarly defend the existence of such types (adding that such types are the only wholes) from similar objections and puzzles.

Keywords

MereologyUniversalismRestrictivismModalSupervenienceDavid LewisPeter van InwagenCompositionWholesPartsProblem of the Many

1 Introduction

This paper critiques the universalist David Lewis and the restrictivist Peter van Inwagen (and others) on their respective mereological metaphysics, and offers an alternative view. Lewis insists that ‘restrictivist’ composition must be motivated by and occur due to some intuitive desiderata for a relation R among parts that compose wholes, and insists that a restrictivist’s relation R must be vague. Examples Lewis gives as candidates for restrictivist relation R include ‘parts acting jointly,’ ‘parts sticking together,’ and ‘parts being adjacent to each other in space–time’ (1986, pp. 211–212).1 Van Inwagen (1995) and others2 do indeed favor using a version of relation R as a key feature of mereological composition. My ‘Modal Mereology’ account of restrictivism does not require that such versions of relation R serve as a necessary or sufficient condition for composition, and thus my account can avoid a number of problems the Lewis and others attribute to restrictivism. In this paper, I argue that restrictivists need not use such examples of relation R as a criterion for composition, and should reject a number of related mereological theses, including the Duplication Principle (DP), on which a physical duplicate of a whole also must compose a whole. On my account, restricted composition is rather motivated by and occurs due to a possible whole’s instantiating an actual type. I will argue (a) that universalists give accounts of such types that have resources to solve puzzles about vagueness and the Problem of the Many, and (b) that the restrictivist can borrow these resources to solve the same puzzles if the restrictivist uses ‘typehood’ to demarcate ‘possible wholes’ from ‘actual wholes’.3

Contrary to Lewis’ focus on relation R, I believe mereological restrictivism, often called the restricted mereological composition view, can be motivated as a more common sense alternative to and a Golden Mean between two extremes: mereological nihilism and mereological universalism. Mereological nihilism is the extreme view that there is nothing that has any parts, and there are no composite objects (composite wholes) made up of parts. According to mereological nihilism, there are no whole tables, chairs, planets, or organisms, since they would presumably need to be made of parts like atoms. Mereological universalism, often called the unrestricted mereological composition view, is the opposite extreme view that any objects compose a composite, whole being. According to mereological universalism, any group of things that exists compose something—e.g., my ear and the moon and a car in France composes a true mereological whole (call it the ‘ear-moon-car’) simply in virtue of there being an ear, moon, and car.

In this paper I argue that, on any restrictivist account of mereological composition, a number of commonly held metaphysical theses (theses which some universalists and restrictivists consider to be good-making features of a mereological theory) are false. I argue that the Duplication Principle and what I call the Internalist Principle, Classical Mereology, and Classical Mereological Supervenience must be false for restrictivists (but all can be true for universalists).4 Call these mereological theses the ‘Mereological Theses’. As the paper progresses, I will clarify various strong and weak versions of the Mereological Theses. A commitment to the truth of the Mereological Theses is natural if one is also committed to a Lewisian version of relation R as a core criterion of composition. To put these closely related Mereological Theses initially and rather crudely, (a) the Internalist Principle expresses the idea that composition occurs because of features internal to the parts (e.g., because of the parts plus relation R obtaining), (b) the DP expresses the idea that if a composite whole exists, then its exact physical duplicate exists as well, and (c) Classical Mereological Supervenience and Classical Mereology express the idea that each whole supervenes on and exists in virtue of its parts (restrictivists requiring the addition of some internal relation R among the parts).

According to the arguments of this paper, on any standard restrictivist account of mereology, it is not the case that a perfect duplicate of a whole composite object must also be a whole composite object.5 I will also argue that, on standard restrictivist views, Cambridge changes can create and destroy whole organisms, since according to my arguments, Cambridge changes can create and destroy any composite wholes on restrictivism.6 However, I will argue that similar Cambridge changes concerning organisms and other types can occur on Lewis’ and other universalist accounts. Thus, I will argue that Cambridge changes can occur for the composition of almost any type, including organisms, bodies, and planets, for both universalists and restrictivists.

The thesis of this paper is that mereological restrictivists should reject what I call Classical Mereology for Modal Mereology, and that a restrictivist Modal Mereology can borrow philosophical machinery from mereological universalists, thus undercutting some of the purported advantages of universalism over restrictivism. Restricted composition occurs, on my account, when a possible whole plays the role of an actual type (actual types which many universalists also believe in). Moreover, my Modal Mereology restrictivist account answers the charge, from Rea (1998) and other universalists, that restrictivists cannot account for the composition of artifacts (artifacts which clearly exist as composite wholes). If a restrictivist relied on a restricted relation R, the composition of artifacts would indeed be problematic, since artifacts are so diverse in nature and do not seem to have any such relation R to account for their composition. However, on my restrictivist account, if some possible whole instantiates the type ‘art’, for example, that possible whole composes an actual whole artwork (sans any need for a relation R doing substantial metaphysical work beyond what it already does for universalists).

2 The Mereological Theses

Consider some distinctions and definitions. As a result of needing to reject the Mereological Theses, I believe that restrictivists should replace Classical Mereology for Modal Mereology, and reject Classical Mereological Supervenience for Modal Mereological Supervenience.7 On Weak Classical Mereology, a whole exists merely in virtue of its parts; so if its parts exist, then the whole exists. Restrictivists tend to modify and strengthen this classical mereology thesis. On a modified restrictivist, Strong Classical Mereology, a whole exists in virtue of its parts given that the parts also have some internal relation R among themselves (e.g., these internal relations make the parts at least possibly instantiate a type of whole such as a body). Universalists can easily accept Classical Mereology. On universalism, since any group of parts composes a whole in virtue of the parts simply and actually existing, then such parts automatically compose a whole.

I believe that restrictivists, however, should reject both types of Classical Mereology for one of two versions of Modal Mereology. On Weak Modal Mereology, a possible whole exists in virtue of its parts and the internal relations among its parts, but an actual whole does not. On Strong Modal Mereology, one adds to Weak Modal Mereology a universalism about the possible composition of wholes from parts, keeping the restrictivism about the actual composition of wholes from parts. I will motivate Strong Modal Mereology restrictivism later in the paper by arguing that we should take artifacts to compose something (Rea, for example, thinks the existence of artifacts is a strong motive for accepting universalism over restrictivism).

