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Somewhere Together: Location, Parsimony and Multilocation

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Abstract

Most of the theories of location on the market appear to be ideologically parsimonious at least in the sense that they take as primitive just one locative notion and define all the other locative notions in terms of it. Recently, however, the possibility of some exotic metaphysical scenarios involving gunky mixtures and extended simple regions of space has been argued to pose a significant threat to parsimonious theories of locations. The aim of this paper is to show that a theory taking as primitive a notion of plural pervasive location and allowing for irreducibly plural locative facts can account for all the putatively problematic scenarios for parsimonious theories of location. Furthermore, I will also argue that the notion of plural pervasive location is compatible with the possibility of multilocation.

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Notes

  1. See, among others, Casati and Varzi (1999), Parsons (2007), Gilmore (2018) and Kleinschmidt (2014). As Kleinschmidt (2016: 188, fn 5) notices, possible exceptions to this claim are represented by the theories defended by Fine (2006) and Simons (2014), who posit different relations for objects located in space and those located in time.

  2. Parsons (2007: 204-205).

  3. In addition, the notion of entire location can be defined in S@ and S@O, respectively, as follows:

    (ENT-@) x is entirely located at r =df x is exactly located at a subregion of r

    $$x{@_<}r{=}_{df}\exists s\left(x{@}s \wedge s\le r \right)$$

    (ENT-@O) x is entirely located at r =df x is weakly located at r and all the regions at which x is weakly located overlap r

    x@_< r=_df x@_o r∧∀s(x@_o s→r∘s).

  4. See also Loss (2019: 252; 257).

  5. For some recent discussion on extended simple regions and the possibility of Kleinschmidt’s problematic cases see Goodsell, Duncan and Miller (2019: 8–10) and Eagle (2019: 166–167).

  6. Hudson (2005) may have been the first one to consider the possibility of a fundamental locative location that is plural in one of its places (many thanks to an anonymous referee for this Journal). In fact, Hudson (2005) assumes that regions may be identified with pluralities of points, which appears to entail that facts concerning single objects being located at single regions may be construed as facts concerning single objects being located at pluralities of points, taken together: ‘When being ontologically serious about regions, I prefer that they be identified either with pluralities of or with mereological fusions of concrete, unextended, simple points.’ (Hudson 2005: 17).

  7. Following Loss (2019), I take an entity x to be a fusion of the yy just in case (i) each of the yy is part of x and (ii) every part of x overlaps some of the yy.

  8. On multigrade predicates see Oliver and Smiley (2004).

  9. The choice of taking the two-place predicate ‘@>’ to be multigrade in its first place entails that, for every x and yy such that x is the only entity among the yy (so that the yy are an ‘improper’ plurality of entities), the fact that x@> r and the fact that yy@> r are the same fact. Alternatively, one could take @> to be strictly many-one. In that case the only way to express what I call here ‘singular’ pervasive location would be that of employing a plural term standing for an improper plurality of entities. Here I choose the first option mainly for simplicity’s sake.

  10. I am assuming in this paper a classical mereology of regions of space, which guarantees the existence of the fusion of all the regions of space (for some discussion on the possibility of ‘junky’ or ‘knuggy’ space see Parsons 2007: 209-210)

  11. In addition, the notion of entire location can be defined as follows:

    (ENT- xx@>S) x is entirely located at r =df x is maximally omnipresent at a subregion of r

    $$x{@_<}r{=}_{df}\exists s\left(xMs \wedge s\le r \right)$$
  12. Parsons (2007: 205).

  13. Many thanks to an anonymous referee for this Journal for suggesting me to follow Casati and Varzi’s (1999) approach and to (somehow) define the notion of region in locative terms.

  14. Casati and Varzi (1999: 121) call a similar principle (formulated by means of the notion of exact location) ‘Conditional Reflexivity’

  15. Proof. Suppose x is a region. By (17) x fills itself. Suppose that x fills a region s and that x is part of s. From axiom 5 we have that, since x fills s and x is a region, then s is part of x. By the anti-symmetry of parthood (a theorem of classical mereology; see footnote 9), it follows that x is identical to s. We have thus (i) x fills x and (ii) for every region s, if x fills s and x is a part of s, then x identical to s. It follows from the definition of exact location given in (11) that x is exactly located at x.

  16. Proof. Suppose that x is a region that is exactly located at a region y. From (17) we have that x fills itself. From the definition of exact location given in (11) we have that x fills y. By axiom 5, y is part of x. However, since x is exactly located at y it also follows from (11) that every region s that x fills and that has y as part is identical to y. Therefore, x is identical to y.

  17. Since xx@>S allows for irreducibly plural locative facts, the following principle (banning irreducibly plural locative facts when the entities that are located at regions are themselves regions) also appears to be highly plausible:

    Axiom 7 If the rr collectively fill s, then some regions tt are such that the rr are all pervasively in the tt, pervasively cover the tt and s is the fusion of the tt

    $$rr{@_>}s\rightarrow {\exists}tt \left(rrIN_{>}tt \wedge rrCOV_{>}tt \wedge s = f(tt) \right)$$

    Notice that axiom 7 is just the converse of axiom 1 restricted to regions.

  18. See footnote 11.

  19. Notice that xx@>S already allows for what may be seen as a ‘weak’ form of multilocation. Consider, in fact, the following principle, which can be labelled ‘Strong Functionality’:

    Strong Functionality If an object x is exactly located at a region r, then every region s at which x is weakly located overlaps r

    $$x{@}r\rightarrow \forall s\left(x{@}_{o}s\rightarrow s\circ r \right)$$

    Imagine that someone, mixing a gunky Spritz, spills a drop of water, so that the drop of water ends up filling by itself a region r disjoint from the region of space enclosed by the gunky glass containing the gunky Spritz. In that case, r is the biggest region of space that is filled by the water alone. In fact, all the other regions of space that are (partially) filled by the water are subregions of the region inside the gunky glass, but the water doesn’t manage to fill any subregion of that region by itself. It follows, thus, that according to xx@>S, the water is exactly located at r, even if it is also weakly located at a region that is disjoint from r (that is, inside the gunky glass). However, this kind of multilocation appears to be indeed too weak to be used for the common uses of multilocation, like the locative interpretation of endurantism (see, among others: Sattig 2006; Eagle 2016; Gilmore 2018; Leonard 2018).

  20. The notion of singular derivative filling can be defined as in Derivative Filling. Notice that, assuming axiom 3 (expressed by means of the notion of basic singular filling), this notion of derivative filling is additive in the sense of Additive Filling. Proof. Suppose that r is the fusion of the ss and that x derivatively fills each of the ss. From the definition of derivative filling it follows that each of the ss is part of a fusion of exact locations of x. Let tt be the plurality of exact locations of x that overlap some of the ss. It follows from classical mereology that r is part of the fusion of the tt. Axiom 3 entails that that if x basically fills r, then it also basically fills every subregion of r. Each of the ss is a part of r that is only derivatively filled by x. Therefore, x doesn’t basically fill r. We have, thus, from the definition of derivative filling that x derivatively fills r.

  21. Recall that the notion of plural basic filling is more general than the notion of singular basic filling because it subsumes cases of singular basic filling as cases in which the plurality of entities in question is an improper plurality, that is, a plurality of entities identical to just one entity (like the ‘plurality’ of things that are identical to x). See, also, footnote 8.

  22. See footnote 9.

  23. Many thanks to two anonymous referees for this Journal.

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Loss, R. Somewhere Together: Location, Parsimony and Multilocation. Erkenn 88, 675–691 (2023). https://doi.org/10.1007/s10670-021-00376-y

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