Abstract
This article offers a novel solution to the problem of material constitution: by including non-concrete objects among the parts of material objects, we can avoid having a statue and its constituent piece of clay composed of all the same proper parts. Non-concrete objects—objects that aren’t concrete, but possibly are—have been used (by Bernard Linsky, Ed Zalta and Timothy Williamson) in defense of the claim that everything necessarily exists. But the account offered shows that non-concreta are independently useful in other domains as well. The resulting view falls under a ‘nonmaterial partist’ class of views that includes, in particular, Laurie Paul’s and Kathrin Koslicki’s constitution views; ones where material objects have properties or structures as parts respectively. The article gives reasons for preferring the non-concretist solution over these other non-material partist views and defends it against objections.
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Notes
Vagueness as a linguistic phenomenon has also been a strong motivation for temporal and modal parts (e.g, Sider 2001; Wallace 2014a). Such a motivation can also be given for non-concrete parts. But it’s not really a separate argument for such parts, since we only arrive at them if we assume—as the problem of material constitution presents things—that no two objects can share the same proper parts. Without this assumption, we only get the conclusion that there are multiple coinciding objects with different temporal or modal properties.
Graham’s Actualist Five-Dimensionalism is like Modal Parts Theory, except that only an object’s actual modal proper part exists (if he wants to say the same for an object’s present temporal part, then it’s not a partist view). This might make it sound as though his is a Worm Theory where a tree, say, is identical to some temporally extended worm—it’s not modally extended since there are no other modal parts to be extended over. Yet this isn’t quite right either. On his view, a tree isn’t identical to its longest temporal part (its actual modal part)—such a temporal part is world-bound, but the tree is not (p. 18). Graham’s view turns out to be an unhappy middle ground between Modal Parts Theory and Worm Theory since it doesn’t avoid non-identical completely overlapping objects. A tree and its actual modal part are distinct (unlike Worm Theory), yet they don’t differ in parts (unlike Modal Parts Theory) since the tree doesn’t have any other-worldly parts.
At least this is true of the class of non-concrete objects I’m interested in. This is in contrast to the suggestion that there might be non-concrete objects that, when concrete, would just be ‘pure spiritual beings’—that is, conscious non-material objects.
Necessitism implies that the Eiffel Tower, for example, couldn’t have failed to exist. Yet it would be absurd to say that in every possible world someone builds the Eiffel Tower. Instead, we should think that in worlds in which it isn’t built, it’s simply a non-concrete (and existent) object.
This formulation is taken from Varzi (2008).
Lesniewski’s Axiom IV reads “If P is a class of objects m, and \(\hbox {P}_{1}\) is the class of objects m, then P is \(\hbox {P}_{1}\)” (Barnett 1992, p. 136). Given his definition of a ‘class of objects m’ (p. 135), the phrase is synonymous with what we would now call a ‘mereological sum of m’. Leonard and Goodman use the notion of two objects being ‘disjoint’ to define mereological notions. Their principle 1.12 essentially says: for any x and y, if everything disjoint from the one is disjoint from the other, then \(x = y\). (1940, p. 49)
Defenders say that, unlike a person trying to walk through a wall, the coincidence in question would be unproblematic since the objects would share the same parts (Wiggins 1968; Moyer 2009). The point seems to be that the composite objects don’t themselves have mass, but must ‘borrow’ mass from its parts. Zimmerman (1995, p. 89) thinks this is mysterious since composites are physical objects themselves—as opposed to sets of material objects—so should have mass intrinsically. A second problem is in identifying which objects have mass in their own right; it couldn’t just be the objects at the ‘lowest level’ since this wouldn’t make sense of gunky worlds. (See also Eddon’s 2010 response to Moyer.)
Counterparts might seem irrelevant for de re modality (Kripke 1980, p. 45 n. 13; Plantinga 1974, p. 116), counterpart theory might be semantically inadequate (Feldman 1971; Plantinga 1974, pp. 108–114) or its use of mind and context-dependent modal properties—which are essential to its solution to the problem of material constitution (Graham 2015, p. 19)—might be found objectionable (Merricks 2003, pp. 528–530; Paul 2006, p. 643). For Modal Parts Theory, one might object to its commitment to concrete non-actual worlds [for why should concrete objects spatio-temporally disconnected from us be considered ‘non-actual’ or ‘unrealized possibilities’? (van Inwagen 1986, p. 199; Stalnaker 1976, pp. 69–70)], its commitment to timeless/worldless parts (van Inwagen 2000, pp. 440–443; Olson 2006), having one’s consciousness spread out across worlds (see Yagisawa 2010, p. 116 for discussion), or its license of immoral behavior (Heller 2003).