A standard restrictivist tries to side with ‘common sense’, and typically holds that I have only one body, and only one body is composed of the parts of my body (I will generally presume such a standard view in this paper). Restrictivists also often hold that while a group of parts now composes my body due to how those parts are arranged among themselves (via a relation R), those same parts may still exist in a thousand years (scattered around the world) and yet not compose my body (or any other whole). So, a standard restrictivist (van Inwagen 1995, for example) might hold the Mereological Theses and argue that a whole exists in virtue of its parts plus a relation R among the parts. On restrictivist views that rely on relation R, if my year 2010 body parts exist in the year 3010 but are scattered across the world, my body does not exist and no whole is composed by those parts (since relation R no longer holds for those parts in 3010).

Classical Mereology may hold for universalists, but not for restrictivists. Classical Mereology posits a stronger ‘in virtue of’ relation between parts and wholes than the relation in Classical Mereological Supervenience. Consider the following standard supervenience thesis:
  • (SST) A does not supervene on B if B can exist without A

So, for example, pain does not supervene on c-fibers firing if c-fibers fire but without any pain existing. If pain did in fact supervene on c-fibers firing, then if c-fibers fire, pain must exist. According to Weak Classical Mereological Supervenience, a whole supervenes on its parts, and so if the parts exist, then the whole must exist.8 Clearly universalism can accept this, since on universalism a whole exists in virtue of its parts if those parts exist at all. Strong Classical Mereological Supervenience is the thesis that the whole supervenes on its parts and some relation R among the parts. So if the parts exist and a certain relation R exists among the parts, then a whole must exist. I argue restrictivists should reject classical supervenience.
Also, universalists can easily hold a Weak Internalist Principle (WIP):
  • (WIP) Whether certain objects add up to or compose some larger object need not depend on any external relations to things outside of its parts.

On universalism, something is a whole merely in virtue of the parts existing, so naturally something’s being a composite whole need not depend on things external to its parts. Restrictivists might also hold a Strong Internalist Principle (SIP), which the restrictivist van Inwagen endorses when he says:

Whether certain objects add up to or compose some larger object does not depend on anything besides the spatial and causal relations they [the parts] bear to one another. (1995, p. 12)9

According to this Strong Internalist Principle, for any xs and any y, if the xs compose y, then there is some internal relation R among the xs such that the xs compose y if and only if the xs stand in the relation R among themselves. In this paper, I argue that restrictivists must reject both Strong and WIPs. I argue for an account of restricted composition that avoids the need for such a use of R in composition.10
Consider the related DP, on which, necessarily, if some composite object exists, then its perfect physical duplicate exists as well. Universalists can easily hold DP, but I will argue that restrictivists cannot and should not. Universalists obviously can hold DP, since wholes exist automatically if the parts exist. On universalism, given a perfect duplication of the parts of a composite whole, there will be another composite whole simply because any grouping of parts composes a whole. Van Inwagen, a restrictivist, supports DP when he says:

If the xs compose something, and if the ys perfectly duplicate the xs (both in their intrinsic properties and in the spatiotemporal and causal relations they bear to one another), then the ys compose something. (1995, p. 138)

Van Inwagen says, “My deepest instincts tell me that composition is an internal relation” [my italics], and that he is strongly committed to DP and finds the truth of DP very compelling (p. 138). Using some of van Inwagen’s own beliefs, I will argue that DP is false.
Van Inwagen proposes the following counterexample to his own DP:

But suppose that at the very instant your counterpart’s ear was cut off, it was replaced with some inorganic appendage that perfectly duplicated the causal powers of the severed ear. Then the atoms adjacent to the ‘interface’ would behave exactly as they would have behaved if the ear had not been cut off. (1995, p. 140)

Van Inwagen then gives the following reply to the counterexample:

If the ‘appendage’ perfectly duplicated the causal powers of the severed ear, right down to the atomic level, it would have to be an atom-for-atom duplicate of the ear and would thus not be ‘inorganic.’ The atoms that virtually composed it would immediately be assimilated by my counterpart, who would thereby become a perfect duplicate of me. And that outcome would not contradict the Duplication Principle. (1995, p. 140)

Van Inwagen argues that an organism sans an ear has scar tissue that makes it intrinsically different from the subset of an organism with two healthy ears. Van Inwagen’s commitment to DP may stem in part from a dislike of Cambridge change concerning the existence of organisms (van Inwagen feels he has only the epistemic warrant to believe in organisms and simples, and thus restricts composition exclusively to organisms). If my own counterexamples to DP are true, then something that is an organism can cease to be an organism due to a Cambridge change, and something that is not an organism can become an organism due to a Cambridge change.11 I believe that a restrictivist should hold that while an armless body exists as a whole (a whole body), a restrictivist should hold that the physical duplicate of that armless body would not exist if it was part of a person who actually had arms attached.12

3 Rejecting classical relation R

Van Inwagen rejects what he calls the ‘Doctrine of Arbitrary Undetached Parts’ (DAUP) and argues that he is only one organism and only one organism is made out of his body parts. Van Inwagen states DAUP thusly:

For every material object M, if R is the region of space occupied by M at time t, and if sub-R is any occupiable sub-region of R whatever, there exists a material object that occupies the region sub-R at t. (1986, p. 123)

Van Inwagen rejects DAUP, and believes a person who lacks an appendage is not a counterexample to DP since such a whole cannot be physically identical to a non-whole which is merely a subsection of a larger whole (e.g., due to scarring when an appendage is lost). Standard restrictivists would agree with van Inwagen that his material parts sans his limbs do not compose any whole thing. However, there are a variety of causal stories, many of which van Inwagen himself endorses, that constitute better counterexamples to DP.

On restrictivist accounts that depend on relation R, something’s being a whole (a whole table or a whole body) just is a whole of that type by virtue of the having the parts and internal relationships among the parts that compose the whole. So my body exists as a composite whole body due to having certain parts and internal relations among its parts. There is something internal to those parts themselves that make it constitute a whole body. So, for such a restrictivist, there is something about the parts that constitute my body minus my attached left arm (or even my body minus an attached atom on the end of my finger) that makes it fail to constitute a whole body. The parts of my body compose that one and only one whole body in virtue of the intrinsic physical relations among its parts, and not in virtue of the relations to things outside my body.

