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Mereological Destruction and Relativized Parthood: A Reply to Costa and Calosi

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Abstract

Metaphysicians of various stripes claim that a single object can have more than one exact location in space or time – e.g. endurantists claim that an object persists by being ‘all there’ at different moments in time. Antony Eagle has developed a formal theory of location which is prima facie consistent with multi-location, but Damiano Costa and Claudio Calosi argue that the theory is unattractive to multi-location theorists on other grounds. I examine their charge that Eagle’s theory won’t allow an endurantist to account for certain cases of mereological change. I argue that the charge sticks, but not for the reasons Costa and Calosi think. Along the way, I explore an issue which is underexplored in their paper, namely, how an endurantist might modify Eagle’s theory to incorporate a parthood relation which obtains, not absolutely, but only relative to times.

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Notes

  1. Parsons (2007: 222–223; 228–229). Parsons also develops a theory similar to one found in Casati and Varzi (1999), in which the claim about exact location is an axiom.

  2. See, e.g., Simons (1987: ch.5) and Thomson (1983: 213–218).

  3. Or a four-place relation between two objects and two regions; see note 17.

  4. Here, I leave ‘ ≤ ’ in place as a term for the two-place subregionhood relation. Even if we allow that mereological relations between objects are relative to regions, we needn’t allow that the analogous relations between regions are relative in the same way.

  5. Parsons (2007: 203) explicitly equates existing at a region with being located at that region. See also Donnelly (2011) and Gilmore (2006). Compare Costa (2017), Fine (2006), and Simons (2000: 422–425).

  6. She needn’t choose only one; each principle is consistent with the others. Nor is she limited to these conditions; I’m only concerned with conditions which can help solve the problem of mereological destruction.

  7. They might mean to suggest that it’s the exact location of the whole which matters: y is an r-part of x only if x is exactly located at r. But while the endurantist may accept this as an additional condition on r-parthood – see Sect. 7 – it won’t help her solve the problem of mereological destruction on its own, since she thinks that Tibbles is exactly located at t2.

  8. E.g., we may rely on Gilmore’s (2006: 200) characterization: x is exactly located at r just in case x has (or has-at-r) the exact shape and size as r, and for any y, x stands (or stands-at-r) in all the same spatial or spatiotemporal relations to y as r does.

  9. According to the Filling Condition, y is an r-part of x only if y occupies every subregion of r. Since subregionhood is reflexive, (1) follows as above.

  10. Compare Thomson (1983: 216). This raises another issue for the endurantist. Given Containment, containment implies occupation, as it should, by the reflexivity of (unrelativized) parthood. If we switch to Containment 2, we don’t get this result, since r-parthood isn’t reflexive.

  11. Thomson (1983: 216) claims that x is part of itself relative to any time at which it exists. Generalizing to regions: x is part of itself relative to any region at which it exists. We can give a variant of the argument using this reflexivity axiom. If parthood is relativized to regions, then being an r-part of x requires existing at r. Thus, if y is an r-part of x, then y exists at r, and so (by Thomson’s reflexivity axiom) y is an r-part of itself. By (2), it follows that if y is an r-part of x then y occupies some subregion of r.

  12. The arguments from the Occupation, Filling, and Exact Location conditions proceed as in the previous section. The argument from the Containment Condition relied on Containment 2, but a variant uses Containment 3.

    According to the Containment Condition, any r-part of x is contained in r. By Containment 3, if y is an r-part of x, then y itself has at least one r-part, and each of its r-parts occupies a subregion of r:


    y ≤ r x ⊃ (∃z(z ≤ r y) & ∀v(v ≤ r y ⊃ ∃s(s ≤ r & Occ(v,s)))).

    By Reflexivity, if y is an r-part of x, then y is an r-part of itself. So, if y is an r-part of x, then y occupies some subregion of r. That’s just (1), which is the second conjunct of Containment 3.

  13. Eagle (2019: 176) notes that something like Weak Containment follows even from Containment 2. My discussion shows that the problems for Containment 2 are even worse than this, and that the natural way of avoiding those problems still gives rise to Weak Containment.

  14. See, e.g., Johnston (1987: 125–129) and van Inwagen (1990: 249–250).

  15. McDaniel (2014: 20) makes a similar argument.

  16. McDaniel (2014: 20) makes this point, but doesn’t use it (as I’m about to) to raise trouble for any theory of relativized-parthood + multiple-location.

  17. Gilmore (2009: 101–109) considers a view like this and rejects it on the ground that there’s no ‘simple and straightforward’ transitivity principle for r-parthood so understood. (The simplest principle, ‘If x is an r-part of y, and y is an s-part of z, then x is an s-part of z’, fails if objects can be multiply located in time and survive mereological destruction. Tail is a t1-part of Tibbles’ back half, and Tibbles’ back half is a t2-part of Tibbles, but Tail is not a t2-part of Tibbles.) Gilmore (2009: 113–131) develops an alternative on which parthood is four-place, relativized to both the exact location of the part and the exact location of the whole, rather than to their sum. Kleinschmidt (2011: 257–261) argues that this alternative still has problems with transitivity.

  18. Sum Condition 2 implies that y is an r-part of x only if y is exactly located at a subregion of r. It follows that y is an r-part of x only if y occupies a subregion of r. That’s just (1), which is the second conjunct of Containment 3. Hence, Weak Containment.

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Acknowledgments

This discussion piece began as a commentary on Damiano Costa and Claudio Calosi’s “The multi-location trilemma”, given at the 2019 meeting of the Society for the Metaphysics of Science in Toronto, Canada. Thanks to the audience at that meeting, to Damiano and Claudio for discussion, and to Tuomas E. Tahko for the invitation to give comments. Thanks also to two anonymous referees for this journal for their very helpful feedback. Research was partially funded by a Postdoctoral Fellowship from the Social Sciences and Humanities Research Council of Canada.

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  1. Department of Philosophy, Bilkent University, Ankara, Turkey

    Jonathan D. Payton

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Payton, J.D. Mereological Destruction and Relativized Parthood: A Reply to Costa and Calosi. Erkenn 88, 1797–1806 (2023). https://doi.org/10.1007/s10670-021-00423-8

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