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«There are many arguments against composition as identity.1 One of the more prominent of these maintains that composition as identity (CAI) entails ...»

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It is true that many of us are not modal realists. But this isn’t because we refuse to countenance possible worlds. Typically, the objection to modal realism is the concreteness of the worlds, not their existence. Notoriously, if one denies that there are possible worlds, then one is left with the theoretical burden of accounting for our modal truths. One could take modal facts as brute, but it is not clear that having brute modal truths is any more theoretically elegant than positing possible worlds.32 So while many philosophers will not commit to concrete possible worlds (e.g., One could also be a fictionalist about possible worlds, in which case one would get to use possible worlds talk without committing to them. But modal fictionalism has its fair share of burdens, which arguably outweigh any initial, apparent Lewis’s modal realism), most are inclined towards some kind of ersatzism—the thesis that possible worlds are

Abstract

sorts of things, sets or classes, or some kind of linguistic entities, etc.33 But then the question isn’t whether you think a commitment to possible worlds is outrageous (or objectionable or ontologically excessive), but whether you take a stand on the metaphysical nature of these worlds once you’ve already invited them into your ontology—and this is a different point (which I’ll get to in a second). So denying that there are possible worlds is not going to be an easy position to maintain in light of the wealth of theoretical benefits possible worlds afford.

But if we do quantify over possible worlds, then (assuming a Quinean criterion of ontological commitment) we are committed to having them in our ontology. Whether possible worlds are abstract or concrete is neither here nor there. And if we already have abstract possible worlds in our ontology—if they are already here, so to speak—then they can surely be parts of things.

Indeed, they are admittedly already part of what there is!

Perhaps one thinks that composition only concerns or applies to concrete objects. But we do, in fact, use parthood talk when we discuss traditionally abstract objects. Lewis talks about trigonometry being part of mathematics, omniscience being part of god, the number three is part of the real numbers, etc.34 And we do not just talk about abstract entities (e.g., mathematics) having abstract parts (e.g., trigonometry). We think that concrete objects can have abstract parts—or at least, we talk as if they do. We talk about bowling balls having an axis of symmetry, the earth having an equator, Plato talks about the mathematical axis and circumference of a spinning top35, Peter van benefits of the view. See Brock (1993), Divers (1995), Hale (1995a), (1995b), Rosen (1990), (1993), (1995), et. al. for discussion.

The temporal parallel would be those who commit to times, but think that times (except for the present, perhaps) are abstract.

–  –  –

Plato, Republic, Book IV.

Inwagen talks about the mathematical point of a knife36, etc. One may think that these particular examples of parthood are metaphorical, not literal. But it is sometimes accepted (in the literature) that our notions of parthood are topic-neutral, and that we use the word ‘part’ ecumenically.37 Rather than trying to discern metaphorical part-hood talk from literal parthood talk, I suggest— following Lewis (1991)—taking all of our parthood talk as instructive, and letting all of our parthood talk define the primitive notion of parthood. In which case, we should allow abstract entities as parts (and wholes). But if so, then all of the considerations in favor of modal parts remain as they are. While I assumed modal realism for exegetical purposes, at no point did my definition of modal part, my understanding of a modal part, or its connections to mereological essentialism rely on the assumption that possible worlds are concrete rather than abstract.38 But perhaps this isn’t why you think that abstract worlds are problematic for a modal parts view. Perhaps, you think, the definition of world-bound modal part—unlike the definition of instantaneous temporal part—is unacceptable. And this is indeed due to the metaphysics of possible worlds. If worlds are abstract, you might argue, then the notion of ‘existing at a world’ is mysterious.

How can an (abstract or concrete) thing exist at an abstract thing?

Put a bit more carefully, crucial to the definition of instantaneous temporal part is the idea of existence at a time. Likewise, crucial to the definition of world-bound modal part is the idea of existence at a world.

x is an instantaneous temporal part of y at an instant t =df (i) x exists at, but only at, t, (ii) x is part of y at t, and (iii) x overlaps at t everything that is part of y at t.

Van Inwagen (1981) See Lewis (1991), Simons (1987), McDaniel (2004), (2010), etc.

Moreover, if one is a certain kind of ersatzer, then one may not even need to make use of abstract objects as parts.

One may think that possible worlds are abstract sets of propositions, but that concrete objects are (often) part of these propositions. A proposition about Humphrey, for example, may include Humphrey himself. Sets, while abstract, can have concrete members, and it may be these concrete members that ultimately count as the relevant world parts.

x is a world-bound modal part of y at a world w =df (i) x exists at, but only at, w, (ii) x is part of y at w, and (iii) x overlaps at w everything that is part of y at w.





