Abstract
The notion of multiple location plays an important role in the characterization of endurantism. Several authors have recently offered cases intended to demonstrate the incoherence of multiple location. I argue that these cases do not succeed in making multiple location problematic. Along the way, several crucial issues about multiple location and its use by endurantists are clarified.
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Notes
This is the relation called ‘(exact) occupation’ by Donnelly (2011: 30) and McDaniel (2007: 132); and called ‘(exact) location’ by Balashov (2010: 16) and Hudson (2005: 98).
Note that it is not the relation called ‘exact location’ by Parsons (2007: 203–5). That relation—let us call it ‘P-exact location’—may be defined in the present framework as follows: x is P-exactly located at R = for every region S, S partly overlaps R iff x is exactly located at a region overlapping S. As Parsons notes, it follows from the definition just given that every object has a unique P-exact location; it is crucial to the use I and the other cited authors wish to make of exact location that it is consistent that an object have more than one exact location (Parsons himself is deeply suspicious of the intelligibility of the notion of exact location used by the authors cited above; see Parsons 2008).
That said, Parsons’ gloss on (what I’ve called) P-exact location may be helpful in understanding exact location. He says ‘exact location is like [a] shadow in substantival space’ (2007: 203). Once we note that if an object is illuminated by multiple light sources, it has multiple shadows, and that these different shadows may have different size and shape to each other despite being the shadows of the very same object, the analogy between an object’s shadow in spacetime and its exact location looks close, and the analogy certainly looks more appropriate than any analogy between P-exact location and shadows.
The Barker and Dowe argument is explicitly formulated as a problem for endurantist multiple location. But it is easy to generalize their objection to spatial multiple location. Consider a multiply located object which is exactly located at continuum many 2D spatial regions, and which manages to ‘fill up’ a 3D spatial region by being multiply located at a single time. This object would be both spatially 2D and spatially 3D, by the obvious adaptation of Barker and Dowe’s reasoning. My response below applies equally to this mooted generalization.
Note that this is a generalization of the definition of ‘wholly present’; while the latter relation has objects and times as its potential relata, containment has objects and arbitrary regions as its potential relata. But where t is a time, an object is wholly present at t iff it is contained in t).
This could be so: for example, if perdurance turns out to be the correct account of persistence as a matter of metaphysical necessity, then endurantism might be logically and conceptually coherent, but impossible. If that were to come to pass, endurantism would share a modal status with the hypothesis that water isn’t H2O: conceptually coherent, since the concepts involved are distinct, but impossible, because their referents are identical.
Suppose that x is f-extended. Since x isn’t confined to an unextended region, the region F which is the fusion of x’s exact locations must be extended. But the fusion of x’s exact locations is such that every subregion of it overlaps an exact location of x, by construction. So x fills F.
Hudson (2005: 99) also adopts Parsons’ terminology of ‘entending’ within a framework taking exact location as primitive, though Hudson’s definition has the (unwanted-by-me) consequence that an entending object is mereologically simple.
Minimal (extensional) mereology is the theory comprising the following three axioms (Simons, 1987: 25–31):
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(MEM1) Parthood is anti-symmetric and transitive;
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(MEM2) If x is a proper part of y, then there is part of y that doesn’t overlap x (Weak Supplementation); and
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(MEM3) If x and y overlap, there is a part of both of which all other parts of both are parts (that is, if there is a common part between two things, there exists a Maximal Common Part).
Some endurantists, particularly those who allow for coincidence in location between distinct material objects, will not want to endorse minimal mereology; for coincident objects are often take to violate MEM2. I will briefly discuss such views in the following section.
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Things are slightly more complicated, because Kleinschmidt sets the case up so that Odie is part of something else (‘Kibble’), which in turn is part of Clifford. She’s interested in whether the case violates transitivity of proper parthood. Since endurantists should accept the transitivity of proper parthood, the intermediary Kibble isn’t essential to the problem posed to the locative conception of endurance by her case.
Thanks to an anonymous reviewer for pushing this point.
One of the lessons of Lewis (1976) is that in some contexts we can truly ascribe abilities to time travellers based on what their intrinsic duplicates can do. With this in mind, the moral of the main text is more nuanced: in virtue of being a time traveller identical to Clifford, Odie lacks the ability be a proper part of Clifford. But it is precisely this ability which needs to be truly ascribed to Odie in the context of Klenischmidt’s discussion to make the scenario coherent.
Thanks to an anonymous reviewer for pushing me to consider this interpretation.
Those assignments which assign an object to a region R, but assign none of its parts (or parts-as-at-R) to subregions of R, will presumably be illegitimate.
Consider again Parsons’ framework, discussed in footnote 1. According to Parsons, the path of an object is its only P-exact location. He supports that claim by appealing to a metaphorical account of exact location as being like a geometrical projection of the object into substantival space. That metaphor applies at least as well, if not better, to the present notion of exact location; it thus provides intuitive support for taking the path to be among the exact locations of the object, even when the object has other exact locations too.
It’s also a picture which can make sense of the endurantist ontology one is left with if one accepts van Inwagen’s 1981 arguments against DAUP. He tells us that, for example, there is strictly and literally speaking no such thing as Descartes’ left leg. One way to make sense of that is what I’ve just sketched in the main text: that the fundamental ontology just contains material wholes which have locations, and then various properties that their locations have which can be used to ground derivative talk about apparent material parts of those things. So Descartes has a location; and that location has a left-leg-ish subregion; but strictly and literally speaking, Descartes stands in no interesting mereological relations at all.
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Acknowledgments
This paper began to be as a section of another still in-progress paper; for comments on that larger paper that may have influenced this paper, I’m grateful to these people in particular: Rachael Briggs, Garrett Cullity, Shamik Dasgupta, Cian Dorr, Cody Gilmore, Dana Goswick, Benj Hellie, Peter van Inwagen, Jonathan McKeown-Green, Graham Nerlich, Daniel Nolan, Josh Parsons, Laurie Paul, Olly Pooley, Denis Robinson, Ted Sider, Gabriel Uzquiano, and Jessica Wilson. Thanks also to anonymous referees for their comments.
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Eagle, A. Multiple location defended. Philos Stud 173, 2215–2231 (2016). https://doi.org/10.1007/s11098-015-0605-z
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DOI: https://doi.org/10.1007/s11098-015-0605-z