Abstract
The possibility of multi-location—of one entity having more than one exact location—is required by several metaphysical theories such as the immanentist theory of universals and three-dimensionalism about persistence. One of the most pressing challenges for multi-location theorists is that of making sense of exact location—in that extant definitions of exact location entail a principle called ‘functionality’, according to which nothing can have more than one exact location. Recently in a number of promising papers, Antony Eagle has proposed and defended a definition of exact location in terms of weak location that does not entail functionality. This paper provides the first thorough assessment of Eagle’s proposal. In particular, we argue that it cannot account for (1) the location of immanent universals, (2) the multi-location of mereologically changing three-dimensional objects, (3) the multi-location of mereologically complex objects, and that it (4) makes extended simples impossible.
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Notes
At least some of them. See Sect. 4.
At least some of them. See footnote 12.
A possibility that Parsons does not consider—nor do we—is that exact location can be defined using other locative notions as primitives, such as e.g. entire or pervasive location.
Kleinschmidt (2016) argues that, in any event, no theory of location that uses only one primitive can account for all the metaphysically possible scenarios.
Let us review putative counterexamples to Exactness. We do this in a long footnote so as not to disrupt the flow of the main argument. Failures of Exactness might arise as a result of the mismatch between the mereological structure of objects and space. Suppose you have atomic point-particles but space is gunky, i.e. every region of space admits of further proper parts. A case in point would be Whiteheadean space (Gruszczynski and Pietruszczak Forthcoming; Leonard Forthcoming). These point-like particles would not have any exact location. Yet they would certainly be somewhere in space, that is, they would be weakly located somewhere. Thus, they would violate Exactness.
As for another example, say that an object is omnipresent iff it is weakly located at every region. And say that space is junky iff every region is a proper part of yet another region. Then, omnipresent objects in junky space would violate Exactness. The argument goes roughly as follows. Suppose an omnipresent object, call it oo, has an exact location, r. Then r is the maximal region, i.e. the fusion of all regions of space. To see this, suppose r is not the maximal region. Then there is a region s that is disjoint from r, such that oo is not weakly located at s. But this goes against our assumption that oo is omnipresent. So, if oo has an exact location r, then r is the maximal region. On the other hand, junky space rules out the existence of such a maximal region. So oo does not have any exact location in junky space. Yet it has a weak location. As a matter of fact, it is weakly located everywhere. This constitutes another counterexample to Exactness.
Finally, and to our mind most convincingly, counter-examples to Exactness come from quantum mechanics. Consider the following passage by Bokulich: “In other words, while it makes sense to talk about the particle having the property of position (that is to say the particles are in the room), that property cannot be ascribed a definite (precise) value” (Bokulich, 2014: 467). The passage above suggests that quantum particles can have a weak location without thereby having an exact location, thus violating Exactness.
Perhaps there are two ways of looking at what’s at stake here. On the one hand, one can maintain that Parsons and Eagle are giving two different characterizations of the same notion. On the other hand, one can see Eagle as trying to define a different locative notion that is absent from Parsons’ system. This is an overall interesting suggestion, but developing it goes beyond the scope of this paper. It is important to note that the main point of the paper would still go through in any case. The locative notion that Eagle defines, being it the same notion that Parsons had in mind or a different one, the one that we will label Exact Location 2, is the notion that allegedly supports the possibility of multilocation. And the main argument in the paper is that this is in fact not the case.
The terminology in Eagle (2016a) is slightly different.
This is just a warm-up case. We will provide a more careful characterization of three-dimensional objects in Sect. 5.
We are making a few simplifying assumptions in the rest of the paper, and it is better to make them explicit right from the start. We will be mostly using a separatist framework—the terminology is borrowed from Gilmore et al. (2016)—according to which there are two disjoint and independent manifolds, namely a three-dimensional spatial manifold and a one-dimensional temporal manifold. Separatism contrasts with unitism, according to which there is just one fundamental four-dimensional manifold, space–time, and spatial regions and instants of time—if there are any—are just overlapping spacetime regions of different sorts. This is analogous to what Skow (2015) calls a “3 + 1”-view and a “4D”-view. This is mostly for the simplicity of exposition. The arguments just need a little tweak to go through in a fully unitist, four-dimensional spatiotemporal setting. As a matter of fact, we will advert the reader when a fully blown untist picture is required for the arguments to go through. Also, we work with a characterization of endurantism according to which the relation between persisting objects and time is (some form of) location. While this is widely agreed upon, it is by no means uncontroversial. Fine (2006) and Costa (2017) argue at length to that objects are not strictly speaking located in time. Here we should simply note that while this last claim sounds promising in a separatist-setting, it is unclear whether it can still hold up in a unitist, spatio-temporal one. One could then simply re-phrase the arguments in the main text against a fully-fledged unitist four-dimensional framework.
