Composition, Existence, and Identity

The algebraic strength of GEM, and of its weaker finitary and infinitary variants, is worth emphasizing, but it also reflects substantive mereological postulates whose philosophical underpinnings leave room for considerable controversy well beyond the gunk/junk dispute. Indeed, all composition principles turn out to be controversial, just as the decomposition principles examined in Section 3. For, on the one hand, it appears that the weaker, restricted formulations, from (P.11ξ) to (P.15ψ,i), are just not doing enough work: not only do they depend on the specification of the relevant limiting conditions, as expressed by the predicates ‘ξ’ and ‘ψ’; they also treat such conditions as merely sufficient for the existence of bounds and sums, whereas ideally we are interested in an account of conditions that are both sufficient and necessary. On the other hand, the stronger, unrestricted formulations appear to go too far, for while they rule out the possibility of junky worlds, they also commit the theory to the existence of a large variety of prima facie implausible, unheard-of mereological composites—a large variety of “junk” in the good old sense of the word.
Concerning the first sort of worry, one could of course construe every restricted composition principle as a biconditional expressing both a sufficient and a necessary condition for the existence of an upper bound, or a sum, of a given pair or set of entities. But then the question of how such conditions should be construed becomes crucial, on pain of turning a weak sufficient condition into an exceedingly strong requirement. For example, with regard to (P.11ξ) we have mentioned the idea of construing ‘ξ’ as ‘O’, the rationale being that mereological overlap establishes an important connection between what may count as two distinct parts of a larger (integral) whole. However, as a necessary condition overlap is obviously too stringent. The top half of my body and the bottom half do not overlap, yet they do form an integral whole. The topological relation of contact, i.e., overlap or abut, might be a better candidate. Yet even that would be too stringent. We may have misgivings about the existence of scattered entities consisting of totally disconnected parts, such as my umbrella and your left shoe or, worse, the head of this trout and the body of that turkey (Lewis 1991: 7–8). Yet in other cases it appears perfectly natural to countenance wholes that are composed of two or more disconnected entities: a bikini, a token of the lowercase letter ‘i’, my copy of The Encyclopedia of Philosophy (R. Cartwright 1975; Chisholm 1987)—indeed any garden-variety material object, insofar as it turns out to be a swarm of spatially isolated elementary particles (van Inwagen 1990). Similarly for some events, such as Dante's writing of Inferno versus the sum of Sebastian's stroll in Bologna and Caesar's crossing of Rubicon (see Thomson 1977: 53f). More generally, intuition and common sense suggest that some mereological composites exist, not all; yet the question ofwhich composites exist seems to be up for grabs. Consider a series of almost identical mereological aggregates that begins with a case where composition appears to obtain (e.g., the sum of all body cells that currently make up my body, the relative distance among any two neighboring ones being less than 1 nanometer) and ends in a case where composition would seem not to obtain (e.g., the sum of all body cells that currently make up my body, after their relative distance has been increased to 1 kilometer). Where should we draw the line? In other words—and to limit ourselves to (P.15ψ,i)—what value of n would mark a change of truth-value in the soritical sequence generated by the schema

