Abstract
Einar Bohn has argued that principles of composition must be contingent if gunky objects and junky worlds are both metaphysically possible. This paper critically examines such a case for contingentism about composition. I argue that weak mereological universalism, the principle that any two objects compose something, is consistent with the metaphysical possibility of both gunky objects and junky worlds. I further argue that, contra A. J. Cotnoir, the weak mereological universalist can accept a plausible mereological remainder axiom. The proponent of contingent composition will have to look elsewhere for an argument in favor of his position.
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Notes
Bohn also argues for the contingency of composition from the Humean denial of necessary connections between independent existents (see 2009b, pp. 195–196). An examination of that argument is beyond the scope of this paper.
Sometimes the term ‘mereological sum’ is used in place of ‘fusion’.
I will assume that the quantifier ‘any’ is an actualist quantifier ranging only over collections of objects in the world of evaluation. But a possibilist reading would yield an even more permissive principle. See Lewis (1986, pp. 211–213).
It has been suggested by an anonymous reviewer for this journal that unrestricted composition might be able to address this problem by adopting a slightly revised definition of a junky world. Let us say that a world w is junky* if and only if everything in w is a proper part of something, whether or not that something exists in w. A world could then be junky* despite having a universal fusion as required by unrestricted composition. However, in order for there to be junky* worlds that are not simply junky, there would have to be cross-world composite objects (i.e. objects having proper parts in more than one world) of the sort that Lewis (1986) proposes. To accommodate such objects, we would have to interpret the quantifier ‘any’ in unrestricted composition as a possibilist quantifier ranging over all possible concrete objects. If we do so, it will follow that all possible worlds are junky*. Indeed, any object in any world will be a proper part of (infinitely many) cross-world objects. By contrast, the same type of considerations that Bohn appeals to in order to establish the metaphysical possibility of junky worlds can be used to establish the possibility of non-junky worlds. This suggests to me that the revised definition is too dissimilar from the original to be appealed to in this way by the proponent of unrestricted composition.
Watson (2010, pp. 79–80) notes that the existence of a junky series of objects (a series of objects is junky if and only if every member of the series is a proper part of an object in the series) in a putatively metaphysically possible world does not all by itself prevent that world from having a universal fusion. After all, nothing guarantees that the collection of objects in the infinite series exhausts all concrete objects in that world. It is conceivable that there would be a concrete object (not in the series) that is the fusion of all of the concrete objects in the junky series.
For a fairly compelling defense of the metaphysical possibility of gunky objects, see Jonathan Schaffer (2003). I will not question the metaphysical possibility of gunky objects here.
It is important to note that Contessa ultimately rejects both unrestricted composition and weak mereological universalism (see 2012, p. 457).
Unrestricted composition can be expressed quite simply in a plural logic as: ∀xx∃yCxxy.
Giberman (2015) has argued that, if junky worlds are possible, so too are junky non-worlds (junky series that do not exhaust all of the objects in a given world). Giberman then argues that possible worlds containing junky non-worlds pose as much of a threat to weak mereological universalism as junky worlds pose for unrestricted composition, since there would be two objects in any such world (namely the junky series and some distinct object that does not overlap any element in the series) that fail to compose.
They fail to compose anything because […] junky entities, given the definition of junk, cannot be parts. Suppose a junky entity J were a part of something. This entails that every element in J is a part of that thing, which entails that every element in J co-fuses. But, if every element in J co-fuses then there is some whole that is the fusion of every element in J. And that fusion would be an element in J that is not a proper part of any element in J, thus violating the definition of junk. (Giberman 2015, pp. 439–440)
This seems off track to me. Let us provisionally grant that junky series J is a concrete object. Now imagine that J is a part of a concrete object O. Even if we agree that this entails that every element in series J is a part of O and so every element in J co-fuses, it wouldn’t follow that the fusion of the elements in J is itself an element in J. So, if a junky series is indeed an object, there is no reason to suppose that it cannot be a part of some object, and so, no reason to suppose that junky non-worlds are incompatible with weak mereological universalism. It is independently worth noting that, if a junky series does count as a concrete object, then junky worlds would seem to be impossible. Consider a world w that contains only a junky series S. If S is a concrete object, then it is a concrete object in w that is not itself a proper part of any object in w. In that case, w is not itself junky.
It is worth noting that there are other principles of composition referenced in the literature that, while neither as simple nor perhaps as plausible as weak mereological universalism, are arguably compatible with gunky objects and junky worlds. Ned Markosian’s “brutal composition,” according to which the true principle of composition is “an infinitely long list of every possible situation involving some [collection of objects] that compose a further object”(Markosian 1998, 2008), is presumably compatible with both. Or consider van Inwagen’s preferred principle of composition: any collection of objects (non-trivially) composes something if and only if the activities of the plurality of objects in the collection constitute a life (van Inwagen 1990). This principle would seem to allow for a certain kind of junky world—a world containing atomic simples wherein each atomic simple is a member of some collection of atomic simples the activities of which constitute a first-order living thing, the activities of some collections of first-order living things compose second-order living things, and so on ad infinitum. (One might reasonably ask whether these creatures would have anything to breath, drink, or eat. Perhaps n-order living things can make use of atomic simples arranged, e.g., oxygen-, water-, and food-wise that are parts of higher-order living things.) Further, van Inwagen’s principle is arguably consistent with gunky objects that are living things every proper part of which is itself a living thing. (Such a view is suggested by certain passages of Leibniz’ Monadology.) Similar points apply to other restricted principles of composition referenced in the literature, such as the view that a collection of objects composes something if and only if the members of the collection are in contact or the view that a collection composes if and only if the members of the collection are fastened together.