The claim that objects don’t lose or gain parts might seem implausible. But we should notice that even if claims such as ‘Leafy the leaf is part of Titan at \(t_{1}\) but not \(t_{2}\)’ aren’t strictly speaking true on Non-Concrete Partism, neither are they strictly speaking true on Worm Theory either. On Worm Theory Leafy is temporally ‘too big’ to be a part of Titan (or to fit into \(t_{1})\). Nevertheless, Worm Theorists can analyze the claim as: Leafy has a \(t_{1}\) temporal part that is part of Titan, but Leafy has no \(t_{2}\) temporal part that is part of Titan. (Even though only a proper part of Leafy, and not Leafy itself, is a part of Titan, Heller (1984, pp. 328–329) points out that proper parts can ordinarily characterize the whole object in this sort of way. If Whitey, the piece of paper, were put in a drawer with a corner sticking out, it would be (loosely speaking) true that ‘Whitey is in the drawer’ despite the fact that (strictly speaking) only a proper part of Whitey is.) Non-Concrete Partists can adopt a similar strategy. That is, the claim can be analyzed as: Leafy has a \(t_{1}\) time-bound part that is part of Titan, but Leafy has no \(t_{2}\) time-bound part that is part of Titan. A time-bound part of Leafy at \(t_{1}\) is an object that overlaps all and only the wholly concrete things (things with only concrete parts) Leafy overlaps at \(t_{1}\) and is concrete at no other time.
Note that ‘part’ in (iii) should not be understood as ‘proper part’, otherwise a material object that is concrete at a single time-world coordinate would be a proper part of itself.
It wouldn’t exactly be Modal Parts Theory since it wouldn’t imply that the things that would be a part of an object in some merely possible world do in fact exist. (That is, if we make the Contingentist assumption that \(\lozenge \exists x \hbox {F} x\) doesn’t entail \(\exists x \lozenge \hbox {F} x\).)
Assuming, as I do, that there are time-world coordinates. Notice that I’m not making the controversial claim that TWR-Extensionality implies Extensionality (Worm and Modal Parts Theorists think there’s a ‘timeless’ and/or ‘worldless’ sense of parthood not captured by the time-world-relativized notion).
Non-Concrete Partism can also deny that there are any intelligible versions of Extensionality framed in terms of ‘timeless’ or ‘worldless’ parts.
Say possible-two-poundedness is two pounds at (t, w). Then the problem will arise for whatever object instantiates possible-two-poundedness at (t, w). (And there will be such an object that the property is a part of at (t, w). To deny this is to deny Paul’s view that the properties cannot exist uninstantiated.)
It’s tempting to say that it also has the property possibleness as a part. But I’m skeptical that this is a coherent suggestion. For one thing, it doesn’t seem like there is such a thing as possiblenesssimpliciter. Objects can have the property of being possibly red, possibly true, possibly existent, possibly instantiated etc. but not possible simpliciter. For another thing, even if it had such a property as a proper part, what other proper parts would it have when it’s not red? It seems that there would be none, in which case we arrive at the original problem.
Though Paul adopts the counterpart theoretic strategy of analyzing modality in terms of representation, her view is intended to avoid the context- and mind-dependence of those modal properties by making the representational properties part of the object (2006, pp. 644–645).
And even though it’s only \({\upkappa }\) that would strictly speaking be spherical, it still makes sense to say Clump is spherical in virtue of having the spherical part. For example, it makes sense to say to someone “you’re swelling up like a balloon!” even if only her toe is swelling.
Perhaps it arises if we marry Non-Concrete Partism with the view that there are self-characterizing modal properties like possible-2-poundedness. But I deny that there are such self-characterizing modal properties.
Paul has separate mereological principles given the kinds of parts under consideration: one for qualitative (property) parts and one for spatiotemporal parts. Transitivity holds between parts of a single kind, but not between kinds. For example, my body has a hand as a part, my hand has hand-shapedness as a part. But this doesn’t imply that my body has it as a part since this crosses categories.
On Worm Theory, e is located at more than just S, since e is extended through time. Nevertheless Worm Theorists can preserve the intuitive idea that e is just located at S, since we are restricting our quantifier to the present moment. It’s implausible that a similar move could be made here: when asking where the electron is located, even if we tacitly include a ‘with respect to the present’ qualifier, we aren’t tacitly including a ‘with respect to spacetime point S’ qualifier.
