Abstract
A mereological structure is junky if and only if each of its elements is a proper part of some other. The young literature on junk has focused on junky worlds and whether they are counterexamples to unrestricted composition. The present note defends the possibility of junky structures that are not worlds. This possibility complicates a recent attempt in the literature to render junk consistent with a weakened form of unrestricted composition. The upshot is that junky non-worlds threaten the weakened form of unrestricted composition as much as junky worlds threaten the traditional version.
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Notes
To my knowledge, ‘junk’ in this technical sense first occurs in print in Van Cleve (2008, 323).
I here assume [as is standard—see Simons (1987, 10)] that the proper parthood relation is asymmetric, transitive, and irreflexive. These properties jointly prohibit small finite collections of objects (singles, pairs, trios, etc.) from satisfying the characterization of junk to which this note is appended. Singles are ruled out straightaway by irreflexivity. Pairs are ruled out by asymmetry plus irreflexivity: if a is a proper part of b then b cannot be a proper part of a (by asymmetry) nor can it be a proper part of itself (by irreflexivity); so some third object is needed in order for b to be a proper part (of it). Trios are ruled out by the three properties in tandem: if a is a proper part of b then (as we have just seen) there must be some third object c of which b is a proper part (by asymmetry and irreflexivity); it follows that a is a proper part of c (by transitivity); but c is not a proper part of a or b (by asymmetry) nor is it a proper part of itself (by irreflexivity); so some fourth object d is needed in order for c to be a proper part (of it). It is clear how to proceed for quartets, quintets, etc. Thank you to an anonymous referee for prompting me to make this assumption explicit.
For simplicity, I will speak of worlds as though they are concrete cosmoi. More cumbersome exposition would deploy something like ‘the unique all-inclusive cosmos represented by a world’, which allows that worlds themselves are not concrete.
Here ‘concrete’ indicates a capacity for independent existence and is intended to rule out tropes, on a certain way of understanding them. (It is controversial whether tropes can exist independently. In fact, I am inclined to think they can, but the issue is not important here.) Probably the most prominent stream in the literature on unrestricted composition that focuses exclusively on spatiotemporally located concrete particulars begins with (van Inwagen 1990). To appreciate the extent to which spatiotemporally located concrete particulars are the exclusive relata of the parthood relation in debates about unrestricted composition—sometimes acknowledged as such explicitly, sometimes indicated as such implicitly by choice of examples—see Lewis (1986), (Sider 2001), (Van Cleve 2008), and (Markosian 2008). For alternative characterizations of unrestricted composition that explicitly allow entities outside the category of spatiotemporally located concrete particulars to be parts, see Armstrong (1997) and Lewis (1991).
Cf. (Schaffer 2010), which argues that junk is incoherent and “worldless”.
The sort of constituents of objects that I have in mind are bare particulars, universals, and tropes. These are non-objects in the presently relevant sense because they are not concrete particulars. They are thus ineligible for parthood.
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Giberman, D. Junky Non-Worlds. Erkenn 80, 437–443 (2015). https://doi.org/10.1007/s10670-014-9652-7
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DOI: https://doi.org/10.1007/s10670-014-9652-7