Abstract
Endurantism, the view that material objects are wholly present at each moment of their careers, is under threat from supersubstantivalism, the view that material objects are identical to spacetime regions. I discuss three compromise positions. They are alike in that they all take material objects to be composed of spacetime points or regions without being identical to any such point or region. They differ in whether they permit multilocation and in whether they postulate mereologically coincident entities.
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1.
If one embraces coinciding entities and rejects Strong Supplementation, one can say that material objects lack temporal parts even though they coincide with temporally extended regions that have temporal parts. One can get this far while confining oneself to the perdurantist’s simple fundamental ideology – a two-place predicate for parthood simpliciter.
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2.
If one invokes a more exotic piece of fundamental ideology (a more-than-two-place predicate for a ‘location-relative’ parthood relation), and if one still embraces coinciding objects and rejects Strong Supplementation, then one can say that material objects both lack temporal parts, in the manner of ‘mereological endurantism’, and are multilocated in spacetime, in the manner of ‘locational endurantism’. However, nearly all B-theoretic endurantists already help themselves to a fundamental relativized parthood predicate, even in the context of dualist substantivalism.
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3.
If one is willing to eliminate complex spacetime regions (in favor of sets or pluralities of points) and treat the fundamental parthood predicate as being both location-relative and non-distributive, one can reject temporal parts, retain locational endurantism, and avoid coinciding entities.
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Notes
- 1.
The standard definition of ‘instantaneous temporal part’ runs as follows: ‘x is an instantaneous temporal part of y at t’ means ‘(i) t is an instant, (ii) x is a part of y at t, (iii) x overlaps-at-t every part-at-t of y, (iii) x is present at t, and (iv) x is not present at any other instant’. (This is based on Sider 2001, 59.) For other definitions, see Gibson and Pooley (2006, 163), Parsons (2007), and Balashov (2010, 73). The key point is that, in order for a thing y to count as a temporal part of a thing x, y must be a part of x and y must be spatially co-located with x at any moment at which y is present.
- 2.
A-theories of time all say that there is a time that is present in some absolute, not-merely-indexical sense. That is, they say that there is a ‘metaphysically privileged’ present time. The B-theory of time denies this. Presentism is an A-theory of time according to which there are no non-present entities (such as, presumably, pre-Socratic philosophers and Martian outposts). Eternalism is the view that the past, present, and future all exist equally. See Sider (2001) and Markosian (2010) for more on these views.
- 3.
See Haslanger (2003) for an overview of these issues.
- 4.
See Hawthorne and Sider (2006) for a sophisticated discussion of this issue.
- 5.
They can’t identify an object with its location in space, since objects often occupy different regions of space at different times, but no region of space occupies different regions at different times. And of course they can’t identify an object with its location in time – say, the interval that is the object’s total timespan. There are many reasons for this, but one of them is that, again, an object typically occupies different regions of space at different times, but no interval of time does this. Finally, they can’t identify a material object with a spacetime region, since they either reject spacetime regions altogether or treat them as set-theoretic constructs; and presumably material objects are not set-theoretic constructs. The shift from space and time to spacetime solves these problems. No region of space is in different places at different times, but there are regions of spacetime that are. And spacetime substantivalists are free to deny that spacetime regions are set-theoretic constructs.
- 6.
As I will understand it, supersubstantivalism is neutral as to which regions count as material objects. (Every region? Every ‘matter-filled’ region? Every maximal continuous matter-filled region?) And then there is the further question of what counts as being ‘matter-filled’. Presumably this will need to be spelled out in field-theoretic terms, but even so the answer is hardly straightforward. Again, supersubstantivalists are free to disagree amongst themselves on these questions. They are united only in claiming that all material objects are regions.
- 7.