(62)	The set of all φ-ers has a sumi if and only if every φ is ψ,

when ‘φ’ picks out my body cells and ‘ψ’ expresses the condition ‘less than n+1 nanometers apart from another φ-er’? It may well be that whenever some entities compose a bigger one, it is just a brute fact that they do so (Markosian 1998b), perhaps a matter of contingent fact (Nolan 2005: 36, Cameron 2007). But if we are unhappy with brute facts, if we are looking for a principled way of drawing the line so as to specify the circumstances under which the facts obtain, then the question is truly challenging. That is, it is a challenging question short of treating it as a mere verbal dispute, if not denying that it makes any sense to raise it in the first place (see Hirsch 2005 and Putnam 1987: 16ff, respectively; see also Dorr 2005 and McGrath 2008 for relevant discussion). This is, effectively, van Inwagen's “Special Composition Question” mentioned in Section 4.1, an early formulation of which may be found in Hestevold (1981). For the most part, the literature that followed has focused on the conditions of composition for material objects, as in Sanford (1993), Horgan (1993), Hoffman and Rosenkrantz (1997), Merricks (2001), Hawley (2006), Markosian (2008), Vander Laan (2010), and Silva (2013). Occasionally the question has been discussed in relation to the ontology of actions, as in Chant (2006). In its most general form, however, the Special Composition Question may be asked with respect to any domain of entities whatsoever.
Concerning the second worry, to the effect that the unrestricted sum principles in (P.15i) would go too far, its earliest formulations are almost as old as the principles themselves (see e.g. V. Lowe 1953 and Rescher 1955 on the calculus of individuals, with replies in Goodman 1956, 1958). Here one popular line of response, inspired by Quine (1981: 10), is simply to insist that the pattern in (P.15i) is the only plausible option, disturbing as this might sound. Granted, common sense and intuition dictate that some and only some mereological composites exist, but we have just seen that it is hard to draw a principled line. On pain of accepting brute facts, it would appear that any attempt to do away with queer sums by restricting composition would have to do away with too much else besides the queer entities; for queerness comes in degrees whereas parthood and existence cannot be a matter of degree (though we shall return to this issue in Section 5). As Lewis (1986b: 213) puts it, no restriction on composition can be vague, but unless it is vague, it cannot fit the intuitive desiderata. Thus, no restriction on composition could serve the intuitions that motivate it; any restriction would be arbitrary, hence gratuitous. And if that is the case, then either mereological composition never obtains or else the only non-arbitrary, non-brutal answer to the question, Under what conditions does a set have a sumi?, would be the radical one afforded by (P.15i): Under any condition whatsoever. (This line of reasoning is further elaborated in Lewis 1991: 79ff as well as in Heller 1990: 49f, Jubien 1993: 83ff; Sider 2001: 121ff, Hudson 2001: 99ff, and Van Cleve 2008: §3; for reservations and critical discussion, see Merricks 2005, D. Smith 2006, Nolan 2006, Korman 2008, 2010, Wake 2011, Carmichael 2011, and Effingham 2009, 2011a, 2011c.) Besides, it might be observed that any complaints about the counterintuitiveness of unrestricted composition rest on psychological biases that should have no bearing on the question of how the world is actually structured. Granted, we may feel uneasy about treating shoe-umbrellas and trout-turkeys as bona fideentities, but that is no ground for doing away with them altogether. We may ignore such entities when we tally up the things we care about in ordinary contexts, but that is not to say they do notexist. Even if one came up “with a formula that jibed with all ordinary judgments about what counts as a unit and what does not” (Van Cleve 1986: 145), what would that show? The psychological factors that guide our judgments of unity simply do not have the sort of ontological significance that should be guiding our construction of a good mereological theory, short of thinking that composition itself is merely a secondary quality (as in Kriegel 2008). In the words of Thomson (1998: 167): reality is like “an over-crowded attic”, with some interesting contents and a lot of junk, in the ordinary sense of the term. We can ignore the junk and leave it to gather dust; but it is there and it won't go away. (One residual problem, that such observations do not quite address, concerns the status of cross-categorial sums. Absent any restriction, a pluralist ontology might involve trout-turkeys and shoe-umbrellas along with trout-promenades, shoe-virtues, color-numbers, and what not. It is certainly possible to conceive of some such things, as in the theory of structured propositions mentioned in Section 2.1, or in certain neo-Aristotelian metaphysics that construe objects as mereological sums of a “material” and a “formal” part; see e.g. Fine 1999, 2010, Koslicki 2007, 2008, and Toner 2012. There are also theories that allow for composite objects consisting of both “positive” and “negative” parts, e.g., a donut, as in Hoffman and Richards 1985. At the limit, however, the universal entity U would involve parts ofall ontological kinds. And there would seem to be nothing arbitrary, let alone any psychological biases, in the thought that at least such monsters should be banned. For a statement of this view, see Simons 2003, 2006; for a reply, see Varzi 2006b.)
A third worry, which applies to all (restricted or unrestricted) composition principles, is this. Mereology is supposed to be ontologically “neutral”. But it is a fact that the models of a theorycum composition principles tend to be more densely populated than those of the corresponding composition-free theories. If the ontological commitment of a theory is measured in Quinean terms—via the dictum “to be is to be a value of a bound variable” (1939: 708)—it follows that such theories involve greater ontological commitments than their composition-free counterparts. This is particularly worrying in the absence of the Strong Supplementation postulate (P.5)—hence the extensionality principle (27)—for then the ontological exuberance of such theories may yield massive multiplication. But the worry is a general one: composition, whether restricted or unrestricted, is not an ontologically “innocent” operation.
There are two lines of response to this worry (whose earliest formulations go as far back as V. Lowe 1953). First, it could be observed that the ontological exuberance associated with the relevant composition principles is not substantive—that the increase of entities in the domain of a mereological theory cum composition principles involves no substantive additional commitments besides those already involved in the underlying theory without composition. This is obvious in the case of modest principles in the spirit of (P.11ξ) and (P.14ψ), to the effect that all suitably related entities must have an upper bound. After all, there are small things and there are large things, and to say that we can always find a large thing encompassing any given small things of the right sort is not to say much. But the same could be said with respect to those stronger principles that require the large thing to be composed exactly of the small things—to be their mereological sum in some sense or other. At least, this seems reasonable in the presence of extensionality. For in that case it can be argued that even a sum is, in an important sense, nothingover and above its constituent parts. The sum is just the parts “taken together” (Baxter 1998a: 193); it is the parts “counted loosely” (Baxter 1988b: 580); it is, effectively, “the same portion of Reality” (Lewis 1991: 81), which is strictly a multitude and loosely a single thing. That's why, if you proceed with a six-pack of beer to the six-items-or-fewer checkout line at the grocery store, the cashier is not supposed to protest your use of the line on the ground that you have seven items: either s/he'll count the six bottles, or s/he'll count the one pack. This thesis, known in the literature as “composition as identity”, is by no means uncontroversial and admits of different formulations (see van Inwagen 1994, Yi 1999, Merricks 1999, McDaniel 2008, Berto and Carrara 2009, Carrara and Martino 2011, Cameron 2012, Wallace 2013, Cotnoir 2013a, Hawley 2013, and the essays in Baxter and Cotnoir 2014). To the extent that the thesis is accepted, however, the charge of ontological exuberance loses its force. The additional entities postulated by the sum axioms would not be a genuine addition to being; they would be, in Armstrong's phrase, an “ontological free lunch” (1997: 13). In fact, if composition is in some sense a form of identity, then the charge of ontological extravagance discussed in connection with unrestricted composition loses its force, too. For if a sum is nothing over and above its constituent proper parts, whatever they are, and if the latter are all right, then there is nothing extravagant in countenancing the former: it just is them, whatever they are. (This is not to say that unrestricted composition is entailed by the thesis that composition is identity; indeed, see McDaniel 2010 for an argument to the effect that it isn't.)
Secondly, it could be observed that the objection in question bites at the wrong level. If, given some entities, positing their sum were to count as further ontological commitment, then, given a mereologically composite entity, positing its proper parts should also count as further commitment. After all, every entity is distinct from its proper parts. But then the worry has nothing to do with the composition axioms; it is, rather, a question of whether there is any point in countenancing a whole along with its proper parts or vice versa (see Varzi 2000, 2014 and Smid 2015). And if the answer is in the negative, then there seems to be little use for mereologytout court. From the point of view of the present worry, it would appear that the only thoroughly parsimonious account would be one that rejects any mereological complex whatsoever. Philosophically such an account is defensible (Rosen and Dorr 2002; Grupp 2006; Liggins 2008; Cameron 2010; Sider 2013; Contessa 2014) and the corresponding axiom,

