Abstract
Unrestricted Composition (UC) is, roughly, the claim that given any objects at all, there is something which those objects compose. (UC) conflicts in an obvious way with common sense. It has as a consequence, for instance, that there is something which has as parts my nose and the moon. One of the more influential arguments for (UC) is Theodore Sider’s version of the Argument from Vagueness. (A version of the Argument from Vagueness was first presented by David Lewis (1986), pp. 212–213). That argument purports to show that some plausible claims concerning the nature of vagueness entail (UC). In this paper I will suggest a response to this argument. I will show that the proponent of Supersubstantivalism (SS)—the view that material objects are identical to regions of spacetime—can reject a premise of Sider’s argument without denying the plausible claims concerning vagueness. Doing so requires only rejecting a certain view concerning the relationship between the proper sub-region relation and the proper parthood relation. So, proponents of (SS) are in a better position than many of us to side with common sense regarding composition. In the first section of the paper, I will present Sider’s argument. In the second section, I will introduce (SS) and briefly discuss some reasons one might have to believe that it is true. In the third section, I will show how the proponent of (SS) can avoid commitment to (UC) and reject a premise of Sider’s argument. Last, I’ll briefly consider and respond to some objections.
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Notes
I will make frequent use of plural quantification. Plural variables and quantification over those variables stand to plural pronouns, like ‘they’ and ‘them’, in the way that singular variables and quantification of those variables stand to singular pronouns like ‘it’. For a defense of the use of plural quantification see van Inwagen (1990, pp. 24–28).
The xxs compose y just in case each of the xxs is a part of y, and any part of y overlaps one of the xx.
Proponents of (UC) have something to say, of course, about why we should, upon reflection, think this result is not as counter-intuitive as it initially seems. What they say frequently involves some claims concerning the way in which the folk restrict their quantifiers. See, for instance, Lewis (1986, p. 213).
I am assuming, for ease of exposition, that there are fundamental physical particles. What I say throughout the paper could be restated without this assumption.
The view Ned Markosian (1998) calls Brutal Composition comes closest to a denial of this claim. However, Markosian is careful to note that his view is consistent with the global supervenience of compositional facts on non-mereological properties and relations. I intentionally remain neutral concerning the properties and relations upon which the property of being a case of composition non-trivially supervenes. Given a sufficiently robust view of properties, the supervenience claim here is no stronger than Markosian’s global supervenience.
This assumes that, for any member of the series, x, there will be some member of the series, y, which is adjacent to x. If the series is dense, as it is likely to be, then that assumption will turn out to be false. I will not worry about this complication. Talk of members of the series which are adjacent to x can, I think, be paraphrased without harm into talk about members of the series which are arbitrarily close to x.
This is obviously—and, I suspect, unavoidably—imprecise.
I mean to use the operator 'it is indeterminate whether' so that if it is indeterminate whether p, it is neither true nor false that p. This rules out an epistemic interpretation of the operator according to which, roughly, it is indeterminate whether p if p is either true or false, but we cannot tell which. So interpreted, I take it that an epistemicist about vagueness will be committed to rejecting premise (6) of the argument and not premise (3).
Sider (2001, p 123). It is also worth noting that if there are cases of composition (or, mere cases), but there are no cases that are determinately cases of composition (or, determinately mere cases), then premise one would turn out false. I do not know what might motivate such a view. I will not speculate about the plausibility of denying premise one in this way.
See, for instance, the suggested restrictions in van Inwagen (1990). There, he suggests as possible restrictions on composition relations like being in contact or being fused together. The restriction he settles on in the end—jointly constituting a life—also would seem to imply that there are compositional series.
More carefully, the claim that there are n things is logically equivalent to a claim which has as constituents only the quantifier, logical connectives, and the identity sign. For instance, the claim that there are exactly two things is logically equivalent to the following sentence: (∃x) (∃y) ((x ≠ y) and (∀z) ((z = x) v (z = y))).
This ignores a long and on-going debate concerning whether absolutely unrestricted quantification is coherent. See, for instance, the papers in Rayo and Uzquiano (2006). That debate is outside of the scope of this discussion.