Here are four such views. (i) Extended Simple Regions. Spacetime might be composed of spatially and temporally extended but mereologically simple ‘grains’. (See Braddon-Mitchell and Miller (2006) and Dainton (2010) for discussion of related views.) Such a grain might count as persisting (since it’s temporally extended), but it wouldn’t have any proper temporal parts, and so might not count as perduring. (ii) Spatially Gunky Spacetime. Spacetime might be ‘spatially gunky’ and altogether lacking in proper temporal parts: suppose that every spacetime region is complex, spatially extended, and of infinite temporal extent in both temporal directions, so that each region is eternal and composed of spatially smaller regions. These regions would count as persisting but not as perduring (and even opponents of extended simples can believe in them). (iii) Restricted Composition on Spacetime Points. Suppose that all spacetime regions are composed of spatially-and-temporally-unextended, mereologically simple spacetime points, and that some spacetime points compose something iff they are arranged ‘complete path of a living organism’-wise. Then, since no living organism has a spacetime point or another living organism as a proper temporal part (let’s assume), it’s plausible that no temporally extended region has any proper temporal parts. (The pluralities of simples that would compose the temporal parts of such regions, if they composed anything, do not in fact compose anything.) In that case there could be regions that persist but do not perdure. (iv) Mereologically Coinciding Regions Without Strong Supplementation. Suppose that all spacetime regions are composed of spatially-and-temporally-unextended simple spacetime points and that every plurality of points composes a region. But suppose further that there is at least one plurality of points, the ps, that compose two different regions, r1 and r2, such that: (a) r1 and r2 are both spatially and temporally extended, (b) r1 has a full distribution of proper temporal parts, and (c) r2 does not have any proper temporal parts. Thus the relationship between r1 and r2 is like the relationship between a statue and a lump that are composed of the same simples but that differ in that the head of the statue is a part of the statue but not of the lump. (Strong Supplementation – the principle that if x is not a part of y, then x has some part that fails to overlap y – is violated in such cases.) In such a case r2 would persist but not perdure. (Eagle (2010) floats a view that sanctions mereologically coincident spacetime regions but does not suggest that they might different with respect to having temporal parts.)
- 8.
Hawthorne (2006) and Schaffer both seem to think that the constitution version is friendlier to certain forms of endurantism than is the identity version, although neither goes into much detail on this point. Hawthorne focuses mostly on forms of endurantism (framed in terms of grounding or metaphysical dependence) that will not concern us here. Schaffer’s reason for taking the constitution-version to be endurance-friendly is not clear to me. He writes that ‘the constitution view …does not entail four-dimensionalism …. Presumably the constituted object could have different persistence conditions than its constituting matter [a spacetime region]’ (Schaffer, 2009, 137).
- 9.
Henceforth points (if there are any) count as regions.
- 10.
This view would fail if (i) some sets of regions had no fusion at all, in which case a form of restricted composition would be true or (ii) some set of regions had more than one spacetime region as a fusion, as discussed in note 7.
- 11.
To see this, note first that, given PCV together with our set-up, no region occupied by m is a part of any region occupied by Obama. But then, by Parts of Objects, we get the result that m is not a part of Obama. So the fundamental parthood relation expressed by ‘is a part of’ doesn’t hold between m and Obama. And according to Absolutism, this is the only fundamental parthood relation.
- 12.
Many have argued that the fundamental parthood relation for material objects is a three-place relation expressed by ‘x is a part of y at z’, with two slots for material objects and one slot for a time (Thomson, 1983; Van Inwagen, 1990; Koslicki, 2008) or a region of space or spacetime (Rea, 1998; Hudson, 2001; McDaniel, 2004; Donnelly, 2010). As far as I am aware, the only self-described B-theoretic endurantist who accepts Absolutism is Parsons (2000, 2007).
- 13.
Kleinschmidt (2011) independently proposes 4P and some of the same 4P-appropriate mereological principles to be given here. But she eventually rejects 4P.
- 14.
B-theoretic endurantists who are on record in opposition to mereological coincidence without identity include Van Inwagen (1990), Burke (1994), Olson (1997), Rea (1998, 2000), Hershenov (2005), McGrath (2007), and Koslicki (2008). The argument for locational endurantism given in Gilmore (2007) depends upon the impossibility of mereological coincidence without identity.
- 15.
See Linnebo (2012) on ‘is one of’ and plural quantification. My notation follows his.
- 16.
Similarly, the dominant-kinds view developed in a dualist-substantivalist context by Burke (1994) and Rea (2000) can be developed in monist-substantivalist context with an appropriate replacement for ‘R’ in (i). Likewise for virtually any uniqueness-friendly endurantist theory of persistence-and-composition. See Markosian (2008) for more on restricted composition.
- 17.
And if spacetime is composed of spatially extended simple ‘grains’, the existence of ‘spatially-grain-like’ material objects would be equally problematic for all three compromise positions, for parallel reasons.
- 18.
We will assume that (i) x and y mereologically coincide, (ii) z is simple, and (iii) z is a part of x; we will show that z is a part of y, too. By (i) and the definition of ‘mereologically coincide’, it follows that (v) x and y overlap exactly the same things. By the reflexivity of parthood, (vi) z is a part of itself. Together with (iii) and the definition of ‘overlaps’, this entails that (vii) x overlaps z. Together with (v), this entails that y overlaps z. So, by the definition of ‘overlap’, (viii) there is a thing, call it w, that is a part of z and a part of y. But by the definition of ‘simple’, the only part of z is z itself. So w=z, and hence z is a part of y.
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Gilmore, C. (2014). Building Enduring Objects Out of Spacetime. In: Calosi, C., Graziani, P. (eds) Mereology and the Sciences. Synthese Library, vol 371. Springer, Cham. https://doi.org/10.1007/978-3-319-05356-1_1
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