Consider the contrast between composition depending on relation R versus composition of a prison population. A camp’s population can (legally) compose some type of thing (a prison) because of an external legal framework that has just been put into place (and which makes no causal difference to the camp at the time). An official governing group can simply decree that a pre-existing camp is now a prison. Under such circumstances, a population in a camp can simply undergo a Cambridge change and legally become a prison population by proclamation.

For restrictivists like van Inwagen who depend on relation R, similar Cambridge changes cannot affect whether or not body parts add up to a mereological whole of a certain type. However, I will argue now that a Cambridge change can affect whether some parts compose a whole. Consider the possibilities, which van Inwagen accepts, that God’s actions or random events can lead to the creation or annihilation of physical things ex nihilo (1995, pp. 159, 165). Consider Larry Limbful, who has all four limbs, and Gary Limbless, who lacks limbs. Limbful is composed entirely of the ys, and Limbless is composed entirely of the xs. Limbless’s xs are intrinsically identical to a subset of Once-Limbfuls ys. Via ex nihilo causation and annihilation, God (or random events) perfectly duplicates the causal nexus at the interface of each of Limbless’s severed limbs without creating an atom-for-atom duplicate of any lost limb. The relevant features of the limb interface, including the electromagnetic and gravitational fields, come into and out of existence ex nihilo at the limb interfaces.13 For example, God mimics the causal powers at Limbless’s arm-torso interface by creating ex nihilo the parts that are flowing into Limbless, and annihilating the parts that are flowing out of Limbless.

Thus, the xs that compose Limbless are intrinsically identical to a subset of the ys in Limbful, and there are no intrinsic differences due to scar tissue or the like. However, Limbless’s xs compose a whole person and yet the corresponding parts in Limbful do not. Limbless should make the ‘clear and distinct’ Cartesian observation that ‘I obviously exist.’ But Limbless is a whole, composite organism that is identical to something that does not exist (i.e., some subset of Limbful). Thus, it seems, DP fails.

Now consider a slightly different case that illustrates a Cambridge change that creates a new whole material being where there previously was none. Consider Larry’s good friend Barry Once-Limbful, who had two arms at time t1, but then suddenly had one arm spontaneously annihilated by God and replaced with an ex nihilo arm at time t2. At time t1 Once-Limbful is composed of the ys, and at time t2 he is composed of the ys-arm, which are just the subset of the ys minus all the parts of his now missing arm. When the ex nihilo annihilation occurs, there are no changes intrinsic to ys-arm. However, at time t2 the ys-arm now constitute a whole organism. Thus, a Cambridge change obtains and suddenly creates an organism out of a non-organism (creating an existing whole that is intrinsically identical to a non-existing non-whole).

However, a proponent of DP might insist that there are intrinsic differences between Once-Limbful at time t2 and the relevant subset of Once-Limbful at time t1. The proponent of DP might insist that Once-Limbful at time t2 is not entirely a material being, but has absorbed non-physical God parts, thus becoming a physical/non-physical hybrid. I will argue that this ‘hybridization’ solution is misguided, but it is nevertheless instructive. Let me motivate the hybridization reply with more detail from van Inwagen’s account of the composition of organisms. Van Inwagen argues that an organism’s life is a “well-individuated jealous event” because a “life takes the energy it finds and turns it to its own purposes” while an ocean wave does not (1995, pp. 87, 89). Van Inwagen gives the following ‘caught up in a life’ criterion for proper parthood:

x is a proper part of y if and only if y is an organism and x is caught up in the life of y. (1995, p. 94)

On van Inwagen’s view, nothing in the material world (that he knows of) has a part other than an organism whose parts are ‘caught up in a life.’

The hybridization reply is similar to van Inwagen’s ‘inorganic ear’ reply, since peculiar new parts are getting ‘caught up in a life’. According to this hybridization solution, God parts get caught up in and thus assimilated into both Once-Limbful’s life and Limbless’s life. Once-Limbful and Limbless are physical/non-physical hybrids.14 Thus, for example, Limbless’s parts are intrinsically different from any subset of Limbful’s parts, and thus there is seemingly no counterexample to DP. Of course, Limbful and Limbless still have corresponding physical parts that are intrinsically identical, but Limbless has some non-physical part that Limbful lacks (the God parts). So it might seem that DP has been successfully defended.15

The hybridization solution has some serious shortcomings, however. One shortcoming is that the hybrid organisms are no longer material beings (they are physical/non-physical hybrids). Another shortcoming is that ostensibly ‘body shaped bodies’ have strange non-physical extensions, which may or may not be extended in space and time (depending on God’s relation to space and time). This goes against some intuitions about the physical nature of and shape of bodies.16 A more significant problem, however, is that this hybridization solution does not seem to work in non-divine cases in which ex nihilo causation occurs due to completely random, spontaneous events. Van Inwagen accepts that random, spontaneous ex nihilo creation and annihilation are possible (1995, pp. 159, 165). It seems that ex nihilo causation and annihilation are possible, albeit uncommon in the actual world outside of events like the Big Bang. Similarly, it is also possible (albeit unlikely) for matter and energy to be suddenly transferred by quantum events to and from faraway places in a way that mimics the arm. So it seems that it is also possible to mimic an arm without ex nihilo annihilation and creation, but with just spontaneous movement in unlikely but possible quantum shifts of matter and energy. If Limbless’s ‘ex nihilo arm’ is due to just random (and albeit unlikely but possible) quantum shifts or annihilations and creations, one cannot straightforwardly attribute any additional parts (such as God parts) to Limbless. Limbless still exists and his parts are intrinsically identical to parts of Limbful that do not compose anything at all.

The hybridization solution also fails to avoid Cambridge changes in similar non-divine versions of the Once-Limbful case. On the hybridization view of the divine case, God is an internal part of the organism Once-Limbful at time t2 but not at t1. But the workings of God can be replaced by either random creation and annihilation of parts or random quantum shifts in matter to and from the interface of the arm of Once-Limbful. It would be absurd to say that these random events are jealously caught up in the life of Once-Limbful. But then we should accept that Once-Limbful’s ys-arm at time t2 compose the whole organism at t2, since Once-Limbful obviously has a body and is not dead when the ex nihilo events are doing their work. However, these ys-arm are identical to a subset of Once-Limbful’s parts at t1. Since the ys-arm undergo no intrinsic changes from time t1 to time t2, a whole suddenly exists by a Cambridge change and is physically identical to what just previously was not a whole.