There is an additional complication that I am ignoring. As Sider notes, if we assume that it is a necessary truth that there are infinitely many objects, then premise (4) of the Argument from Vagueness and premise (1*) of the argument I formulate below are true only if their antecedents are false. So, those premises are not likely to be plausible to anyone who rejects the conclusions of those arguments. Sider responds by modifying both arguments so that they employ the predicate ‘concrete’. Because the response I offer to Sider's argument is independent of this complication, I think I can safely ignore it.
All of the arguments given here for (SS) assume that Substantivalism is true. None of these arguments, I take it, would convince the committed Relationalist. For some proponents of (or at least, sympathizers with) Supersubstantivalism, see Schaffer (2009), Sider (2001, pp. 110–114), Heller (1990), Lewis (1986), Quine (1976).
This assumes, perhaps falsely, that material objects and spacetime regions are the only occupiers of spacetime regions. If, for instance, events occupy spacetime regions, then either we will need a fundamental locative relation to relate events to the regions they occupy, or we will need to identify events, as well, with regions.
Sider (2001, pp. 110–119).
I assert a number of sentences below which, on the view I'm suggesting, have as constituents vague expressions. I'm going to assume a supervaluationist semantics according to which such a sentence expresses a truth just in case it is true on every legitimate way of making the vague expressions precise, false just in case it is false on every legitimate way of making the vague expressions precise, and indeterminate in truth value otherwise. While supervaluationism is not an uncontroversial view, it fits naturally with a Linguistic Theory of Vagueness and I don't employ any of its controversial consequences. For more on supervaluationism, see Keefe (2000).
I do not intend to come down on either side of the dispute concerning whether or not every region of space has some proper sub-region. I am assuming, for simplicity, that there are spacetime points and that such points have no proper sub-regions. What I say could be restated without this assumption.
Thanks to Kris McDaniel for suggesting this sort of view.
It is worth noting, though, that—assuming that only regions of spacetime can stand in the proper sub-region relation—(P) has as a consequence that only regions of spacetime can stand in the proper parthood relation. This consequence might be undesirable. If so, we can consider (PM) instead: (PM) Necessarily, for any x and y, if x is a material object and y is a material object, then x is a proper part of y iff x is a proper sub-region of y. (PM) and (P) will both provide an explanation of the connection between the sub-region relation and the parthood relation, and (PM) will partially reduce the parthood relation to the proper sub-region relation. Rejecting both (PM) and (P), though, will be consistent with advocating the response to Sider's which I suggest below.
van Inwagen (1990, p. 82).
It is important to note that van Inwagen is not committed to (L). The General Composition Question asks for an analysis of the composes relation. Van Inwagen thinks that the General Composition Question probably cannot be answered (1990, p. 51). (L) entails an answer to the General Composition Question. Further, (L) has a number of consequences which van Inwagen is sure to reject. For instance, given plausible views about spacetime, (L) entails the Doctrine of Arbitrary Undetached Parts (DAUP) according to which, for any occupiable sub-region, r, of the region at which some object, x, is located, x has a part located at r. van Inwagen (1981) rejects (DAUP). Thanks to Earl Conee for helping me see this.
Though, it is also true that the moon does not exist—or, better, that 'the moon' doesn't designate anything.
Thanks to Brad Weslake for pressing the issue discussed in this section.
See, for instance, Kripke (1971).
I have in mind certain sorts of modal fictionalist views. Rosen (1990) may be a case.
See, for instance, Forbes (1989).
Thanks to an anonymous referee for noting this worry.
Geach (1980, p. 215).
Sider (2001, p. 130).
Thanks to an anonymous referee for pressing me to say more.
For more discussion of arguments in support of (SS), see Schaffer (2009).
Substantivalism does not entail this claim, of course. One could think that there are spacetime regions without thinking that any such regions are discontinuous. But, it is hard to see what would motivate this.
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Acknowledgments
Thank you to David Braun, Earl Conee, Gregory Fowler, Kris McDaniel, Alyssa Ney, Joshua T. Spencer, and Brad Weslake for helpful comments and discussion. Thank you, as well, to two referees for providing extremely thorough and helpful reports.
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Wake, A.V. Spacetime and Mereology. Erkenn 74, 17–35 (2011). https://doi.org/10.1007/s10670-010-9262-y
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DOI: https://doi.org/10.1007/s10670-010-9262-y