Put more precisely: suppose a theory fails to entail that electrons are repelled from S. Adding the claim “located-at-S-ness is fused to negative-charghood” to the theory won’t remedy the issue.
This sentiment echoed in Rea (2011).
Such a concept of matter would be on a par with Alan Sidelle’s conventionalist view on which “what is primitively ostended is ‘stuff,’ stuff looking, of course, just as the world looks, but devoid of modal properties, identity conditions, and all that imports” (1989, p. 55). See Carter and Bahde (1998), Blackson (1992), and Rea (2002) for objections to the coherence of such a conception.
Furthermore, in gunky worlds Koslicki’s account would run into the composition problem I raise below.
Koslicki denies that elementary particles would be hylomorphic compounds. She says “whether there is a first level of composition is not a question that philosophy is qualified to answer. And if it turns out that there is such a level, then the structure/[matter] dichotomy simply breaks down at that point. For the very fact that what we are dealing with is a first level of composition, i.e., one whose constituents are completely basic, means that we cannot think of these entities as being composed of anything.” (ibid., p. 119) But this response confuses the distinction between spatiotemporal parts and parts simpliciter. It’s the scientist’s job to figure out if quarks have spatiotemporal parts. But even if they lack such parts, it’s the philosopher’s job to figure out if quarks have structures as parts. After all, such parts couldn’t be literally cut out from the object. And if Koslicki is right that statues and pieces of clay have formal parts, then material simples also have such parts: they still have mass and charge properties; also it would have the modal property of indivisibility, and there would be facts about whether it could have a different mass or charge. Things without spatial parts would therefore still need structural parts that are responsible for these properties.
Though see Sect. 5 for a challenge to this claim.
Markosian leaves it open whether non-spatial, non-physical objects can enter into parthood relations (2014, p. 69).
It might be objected that we not only have an intuition that can be expressed as “Davey could have failed to exist”, but also a higher-order intuition that the “exist” expresses the logical sense of the term. Nevertheless the higher-order intuition seems much less certain and more negotiable than the lower-order intuition.
It might be objected that in conjunction with Mereological Universalism, the view does imply Davey’s possible non-concreteness. The reason is that Universalism—which can be defined for our purposes as the view that for any set of concrete or non-concrete objects, there is a fusion of its members—would imply that there is a world where Davey doesn’t have any concrete parts, yet the time-world-bound objects, the xs, that would compose Davey still compose some object o (this would hold true if there’s such an object as ‘the universe’ that has all of the x’s as parts). Since o and Davey have all the same parts in @ (where Davey is concrete), Davey must be identical to o—hence Davey must also exist in worlds where he isn’t concrete. There are a few reasons to doubt this line of thought. First, the claim that o and Davey must exist at the same time doesn’t seem obvious. Why not hold that the xs compose different objects at different times? Why not say they compose Davey only in worlds where one of the xs is concrete? Second, the Non-Concrete Partist needn’t be a Mereological Universalist. Perhaps it’s a natural answer to the question ‘why does that set of concrete and non-concrete objects compose something?’ But it’s not the only one available. One could instead hold to a version of Closest-Continuer Theory (see Yagisawa’s 2010, pp. 101–106) or Brutalism (see Markosian’s 1998).
Another difference is that Paul thinks mereologically fusing the sphericality property to a location property suffices for having a spherical object. I have argued that this is incorrect (Sect. 4.2); just because Clumpy has a spherical non-concrete object as a part, that doesn’t suffice for Clumpy being spherical in the sense of importance—that is, when you look at Clumpy, it will still be in the shape of a man, rather than a ball.
Though a Presentist that believes in an extended-present might be able to incorporate the insights given here.
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I want to thank Rebecca Chan, Peter Finocchiaro, Liz Jackson, Kathrin Koslicki, Daniel Nolan, David Pattillo, Mike Rea, Sarah Schramm, Jeff Speaks, David Squires, Meghan Sullivan and Peter van Inwagen for much helpful discussion and comments on earlier drafts. I especially want to thank an anonymous referee for many detailed and helpful suggestions and comments.
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Longenecker, M.TS. Non-concrete parts of material objects. Synthese 195, 5091–5111 (2018). https://doi.org/10.1007/s11229-017-1451-7
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DOI: https://doi.org/10.1007/s11229-017-1451-7