Consider a slightly different case. Consider the case of ‘Sally Slightly-Smaller’, in which Sally Slightly-Smaller suddenly and spontaneously loses the smallest possible part by spontaneous annihilation, the possibility of which van Inwagen seems to concede (1995, pp. 159, 165). Also consider the similar case in which Slightly-Smaller’s part spontaneously and randomly quantum shifts to a faraway location (rather than the part’s being annihilated). In either case, for a split second in Slightly-Smaller’s life, none of the surrounding parts of Slightly-Smaller are affected by or ‘notice’ this loss of a small part. Thus, at time t1, Slightly-Smaller’s body is composed of the ys, and at time t2, Slightly-Smaller’s body is composed of the ys − 1 (the ys minus one small part). But the ys − 1 are the same intrinsically at t1 and t2, and yet they fail to compose a whole at t1 and do compose a whole at t2.

Lastly, consider a similar case in which nothing spontaneously disappears or moves far away by a quantum jump. Consider ‘Cathy Hanging-by-a-Thread’, whose finger hangs onto her body by the smallest possible thread. That thread is cut as quickly as possible by a process that momentarily does not causally interact with the surrounding parts. The case of Hanging-by-a-Thread works much as the case of Slightly-Smaller. At time t1, Hanging-by-a-Thread’s body is composed of the ys, and at time t2, Hanging-by-a-Thread’s body is composed of the ys − 1 (the ys minus a part). But the ys − 1 are the same intrinsically at t1 and t2, and yet they fail to compose a whole at t1 and do compose a whole at t2. In the Slightly-Smaller and Hanging-by-a-Thread cases, like the Once-Limbful case, a Cambridge change creates a whole organism (a whole body) where no such (actual) thing previously existed. On Modal Mereology, which I will discuss on the next section, an actual body did not previously exist there, but a possible body did. Such cases contradict DP. Since such cases cannot be reasonably thought to be adding additional ‘hybrid’ parts to the various ys-minuses, the hybridization solution is unsound.

Note that these kinds of counterexamples to DP apply to any standard account of three-dimensional or four-dimensional accounts of restrictivism. My various ‘body-minus’ counterexamples apply to four-dimensional or three-dimensional bodies (after all, it makes no difference to my arguments whether a body wholly exists at one time or is extended through both ‘past and present’ time). Also, these counterexamples apply on any standard account of restrictivism to a variety of types of material objects; it applies to artifacts, natural kinds, planets, rocks, etc. There is nothing peculiar about the ‘body-minus’ examples that would not also apply to planets or chairs. Thus, my arguments imply that any three-dimensional or four-dimensional restrictivist should reject the DP (assuming, of course, that the restrictivist holds the standard view that the xs that compose the planet Mars only compose one planet, etc.).

4 Weak Modal Mereology

Given that it is likely that at least one of the counterexamples to DP is possible, I reject restrictivist versions of DP and the related Mereological Theses, and replace them with Modal Mereology. On a Weak Modal Mereology, the possibility of a group of parts composing a whole of a certain type may depend on the intrinsic properties of and relation R among its parts, but the actuality of a group of parts composing a whole of a certain type supervenes additionally on more global and holistic features of the world. Consider, for the sake of illustration, an oversimplified account of the composition of a book. For argument’s sake, imagine that books are composed of parts, and those parts are words. Imagine that the internal ‘relation R’ for books is ‘How and in what order the words are arranged.’ Also imagine Aldous Huxley’s book Brave New World (BNW) follows standard restrictivist mereology (and only one book is composed of the words). BNW ends with the following lines:

Slowly, very slowly, like two unhurried compass needles, the feet turned towards the right; north northeast, east, south east, south, south southwest; then paused, and, after a few seconds, turned as hurriedly back towards the left. South southwest, south, southeast, east….

Imagine the same group and organization of words (the same order, etc.) but minus only the last word (‘east’). Call that ‘BNW-minus.’ Imagine that no one has written and published a book composed as BNW-minus is; we are merely imagining this arrangement of book parts. We need not accept that BNW-minus composes an actual book, since only one book (at least now) is composed by the exact words of BNW.

Imagine that in a hypothetical state of nature under a veil of ignorance, a person were to read the words, in order, of BNW-minus without knowing the wider context of how those words actually came into being and are presented to the actual world. Under the veil, the person knows that these words do appear in this order somewhere in the actual world. This person should conclude that these words (with their ordering) at least compose a possible book (e.g., “In some possible world this is a book, since it makes some sense as a complete book”), but this person should not conclude it is definitely an actual book, since there might be more (or fewer) words that the actual author put in the actual book that is actually presented to the word for publication and consumption.

Analogously, if a restrictivist merely knows everything about the intrinsic properties of and internal arrangements of the ys-minus parts of Limbful but not the wider context in which those ys-minus parts occur, that restrictivist should conclude that the ys-minus parts of Limbful composes a possible whole (i.e., in some possible world these parts compose a whole body) but not necessarily an actual whole (i.e., an actual whole body).

The Weak Modal Mereology restrictivist view establishes a few things. First, it establishes that there are many more possibilities for parts composing a whole of a certain type than there are actualities for parts composing an actual whole of a certain type. This makes intuitive sense, since possibilities should be much more widespread than actualities. For example, the following is typically true of an arbitrary cup of water: “That cup of water could possibly drown someone, but is unlikely to actually do so.” While some cups of water actually have drowned someone, it is the case that far more cups of water have only the un-actualized potential to do so. Possibilities are easier to come by and more widespread than actualities.

Second, the Weak Modal Mereology restrictivist view establishes that what converts a possibility into an actuality is not necessarily internal or intrinsic to the thing (the parts with their internal relation R among them). Context, relations, or the wider environment often are required to actualize potentials that create actual bodies out of possible ones, and actual persons out of possible ones.

Also, consider the following principle of possibility and actualities:

The Principle of Modal Natural Kinds: Necessarily, if there is a possible natural kind K made of the xs in the actual world, there is an actual natural kind K whose ys significantly overlap with the xs.