Sider explains that the exists-at predicate in the definition of instantaneous temporal part is “analogous to the spatial predicate ‘is located at’…”. Similarly, then, we should understand the exists-at predicate in the definition of world-bound modal part as analogous to the spatial predicate ‘is located at.’ But if this is right, one may argue, then if we think that possible worlds are abstract rather than concrete, then the definition of a modal part becomes mysterious at best and incoherent at worst.39 But notice that the same can be said in the temporal case. If one thinks that times (other than the present) are abstract rather than concrete, then the definition of temporal part—and in particular, the existing-at relation—becomes mysterious at best and incoherent at worst. Yet rarely (and to my knowledge: never) does anyone object to temporal parts on the grounds that if one takes times (other than the present) as abstract then the notion of a temporal part is incoherent. I suspect this is either because very few are committed to abstract times and so it is not often considered as a response, or else because it is assumed that anyone who endorses abstract times has a relation that fills in and does the theoretical duty that the exists-at (a time) relation is suppose to do for the temporal parts theorist. So either there is a problem with temporal parts because the definition of temporal part does not accommodate those who believe in abstract times, or else in the modal case, we can assume (as is done in the temporal case) that anyone who endorses abstract possible worlds has a relation that fills in and does the duty of the exists-at (a world) relation. Either way, if this worry is a legitimate one, it not a problem for the modal parts alone: the coherence of temporal parts and modal parts stand seem to stand of fall together here.

Thanks to an anonymous referee for raising this point.

One may object that even if the coherence of the exists-at relation is a problem for temporal and modal parts alike, it is only a pressing problem for modal parts since very few (if any) embrace abstract times, but many more accept abstract possible worlds.40 This may be true but it is ultimately irrelevant. For the view I am proposing here can easily deflate the original worry. As suggested above, a modal parts theorist would have a liberal notion ‘part’, allowing that abstract things are parts of concrete things (and the other way around). If one is a (certain kind of) ersatzer, then one already grants that possible worlds are abstract sets with abstract (and maybe concrete41) members.

Thus, the exists-at predicate could be cashed out in terms of being part of (or being a member of) a particular (abstract) world. This may not be as analogous to the spatial is-located-at predicate as Sider originally intended, but it is difficult to see how this undermines coherence for the notion when part of and member of are presumably well understood by the modal parts theorist and ersatzer, respectively.42 Perhaps you object to modal parts not because of the metaphysical burdens it seemingly incurs (which I hope I have at least minimally convinced you it doesn’t), but because it is just too unintuitive. It is simply not the case, you might argue, that when we think of ordinary objects, we are thinking about these strange modally extended, trans-world mereological sums.

It is true that we may not seem to explicitly think about cross-world objects; indeed, thinking about possible worlds in general is a highly theoretical philosopher’s notion that is far outside the realm of common sense. But common sense does think a lot about—and has strong intuitions about—the persistence conditions of ordinary objects. I can admit that we don’t think of ourselves as trans-world objects, but we do think an awful lot about what is possible and impossible for us, Thanks to Aaron Cotnoir for pushing this point.

–  –  –

Thanks to Don Baxter for input here.

and we do think that such modal attributes are part of what makes us who we are. We think that our modal facts are a large part of what makes us who we are; other modal facts are a large part of what makes other things what they are, etc. I do not mean to be leaning too heavily on our metaphorical talk about what is part of us and other things. But it is the case that we all have strong intuitions about various objects and their persistence conditions or modal facts, and there are various philosophical puzzles that rely on them (e.g., Gibbard’s Goliath and Lumpl43). And if it is the case— as many of us assume—that our modal facts and properties are made true by various things going on in various possible worlds (whether these worlds are concrete or abstract), then the theory of modal parts is a position that deserves serious attention.

Even if we accept modal parts, however, you might worry that we have now strayed too far from our original motivations for composition as identity. CO-LOCATION and ODD THINGS, recall, purportedly show that CAI (i) makes mereological universalism more ontologically parsimonious and (ii) solves co-location puzzles. But by pairing CAI with MP, one might argue, we have now undermined these particular advantages for CAI.

Take (i). Even if CAI makes universalism more ontologically innocent, one might argue, by accepting modal parts, we have now amplified our commitments to all of these trans-world individuals, thereby dwarfing any ontological savings by adopting CAI in the first place. Not only do we have gerrymandered sums of any objects you please (my right ear and my coffee mug, say), but now we have gerrymandered sums across possible worlds (my (actual) right ear and a coffee mug in a different possible world)! But I am assuming that all of us are already committed to possible worlds (in light of objections addressed above). And whether these worlds are abstract or concrete, the modal parts theorist accepts mereological sums of these very things that we already accept. I will admit that just accepting modal parts without CAI would be ontologically excessive—for every new Gibbard (1975).

trans-world mereological sum would be a new object in our ontology. But this is where CAI comes in: CAI gives us all of these trans-world sums for free. And genuinely for free; the sums are simply identical to things that all of us already accept.44 So modal parts does not undermine this particular motivation for CAI; that motivation is still very much in play—indeed, it makes (to my mind) modal parts even more attractive.



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