Calosi and Costa (2015) is particularly interesting in the present context. For their argument crucially depends on a principle they call Region Dissection, that is roughly the following: if x is exactly located at R1, y is exactly located at R2, and R2 is a proper subregion of R1, then, if x and y are mereologically related, y is a proper part of x. This makes what we shall label “nested multi-location” impossible. This is important insofar as Eagle’s definition of exact location makes nested multi-location impossible as well. We shall return to this in due course.
Location is not the only relation that can be used to characterize the relation between immanent universals and things that instantiate them. Two other non-locative relations that can do the job are dependence and grounding. We need not to take side here. Perhaps immanent universals are indeed best characterized using dependence rather than location. As we will point out in due course, we don’t want to rely too much on the case from universals. We are discussing this case mostly because it was one of the motivating examples in the literature on multi-location. Alternatively, we might want to make sense of the spatiotemporal profile of universals along the following lines. Immanent universals are somewhere and somewhen not in the sense that they are located at some regions of spacetime, but only in the sense that they are exemplified by something which, in turn, is located at regions of spacetime (Costa 2017).
Here is a relevant quote: “Suppose we begin by helping ourselves to a respectable posit of speculative metaphysics—immanent universals. Immanent universals, by contrast with Platonic universals, are as fully present in space and time as their bearers. Moreover, they are capable of being fully present in many places at the same time; if two spheres are red, then the single immanent universal redness is in each of the spheres (O'Leary Hawthorne and Cover 1998: 205, italics added).
Clearly, with the locution “the region of x”, we simply mean the exact location of x.
We owe this suggestion to an anonymous referee for this journal. The following discussion is indebted to his or her remarks.
Note that this reply is different from the ones we sketched in footnote 12. The thought here is that universals still enter into some sort of locative relation, albeit with no region.
Thanks to Antony Eagle here.
See footnote 11.
It is worth noting that Eagle is upfront in Eagle (2016a) that he is really interested in the persistence of simples. He writes: “the present conception of endurance is perhaps best suited to capture the persistence of simple objects that cannot gain or lose parts, like fundamental particles, rather than complex objects” (Eagle 2016a: 513). In a footnote to that passage Eagle mentions Fine's idea that complexes might be variably embodied by collections of simples-at-times rather than time-relativised mereological fusions. We note two things: first, this amounts to abandoning the idea that apparent change of parts is to be understood in standard mereological terms. And this is a fairly radical revision to orthodox endurantism. Second, we are about to argue that Eagle’s theory of location cannot accommodate extended simples. Putting all this together—as we note later on—this amounts to the claim that Eagle’s theory of location only applies to point-sized simple material objects. Thanks to an anonymous referee here.
We are well aware that this is physically unrealistic. Also, it will entail that Tibbles has uncountable many parts. Bear with us.
As we pointed out already in footnote 10 the argument would need a little tweak in a unitist, spatio-temporal setting, but it would still go through. The reader can check for herself.
This is where a fully-fledged unitist framework enters crucially into the picture. It is widely agreed that relativistic physics favors unitism. For an introductory review of different arguments see Gilmore et al. (2016).
Thanks to Antony Eagle here.
We should also note that there no Additivity principle for location is needed to run the argument.