A restrictivist may find this principle compelling. On this principle, if there is a possible body in a world (the actual world, and maybe also in worlds sufficiently like the actual world), there is an actual body in the vicinity. This principle does not apply to artifacts, however. A random pile of driftwood made of the xs may constitute a possible work of art, but that does not mean there is an actual work of art in the vicinity of the xs.

In this paper I wish to be agnostic about what exactly actualizes possibility (and what types of things are actual types of things), since at this point in the argument there are many options available. For example, Modal Mereology is consistent with (but does not require) functionalism about tables and bodies. For example, a mere possible table could supervene on the parts of a table themselves. In some possible world, any such possible table could be an actual one. An actual table in the actual world is what plays the functional role of the table in the actual world. An actual book plays the functional role of a book in the actual world. The modal mereologist can remain agnostic about theories of actualization (i.e., what makes a possible thing an actual thing of its type), much as William G. Lycan has remained agnostic about theories of teleology while consistently giving a teleological theory (i.e., teleological functionalism). Lycan, when pressed for a theory of teleology, simply says something to the effect, ‘Whatever theory of teleology is true is fine for me, and I need not give arguments for which theory is true.’17 However, later in the paper I suggest that restrictivists can borrow some of the machinery from universalists to give accounts that demarcates actual types from merely possible types.

5 Strong Modal Mereology

The plausibility of the Weak Modal Mereology restrictivist view that I discussed in the last section may lead one to consider another, stronger view: Strong Modal Mereology. On Strong Modal Mereology, one adds to the weak view that one is also a possiblist universalist (any group of things possibly composes something) but an actualist restrictivist (only some groups of things actually compose something). A restrictivist who believes that a wide range of artifacts can be composite wholes may hold Strong Modal Mereology because of a reasonable belief that most any grouping of physical objects could be an artifact. Some restrictivists (myself included) may believe that just about anything could be an artifact, since most anything could be a tool, a hammer, a club, a walking stick, a pry bar, a work of art, a toy, or something else of use or importance to a human being (such that it constitutes an artifact). One might even take this so far as to say that literally any physical group of things could compose an artifact, such that one might accept universalism about possible artifacts.

So, for example, consider a restrictivist who believes in a version of the ‘artworld’ theory of art.18 Briefly and crudely put, on such an artworld theory, anything could be a work of art if it is presented to the public, the artworld, as a work of art in a certain historical and theoretical context for the practice of art. So if Andy Warhol presents Brillo boxes to the artworld in the right way, then the Brillo boxes become art. The artworld restrictivist could believe, for example, that an all powerful God could present anything as art to some such public artworld, and thus anything could be art, including the ear-moon-car.19

If a restrictivist accepts artifacts into his or her ontology and understands artifacts in a similarly liberal way, then one might be inclined to accept Strong Modal Mereology (given my arguments against classical restricted mereology). A proponent of Strong Modal Mereology would hold that the ear-moon-car is possibly an artifact of some sort (since true artifacts exist, and composite artifacts are wholes), but not necessarily actually so. I am very sympathetic to restrictivists who are liberal enough in their ontology to allow for such artifacts.

6 Relation R for modal mereologists

I do not believe that any specific relation R, of the vague sort that Lewis mentions (e.g., ‘objects sticking together’), is either necessary or sufficient condition for actual composition. However, I am sympathetic to some much weaker uses of relation R in a Modal Mereology (but it is very much like a use for R that many universalists would accept as well). Such a relation R would play a different role in Weak Modal Mereology than it does in Classical Mereology for the restrictivist (and an even less significant role on Strong Modal Mereology). On Weak Modal Mereology, a weak relation R can be used to demarcate ‘possible wholes’ (groups of parts that could possibly compose something given their current arrangement) from ‘impossible wholes’ (groups of parts that could not possibly compose something given their current arrangement). On Classical Restricted Mereology, a strong relation R demarcates actual wholes from impossible wholes (e.g., on van Inwagen’s view, if such a relation R holds among some parts, then an actual whole must exist, and if relation R fails to hold, then no whole exists at all). Van Inwagen may be sympathetic to Weak Modal Mereology and a weak relation R if he is forced to give up his admitted ‘strong commitment’ to the DP.

On Strong Modal Mereology, however, relation R does no significant work concerning the mereological composition of wholes, since there is no need to demarcate between ‘possible wholes’ from ‘impossible wholes’. After all, on Strong Modal Mereology there are no impossible wholes (on Strong Modal Mereology, any parts in any arrangement could possibly compose a whole). However, on Strong Modal Mereology, relation R could tell us what is a possible whole of a certain type (but universalists might also find this use of relation R compelling, since even they are likely to demarcate between what can be a human body and what cannot). So, on Strong Modal Mereology, while any group of parts composes a possible whole, only certain parts with certain relation Rs obtaining among the parts could possibly compose a whole human body.

7 ‘Types’ for universalists and restrictivists

Restrictivists generally prefer to restrict wholeness to specific types of things that they know exist. Compare the mereological epistemology of the restrictivists Rosenberg (1993) and van Inwagen (1995). Consider this very brief, first person reconstruction of a portion of van Inwagen’s Cartesian-inspired epistemic argument that only organisms are wholes:
  1. 1.

    I know I exist.

     
  2. 2.

    I know I am a composite organism.

     
  3. 3.

    Therefore, I know composite organisms exist.

     
Van Inwagen goes on to argue that he has no strong epistemic access to the unity of any other kind of composite object, and so he restricts mereological wholeness (and relation R) to composites that are organism. Rosenberg, on the other hand, says that he has strong epistemic access to the existence of tables and chairs (and a wide range of artifacts). So Rosenberg’s argument would go something like this:
  1. 1.

    I know artifacts exist.

     
  2. 2.

    I know artifacts are composite objects.

     
  3. 3.

    Therefore, I know composite artifacts exist.