Note that closed weak mereological universalism no longer has the virtue of being simpler than the principle that all and only finite collections compose something. It too must be expressed in plural logic and involve an additional predicate, ‘T’, indicating that the cardinality of the collection is no more than two: ∀xx(Txx↔∃yCxxy).
In considering collections of objects of infinite cardinality, I will generally focus on collections that are enumerably infinite. Although some of my examples require the assumption that the collection is enumerable, I believe that much (if not all) of what I want to say about weak mereological universalism would apply to non-enumerable collections as well.
Although I arrived at this independently, Cotnoir (2014, p. 657) makes a similar point.
Contessa likewise seems to agree that weak mereological universalism should not be interpreted as placing any genuine restrictions on composition. “[A]ccording to weak mereological universalism, mereological composition would be restricted only if there were pairs of objects that, under some circumstances, did not have a mereological sum…”(2012, p. 456). However, it is far from clear that he takes weak mereological universalism to be consistent with gunky objects.
Bohn himself hints at such an idea when he speaks of fusing objects “two and two at a time.” See Bohn (2012, p. 216, footnote 14).
It is worth asking at this point whether weak mereological universalism, interpreted as a constructive principle, would be capable of constructing all of the non-atomic concrete objects in a junky series. Consider again a world with an (enumerably) infinite number of atomic simples. Taking any two of the atomic simples, we can construct our first properly composite object. We can then take that object and a third atomic simple and compose the second properly composite object. Continuing in this fashion, at each stage n (for n > 1) in the generation of properly composite objects, we take the nth properly composite object and fuse it with the n + 1th atomic simple. While there will be no stage n at which all of the objects in this junky series have been constructed, we do seem to have provided a recipe for constructing any and all of the objects in this series. Since the construction is a logical and not a temporal one, this is plausibly sufficient. But, if weak mereological universalism can construct the infinity of concrete objects in a junky series via an infinity of constructive stages, why can’t it similarly construct an object that is the fusion of an infinite number of atomic simples via an infinity of constructive stages? The answer is that, while there is no stage n at which all of the objects in a junky series have been constructed, each object in the junky series is constructed at some stage n. However, there would be no stage n at which the infinite fusion would be constructed.
If haecceitism is true, it also cannot tell us which atomic simples the world contains. This issue will not arise if, as is plausible, atomic simples are barely, numerically distinct.
It might be suggested that unrestricted composition has the advantage on this score. While unrestricted composition does not allow for the construction of gunky objects out of non-gunky objects, it will allow for the construction of objects that are fusions of an infinite number of atomic simples (or other objects that are not themselves infinite fusions). However, because unrestricted composition is inconsistent with junky worlds, it is not a viable candidate to be a metaphysically necessary principle of composition. As such, this constitutes a reason to prefer unrestricted composition to weak mereological universalism only if the true principle of composition is metaphysically contingent.
Thanks are due to an anonymous referee for bringing this point to my attention.
Thanks are again due to an anonymous reviewer for this journal for this suggestion.
An anonymous reviewer for this journal has noted that there remains an asymmetry between unrestricted composition and weak mereological universalism when it comes to the explanatory deconstruction of a gunky object. By the second stage of decomposition, unrestricted composition is able to deconstruct a gunky object into an infinite number of second-level proper parts of each of the infinite number of first-level proper parts. Weak mereological universalism is only able to deconstruct a gunky object into a total of four proper parts by the second stage. It remains an open question whether or not the relative “speed” of deconstruction afforded by unrestricted composition constitutes an explanatory advantage over weak mereological universalism.
Here, ‘≤’ expresses the parthood relation and ‘O’ expresses the overlap relation. See Cotnoir (2014, pp. 657–658).
Cotnoir also suggests that worlds that are both junky and gunky pose a problem for weak mereological universalism (Cotnoir 2014, p. 658). However, it is not clear why that would be the case. We have already seen that weak mereological universalism can accommodate gunky objects. So, consider a world that contains an (enumerably) infinite number of non-overlapping gunky objects. This world will be junky for the same reason that a world containing an infinite number of atomic simples will be junky given weak mereological universalism. The idea is that the non-overlapping gunky objects can be treated as relative atoms that will entail the existence of a junky series of relatively composite objects on weak mereological universalism.
References
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Smith, D.C. Gunky Objects, Junky Worlds, and Weak Mereological Universalism. Erkenn 84, 41–55 (2019). https://doi.org/10.1007/s10670-017-9946-7
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DOI: https://doi.org/10.1007/s10670-017-9946-7