Occupy Wall: A Mereological Puzzle and the Burdens of Endurantism

Abstract

Endurantists have recently faced a mereological puzzle in various forms. Here I argue that, instead of presenting a genuine worry, the puzzle actually reveals a common misunderstanding about the endurantist ontology. Furthermore, through this discussion of the alleged problem and the misunderstanding which motivates it, I reveal metaphysical commitments the endurantist has that may not be widely recognized. For instance, she is committed to interesting and perhaps controversial views about shape and location. I highlight these commitments and what they mean for the endurantist.

Keywords:

• Endurantism
• Multi-location
• Mereology
• Time Travel
• Shape

Notes

¹ We can press the point further: suppose we say Brick is a spatially extended simple. At least in so far as Wall is visually indistinguishable from an ordinary brick wall, and ordinary brick walls are certainly composite objects, Wall plainly looks like a composite object. And if Wall is a composite object, that would seem to be an important difference between Brick and Wall. (McDaniel [2007], as well as Braddon-Mitchell and Miller [2006], defends the possibility of extended simples.) But we needn't rely on extended simples. Say, instead, that Brick is a quark, classical atom, or whatever you consider to be the smallest fundamental material object. So conceived, we can recreate a structurally similar case and note similar differences (this case would, then, mirror the structure of Gilmore's [2007] ‘Tubman’ case).

² Where a proper part is a part not identical to the whole [Lewis 1991: 2].

³ Not only that, but since F(Brick) looks like an object with parts at all the sub-regions of R—e.g. Brick_-at-1 and Brick_-at-2—some might think F(Brick) looks like a temporally composite object, i.e. an object with temporal parts. (That said, it's important not to conflate claims about temporal extent with claims about temporal parthood. Barker and Dowe aim at showing that the endurantist is committed to contradictory claims about the temporal extent of a persisting object. I’ll say more about their discussion of temporal extent later.)

⁴ For Wall, P may be weighing one tonne, being wall-shaped, etc.; for F(Brick), P may be existing at a 4D region, having temporal parts, etc.

⁵ Eagle [2010a: 75, fn. 27] makes a similar diagnosis.

⁶ Eagle [2010a; 2010b] takes occupies to be a primitive notion here, where an object occupies any region in which it can be found. Although what Eagle calls occupation may not be the location relation endurantists often talk about; being in may be a more appropriate phrase for the notion used here.

⁷ In contrast, the perdurantist would say that a perduring object is located at a 4D region.

⁸ We needn't utilize Eagle's terminology as there are alternatives which can play the same role. For instance, see Gilmore [2007] or Balashov [2010] for other contemporary analyses of location relations that could be employed here.

⁹ This aligns with the endurantist reply to the problem of temporary intrinsics [Lewis 1986: 202–5] developed by Lowe [1987a, 1987b] and defended by McCall and Lowe [2006, 2009]: they argue that changes in physical objects, e.g. making a fist with my hand, amounts to changing the relations of my hands’ parts; ‘These changing relations reduce ultimately to configural changes of the bodies’ fundamental particles, the latter being internally unchanging in that they retain their own intrinsic properties throughout’ [2009: 279].

¹⁰ See Handfield [2008: 301–3; cf. Cameron 2009] for further discussion of the nature of weight.

¹¹ So, contra Effingham and Robson [2007], it isn't the case that the endurantist must abandon the weak supplementation principle. Since the endurantist denies that F(Brick) and Wall are part of her ontology as distinct objects, the weak supplementation principle isn't violated. And so we needn't follow Smith [2009] and Effingham [2010] down the rabbit hole into a revised mereology. But, if we wanted to follow their lead for other reasons, the endurantist would have the same options available as those available to the perdurantist, at least for the weak supplementation principle.

¹² We could further motivate this by drawing parallels with set theory: Consider the set {1} and the set {1, 1}. It's definitional of set theory that, if we call {1} set A and call {1, 1} set B, A and B are just different ways to pick out the same numerical set. So anyone that thinks mereology is a physicalized version of set theory is well motivated for theoretical reasons to think the fusion of an object with itself can be nothing other than that object. This is all just to say that Brick and Wall are the same, just as A and B are the same. Furthermore, we can say that representing Brick as a wall is a misleading way to describe Brick at t_-1 in the same way that it's misleading to describe B as a set with multiple numbers. Put differently, even though we can describe Wall as {Brick, Brick, Brick, Brick} and Brick as {Brick}, these are no more distinct than A and B. (While 1 ≠ {1} and {1} ≠ {{1}}, mereology differs from set theory in this regard; fusions aren't typically thought to have this sort of hierarchical structure that sets do.)

¹³ Certainly the presentist endurantist can make sense of past and future locational facts in the same sort of way as she can make sense of other sorts of facts involving distant times, such that she can meaningfully speak of trajectories through spacetime and spacetime region relative parthoodness. But it's still the case that any spacetime region whose temporal co-ordinate is not in the privileged present is not part of her ontology. While such regions did or will exist, including whatever did or will exist at them, that which exists can only ever be that which exists right now. Enduring objects can never be multi-temporally located in a presentist world.

¹⁴ Keller and Nelson [2001; cf. Daniels 2012] defend the possibility of presentist time travel.

¹⁵ For the sake of completeness, it's worth noting that the perdurantist is also committed to a robust theory of location to avoid certain co-location challenges that arise from cases similar to those discussed here. While the perdurantist can meet those challenges, for her to do so requires the same sort of tools the endurantist employs here [Gilmore 2007, 2010; Eagle 2010a, 2010b]. The perdurantist may also be inclined to consider shape an extrinsic property.

¹⁶ I thank Toby Handfield, John Bigelow, Dana Goswick, Antony Eagle and the audience from the Metaphysics of Time Workshop at Monash University for feedback on earlier drafts and helpful discussions.