     
Both restrictivist arguments for composite wholes center around epistemic access to what types of things exist. Types of things could include artifacts and natural kinds such as organisms, bodies, planets, etc. Rosenberg and van Inwagen restrict composition to such types to which they believe they have epistemic access.20
Universalists such as Lewis (1991, 1993), Sider (1997), and Rea (1995, 1998, 1999) also believe we have epistemic access to such types (and, obviously, believe such types are not composed of just any parts). I believe that restrictivists can borrow from these universalist accounts of types. Of such types, Rea says:

It turns out that the most reasonable way to resist the argument for Universalism is to deny the existence of artifacts; thus, if we believe in artifacts, we have no real choice other than to embrace Universalism…. It just seems obvious that there are tables, chairs, computers, and cars…. [But] if we admit the existence of artifacts, then we must admit the existence of a lot else besides. For example, we must admit the existence of an object whose parts are my left tennis shoe, W. V. Quine, and the Taj Mahal. (1998, pp. 347–348)

However, I believe that we can account for the wholeness of artifacts without recourse to universalism. A Strong Modal Mereology restrictivist can borrow from these universalists the criteria for what and how types exist, and add that ‘typehood’ is a necessary condition for composition that converts a possible whole into an actual whole. Remember that possible composition on the Strong Modal Mereology restrictivist view is ‘automatic’ if the group of things just exists (just as actual composition is ‘automatic’ on classical universalism). ‘Instantiating a type’, on my view, converts a possible whole into an actual whole. Universalists often believe some (and only some) parts instantiate a type, and also give solutions to metaphysical puzzles concerning such types.

If restrictivists can borrow from universalists to get an account of types, then metaphysical problems concerning those types that are shared between universalists and restrictivists are not problems unique to restrictivism. I believe that vagueness puzzles, Cambridge change puzzles, and the Problem of the Many puzzles are not unique to restrictivism, and are shared by many universalists who believe in types. For example, universalists who believe in types (types that are restricted to some parts with some relations R and not others) should accept that Cambridge changes can make a body into a non-body and vice versa (and so on for any type of composite material object). One might think that the Cambridge changes that come out of my arguments against the DP makes restrictivism look implausible. However, similar Cambridge changes also apply to universalists who hold that types exist (see Lewis 1993 and Rea 1998). So universalists often hold (as they should) that types of things exist (such as bodies and tables) and not just any groupings of parts compose such a type. These universalists are universalists about wholes, but in an important sense are restrictivists about types (e.g., these universalists hold that ‘Bodies exist, and not just anything composes a body’).

Lewis, for example, addresses vagueness and Problem of the Many puzzles concerning types (1993). Lewis believes that (i) bodies exist, (ii) not just any group of parts composes a body, and (iii) we should count bodies in a way so that I have only one body. Consider a typical human body with two arms and two legs. Given my Modal Mereology arguments, Lewis may accept that the various ‘body minus’ examples properly motivate that some xs could compose a body (e.g. a body minus arms and legs) but do not actually do so. However, if my arguments are correct, then a future Cambridge change could turn those xs (which do not now compose a body for Lewis, but necessarily compose a whole) into an actual body. Both restrictivists and universalists can believe in types, and that Cambridge changes can create and destroy things that instantiate such types. Both restrictivists and universalists believe they have epistemic access to types of things that exist. The difference is that my restrictivism restricts wholeness to those types, and universalism does not.

I believe that universalists and restrictivists who believe in such types also can share common problems and common solutions to issues of vagueness and the Problem of the Many. Consider Lewis’ response to Peter Unger’s (1980) Problem of the Many for types such as bodies. According to Lewis (1993), there are many equally good candidates for the parts that compose my body. All these equally good candidates overlap significantly, and are ‘almost identical’ to each other (only tiny portions of them are not overlapping), and are ‘almost one’ (so much so that we should only count it as one body). Lewis could be something very much like a Modal Mereologist concerning bodies. For example, Lewis could hold that while my body has two arms and two legs, my body minus those limbs is a non-actual but ‘possible body’ (after all, Lewis says that the equally good candidates for my body are almost identical, and the xs that compose my body minus my limbs are hardly either good candidates or almost identical to the other such candidates). One problem that faces a Modal Mereology restrictivist is ‘Which candidates are the best candidates for composing the actual (as opposed to a mere possible) body?’ Lewis’ account faces a similar problem, and the solutions that Lewis gives can be borrowed by the Modal Mereology restrictivist. So, universalists who believe in types do not seem to have a strong advantage over restrictivists when it comes to the Problem of the Many. Modal Mereology restrictivists can (but need not) borrow accounts of what and how types of things exist from the classical universalist who is a ‘restrictivist’ about the composition of bodies, tables, planets, etc. (as I have suggested in the cases of the Problem of the Many).21 These restrictivists can use the universalist solutions to the Problem of the Many to account for how some possible bodies are actual, but others are not.22

8 Advantages of Modal Mereology

Modal Mereology has some important advantages over Classical Mereology: (1) Modal Mereology posits a common sense restricted composition on the one hand (like classical restrictivism), and (2) Modal Mereology undercuts one major motive for classical universalism since it allows composition to be easy (like classical universalism), since ‘anything can compose something’ (e.g., an ear-moon-car combination could possibly be art, in the right context), and (3) Modal Mereology can borrow some features of classical universalism.

Consider the first advantage of Modal Mereology over Classical Mereology. One main complaint against classical universalism is that it is too ontologically liberal, allowing an excessive number of things exist to solve a simple metaphysical problem (e.g., ‘How can such diverse kinds of composite artifacts exist?’). My Modal Mereology has the advantages of classical restrictivism here, since there are a restricted number of actual things (I am agnostic here as to exactly what the criteria is for how many things there are in the universe, but I consider this flexibility an advantage at this stage of the argument). I believe that it is permissible to be very liberal about possibility, but not actuality. This coheres with the widespread modal intuition that possibility is easy (‘anything is possible,’ as the idiom goes), whereas we should be far more strict about what we claim to be actual. So my Modal Mereology not only has the advantage of the classical restrictivist on the smaller number of actual things, but also it coheres with our more liberal modal intuitions about the number of possibilities.