(P.20)

Simplicity
Ax,

is certainly compatible with M (up to EM and more). But the immediate corollary

(63)

Pxy ↔ x=y

says it all: nothing would be part of anything else and parthood would collapse to identity. (This account is sometimes referred to as mereological nihilism, in contrast to the mereologicaluniversalism expressed by (P.15i); see van Inwagen 1990: 72ff.[25] Van Inwagen himself endorses a restricted version of nihilism, which leaves room for composite living things. So does Merricks 2000, 2001, whose restricted nihilism leaves room for composite conscious things.)
In recent years, further worries have been raised concerning mereological theories with substantive composition principles—especially concerning the full strength of GEM. Among other things, it has been argued that the principle of unrestricted composition does not sit well with certain fundamental intuitions about persistence through time (van Inwagen 1990, 75ff), that it is incompatible with certain plausible theories of space (Forrest 1996b), or that it leads to paradoxes similar to the ones afflicting naïve set theory (Bigelow 1996). A detailed examination of such arguments is beyond the scope of this entry. For some discussion of the first issue, however, see Rea (1998), McGrath (1998, 2001), Hudson (2001: 93ff) and Eklund (2002: §7). On the second, see Oppy (1997) and Mormann (1999). Hudson (2001: 95ff) also contains some discussion of the last point.

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Composition, Existence, and Identity

Composition, Existence, and Identity :: تعاليق

Composition, Existence, and Identity

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