We want to point out that, as duly noted by a reviewer of this journal, we are not using the term “extended simple” in the way in which McDaniel used it in his (2007) or Eagle uses it in his (2019), but rather in the sense defined in the main text, which is also the sense to be found, for example, in Scala (2002), Simons (2004), Pickup (2016) and Gilmore (2018). This sense is closer to what McDaniel (2007) calls a “spanner”. Eagle (2019) distinguishes between f-extended simples and l-extended simples. The former notion is defined in terms of containment alone, whereas the latter notion is defined in terms of what we called entire location in footnote 4. Eagle (2019: 170) claims that l-extended simples can be used to approximate—Eagle’s own words—spanners. It is worth exploring whether the argument could be strengthened, to the point that any theory of location that defines exact location in terms of weak location cannot handle spanners. In general, we think this is not the case. Parsons defines exact location in terms of weak location in his (2007). Yet, it can be shown that every persisting entity counts as a spanner in his system. Parsons’s system, as we pointed out already, entails Functionality. So, the question becomes whether any theory of location that defines exact location in terms of weak location and allows for multi-location makes spanners impossible. The reviewer suggests that this might be the case for, arguably, any theory of location that allows for multilocation and defines exact location in terms of weak location will entail the following principle P: if x is exactly located at R, then x is not contained in any proper subregion of R—the reader can check that, in effect, P does not follow from Parsons’s definition of exact location. Once again, we think that this is not the case. A counterexample is Exact Location 1 in the text. This is because according to Exact Location 1, nothing prevents an object x to be exactly multi-located at two distinct regions R1 and R2, and at their union. Thus, an object could be exactly located at a region and be contained in one of its proper subregions. To be fair, Exact Location 1 makes spanners impossible for the very same reason Exact Location 2 does—the argument being exactly the one in the main text. So, the conjecture, independently of the fate of P, still stands: any theory of location that defines exact location in terms of weak location and allows for multi-location makes spanners impossible. Eagle (2019: 170) contains an interesting argument in this respect. Yet, the argument falls short of securing the aforementioned conjecture, for it crucially relies on the definition of spanners in terms of entire location. As a matter of fact, Eagle claims that if spanners are defined in terms of our notion of exact location—Eagle’s perfect location—the argument does not go through. Thanks to an anonymous referee here.
As a matter of fact, we think that this is but one (overtly simplistic) characterization of extended simples. There are other characterizations that are not extensionally equivalent. See Goodsell et al. (Forthcoming). That being said, even those different characterizations will spell out trouble for Exact Location 2. Thus, we will just stick to the orthodox definition here. We should also note that this definition works only within the orthodox understanding of space, according to which space is “constructed out” of simple, unextended spatial points endowed with the so-called real topology.
Clearly, “having a particular mereological structure” is not among the geometrical properties that Circle and R-Circle share.
This conclusion should be intended as restricted to the notion of extended simple as it is defined in the paper. McDaniel (2007) distinguishes two notions of extended simples, namely multilocaters and spanners. Multilocaters are extended simples insofar as they are simple entities that fill an extended region R of space by being multilocated throughout R. Given Eagle’s theory of location, multilocaters are clearly not impossible. Only spanners are. As we pointed out in footnote 25 it is an interesting conjecture whether any theory of location that defines exact location in terms of weak location and allows for multilocation renders spanners impossible. Thanks to an anonymous referee here.
It should be clear that taking parthood as three-place would be of no help to undermine the Circle 2 argument.
See e.g. Simons (2004) and Braddon-Mitchell and Miller (2006). At this point, one might try to resist the argument simply by claiming that Eagle does not accept the definition of extended simples given above. This reply, we contend, is less than satisfactory. First of all, the notion is clearly definable in Eagle’s terms. The question is whether any such thing is possible. Eagle is committed to the impossibility of such things. And yet, one has reasons to take extended simples (as we defined them) seriously. Electrons might be taken to be good examples. They are extended, and the best physical theory that describes their behavior, quantum mechanics, is usually taken to entail that, at least in some cases, they have exact locations. Does this undermine our previous argument against Exactness, given that we cited Quantum Mechanics as providing counterexamples to it? Not really. Orthodox Quantum Mechanics predicts that sometimes quantum systems do not have exact locations. That does not mean that they never have one. For example, after a measurement of position is made, quantum systems do have an exact location. If the quantum system in question is an electron, it will qualify as an extended simple given the definition we used in the paper (Gilmore 2018). This seems enough to lay claim that extended simples as we defined them are indeed possible, contra Eagle’s theory of location.
Or even, they can try to define weak location in terms of exact location in such a way that Exactness does not follow. We are not aware of any such attempt in the literature.
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Acknowledgements
We would like to thank Antony Eagle, Matt Leonard, Jonathan Payton and audiences in Geneva and at the 2019 annual meeting of the Society for the Metaphysics of Science in Toronto for insightful comments on previous drafts of this paper. We would also like to thank two anonymous referees for their suggestions. Claudio Calosi acknowledges the generous support of the SNF foundation, project number PCEFP1_181088.
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Costa, D., Calosi, C. The Multi-location Trilemma. Erkenn 87, 1063–1079 (2022). https://doi.org/10.1007/s10670-020-00230-7
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DOI: https://doi.org/10.1007/s10670-020-00230-7