Consider the second advantage to Modal Mereology. One chief complaint against classical restrictivism is that it seems to require a specific relation R (e.g., Lewis says such a relation R included ‘objects sticking together’), and that such a relation R restricts the criteria for composition so much that it is hard to understand how the parts of many things (e.g., artifacts) could possibly add up to compose anything at all.23 In other words, restrictivists have a very hard time coming up with a relation R for composition that is liberal enough to include things we typically believe actually exist (like art, tables, planets, molecules, bodies, etc.). Van Inwagen, a classical restrictivist, restricts his relation R to parts that are actively ‘caught up in a life’, and thus for him planets, stars, molecules, and tables do not exist. This is seen as a serious problem by many philosophers. Due to the difficulty of coming up with a relation R that sensibly demarcates which things ‘add up’ to a composite object and which do not, philosophers moved to classical universalism which makes any group of things compose something. The classical universalist criterion for composition is easy and simple: any group of things that exists composes a whole.

On classical universalism, the question then became not ‘What things add up to a composite?’, but rather ‘To what kind of composite do all these things add up?’ After the advent of classical universalism, one common answer to the latter question was ‘They add up to a lot of “lumps” and “arbitrary, spread out objects” (e.g., the ear-moon-car).’ It was not, as I believe it should have been, that there was a widespread considered opinion that a lot of lumps (and spread out objects) existed in the universe and needed to be accounted for by the best mereological theory. It was rather that the theory that accounted for the ‘easiness’ of composition (e.g., of artifacts) did so via a single, lax relation R that demanded the existence of a lot of lumps and spread out objects.

One advantage to Strong Modal Mereology (with its possiblist universalism and actualist restrictivism) is that it does not get the order of explanation backwards here, as classical universalism seems to do. For us strong modal mereologists, we allow lumps to be actual in our ontology only if it is a type of thing that we should account for, much as we should account for tables and chairs as common sense objects (as Rea says above). Presumably, the classical universalist argument does not begin with ‘We noticed that there are a huge numbers of lumps and scattered objects like ear-moon-cars in the world of various shapes and sizes, so let us account for these existing things.’ Rather, the universalist Rea seems to begin more reasonably with merely ‘It seems that a lot of artifacts exist.’ ‘Lumps’ as a serious type of thing that exists in the world should be argued for on the merits of the kind of thing a lump is, just as we should (on my view) argue for the existence of tables and chairs and planets and bodies. However, Modal Mereology has the resources to give the lumps their due (after all, there are a number of philosophers who believe in them). Moreover, Modal Mereology accepts that what people refer to as ‘lumps’ may be possible things that possibly add up to something. The lumps might add up to a chair, a sign, an artwork, a bridge, etc. Strong Modal Mereology demands that we take ‘random lumps’ and ‘arbitrary, spread out objects’ seriously as possibly something, but that does not mean these lumps and spread out objects actually exist as true wholes. We are better off thinking of most ‘random lumps’ and ‘arbitrary, spread out objects’ in terms of possibly being something rather than actually being something. However, if there is an argument that these seemingly random, arbitrary things are an important type of thing that exists (such as tables and bodies), I am willing to listen.

9 Conclusion

I have argued that all restrictivists should reject the Classical Mereological Theses, and replace Classical Mereology with Modal Mereology. On my Modal Mereology restrictivist account, composition occurs when the xs instantiate an actual type, and is not due to what Lewis calls vague, ‘intuitive desiderata’ about relation R (e.g., the parts act jointly, stick together, or are adjacent to each other in space–time). I believe that there is not a relation R that all actual wholes share in common, and I believe that actual composition does not occur due to any such internal relation R. I argued that Modal Mereology, in both its weak and strong variants, has some additional benefits for restrictivists in some debates with universalists. The restrictivist modal mereologists also can borrow from universalist accounts of types. The universalist criteria for the existence of such types can be just what demarcates a mere possible whole from an actual whole, and the universalist arguments solving puzzles for such types (e.g., universalist arguments for solutions to Unger’s Problem of the Many) can be used by the modal mereologists as well.

We should want a mereological theory that both accounts for why the diversity of common sense types of wholes exist (as universalism does), but also does not allow just any arbitrary grouping of things to compose wholes like the ear-moon-car (as restrictivism does). Modal Mereology can do both these things. Modal Mereology shares the strength of universalism, since possiblist universalist composition is easy in an important sense since any things can (possibly) compose a whole. Modal Mereology shares the strength of restrictivism since, on actualist restrictivism, possible composition is only actualized when (for example, on the functionalist reading of Modal Mereology) something is playing the role of a legitimate type of thing in the actual world.

Most classical universalists, like modal mereologists, believe that certain types of things exist (such as art, planets, and bodies), and the arguments for these types of things existing (e.g., not as a mere whole, but as a whole body whose xs compose what we should count as just one body) can be shared by both. The modal mereologist can, however, remain agnostic about theories of actualization (i.e., what makes a possible thing an actual thing of its type), much as Lycan has remained agnostic about theories of teleology while giving a teleological theory (i.e., teleological functionalism). Universalists believe in such actual types, and modal mereologists can believe in them for the same reasons or others. Cambridge changes can occur to such types for both universalists and Modal Mereology restrictivists.

Thus, Modal Mereology is a view worth considering. My sympathies are with Strong Modal Mereology, which answers both Rea’s challenge to restrictivists to account for the existence of a wide range of artifacts and Lewis’s challenge to account for restricted mereology sans a vague relation R (I need not use any relation R beyond what universalists like Lewis might use to account for the existence of types). However, in light of my arguments and in light of their resistance to the existence of a wide range of artifacts, van Inwagen and others might consider accepting Weak Modal Mereology instead.

Footnotes
1

See Smith (2006) for strong arguments against Lewis and Ted Sider’s ‘vagueness arguments’ for universalism and against restrictivism.

 
2

Rea (1998), for example, argues that universalists can accommodate relation R in their mereological theories of composition.

 
3

Such ‘actual types’ exist according to a number of universalists. The universalist Lewis accounts for and defends the existence of such types from vagueness-related objections in his 1993, and the universalist Rea accounts for the existence of such types in his 1995, p. 348ff.

 
4

For a discussion of mereological supervenience, see Kim (1984, 1993, pp. 31, 54–56, 66, 77, 102, 166).

 
5

Van Inwagen believes that organisms are quite possibly the only composite beings that exist, and he believes in the Mereological Theses I reject. To put part of my thesis in the terms of organisms, there can be some exact duplicates of organisms that are not organisms, and there can be exact duplicates of non-organisms that are organisms.

 
6

By standard restrictivist views, I mean the kind of views on which I have either only one body (or at least ‘almost one’ body). To put this in another way, on standard views, I have only one desk in my office and not thousands of desks occupying roughly the same region of space–time.

 
7

Lewis and van Inwagen are classical mereologists. Lewis is a classical universalist and van Inwagen is a classical restrictivist. See van Inwagen (1995) and Lewis (1991).

 
8

Kim expresses some of the basic ideas behind classical mereological supervenience when he says,

Consider mereological supervenience, the thesis that properties of wholes supervene on the properties and relations characterizing their parts…. It seems likely that mereological supervenience represents a metaphysically fundamental, sui generis form of dependence (1993, p. 166).

Kim also states,

The part whole relation is also important; however, its importance seems to derive largely from the belief that many crucial aspects of a whole including its existence and nature are dependent on those of its parts. That is, mereological relations are significant because mereological determination, or ‘mereological supervenience,’ is, or is thought to be, a pervasive fact (1993, p. 54).

 
9

Note that relation R on SIP need not be the same for each case of composition.

 
10

My use of R is consistent with how a universalists might use R in a theory of types (see below).

 
11

The Cambridge changes allow some groups of parts that either compose nothing at all (for restrictivists) or not a thing of its type at all (for universalists) to change into something of a specific type (e.g., a body). I will suggest that external changes can take a possible body and make it into an actual body. This kind of possible-to-actual Cambridge change seems less mysterious that a Cambridge change that makes something that is not anything at all into something substantial. Somewhat analogously, external changes can take ‘a cup of water that could possibly drown someone’ and make it ‘a cup of water that actually drowns someone.’ Similarly, external changes can change the content of a belief without making it an entirely different kind of thing (i.e., a non-belief). Consider the analogy to various Twin Earth and Switching Twin Earth cases in which mental and semantic content can change due to changes in external circumstances. See Putnam (1973) and Burge (1979).

 
12

Van Inwagen believes that only organisms exist as composite wholes, and does not believe in bodies. Van Inwagen claims not to understand what people mean by ‘My body exists’ (1995, p. 76).

 
13

According to van Inwagen’s theological views, God in fact has created a number of things ex nihilo in the cases of miracles, and thus has mimicked certain causal powers perfectly. For an application of such cases to issues of ethical supervenience and intrinsic moral value, see Walsh (2011).

 
14

On van Inwagen’s view, parthood comes in degrees, and thus parthood need not be all or nothing. For van Inwagen, a part of an organism is paradigmatically and completely caught up in a life to the highest degree when it is both the object and the subject of robust maintenance and control for a living system. In the ex nihilo examples, God appears to be the subject of that robust maintenance (the ex nihilo arm is functionally equivalent to a real arm in a number of ways, after all). God also appears to be the object of maintenance (God is reacting to the needs of the biological system, after all). However, even if God is not a part of Limbless to the highest degree in the most paradigmatic sense, God still may be part of Limbless to a lesser degree and in a less paradigmatic sense. See van Inwagen’s (1995) (especially §17–18) on mereological vagueness and varying degrees of being ‘caught up in a life.’

 
15

This hybridization solution can equally apply to the Biblical story of raising Lazarus from the dead. When the New Testament God violated natural laws, God could have used ex nihilo causation to restart Lazarus’ Krebs Cycles. On the hybridization view, God parts then get caught up in the Krebs Cycles of Lazarus. Since van Inwagen as a Christian believes that such miracles have occurred, on this hybridization account van Inwagen would be committed to the existence of physical/non-physical hybrid humans like Lazarus in the actual world.

 
16

However, to these problems it might be replied that these miracle cases are exceptional, and therefore strange non-physical parts are not so problematic (after all, they are parts for principled reasons, qua ‘caught up in a life,’ etc.).

 
17

Lycan says:

[Some] fault me for waffling (as indeed I have) on theories of teleology. They maintain that the teleofunctionalist bears the burden of explaining the teleology to which s/he appeals, because ‘[t]he devil is in the details.’ I think it is important for the teleofunctionalist to resist that demand. It is one thing to offer a theory of mental representation or a theory of consciousness; it is quite another to offer a metaphysical theory of teleology. The former task is for philosophers of mind, the latter for metaphysicians and philosophers of science. Of course I agree that if one’s particular theory of mind happens to commit one to some thesis about teleology that is on its own merits implausible, that would be an objection to the theory of mind. But I myself am not in that position; the connection between teleological theories of mind and particular theories of teleology is too loose, and the options too plentiful. (2001, p. 127)

 
18

The classical article that introduces the artword theory of art is Danto (1964).

 
19

A helpful reviewer for Phil Studies suggested the following account of artifacts: ‘The xs compose an artifact iff the xs are the current object of a history of maintenance and the xs are the best candidate parts for composing the object.’ This is another very liberal account of artifacts, since just about any xs could be identical to something that has such a history of maintenance. Such liberal accounts can motivate Strong Modal Mereology.

 
20

Although there is disagreement about which types we actually have epistemic access, metaphysicians can avoid epistemological questions simply by referring to ‘whatever types there actually are or could be’ (but ‘natural kinds’ is one answer). Lycan (2001) has a similar ‘agnostic’ solution to disagreements about what ‘teleology’ comes to in his teleological functionalism (Lycan says ‘teleology is whatever it is’ and that his teleological functionalist arguments need not say what it is). I also believe that one does not have to believe something exists to have epistemic access to it. So I believe van Inwagen does indeed have epistemic access to tables and chairs, although he denies it.

 
21

Rea (1998), Sider (1997), and Lewis (1993) are mereological universalists who are what I call ‘type restrictivists’.

 
22

Some hold that there are many bodies typically composed out of the parts of one body. See Hudson (2001, Chap. 1).

 
23

See Rea, who is one universalist who makes the latter complaint in his 1999.

 

Acknowledgments

I am indebted to Tristram McPherson, Alex Skiles, Jason Ford, Bill Lycan, Peter van Inwagen, Jaegwon Kim, the participants in the metaphysics colloquium at the Pacific APA, and the people in Peter van Inwagen’s Material Beings seminar for helpful discussions about various stages of the ideas for this paper. This paper is also partly an homage to Chapel Hill’s late, great Jay Rosenberg.

Copyright information

© Springer Science+Business Media B.V. 2010