Abstract
Worries about parthood and location continue to stimulate the debate about persistence over time. It is now widely recognized that physical considerations are highly relevant to it. Recent work investigating the impact of relativity theory on the ontology of persistence has revealed many unexpected aspects of this impact. There now appears to be a broad consensus that no interesting view of persistence (endurance, perdurance, or exdurance) is decisively refuted by relativistic considerations. There is little consensus as to how and to what extent any such view is supported by them.
In this paper I review some recent developments focused on an especially intriguing aspect of relativistic persistence. My goal is not so much to adjudicate a mini-dispute in this area as to use it as a case study to draw some lessons for the broader metaphysical implications of the transition from the classical to the relativistic worldview. Some relativistic phenomena (e.g., relativity of simultaneity and time dilation) have no classical analogs and force us to revise the very fundamentals of common-sense ontology (e.g., reject presentism). Others – those that do most of the work in the arguments discussed in the paper – have more familiar classical limits and, as a result, less dramatic metaphysical consequences.
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Notes
- 1.
Noted in Sect. 2.4, note 22.
- 2.
Intuitively, a material object o can be said to be exactly located at a spacetime region R iff o and R have exactly the same shape, size, and position. Exact location can be taken as an unanalyzed and intuitively clear primitive (as is done, e.g., in Hudson (2001), Bittner and Donnelly (2004), Gilmore (2006), and Balashov (2008, 2010)) or as a defined notion (see, e.g., Parsons 2007 and Gilmore 2008). The choice affects other commitments. Below we abstract from this issue and adopt the first approach.
- 3.
Roughly, o is wholly located at R iff no part of o is missing from R; while o is solely located at R iff no region disjoint from R contains any part of o. An enduring object is (typically) wholly and exactly located at multiple regions of spacetime without being solely located at any of them.
- 4.
For now; we will need to make the notion of path more precise later.
- 5.
As noted above, these formulations are opinionated and gloss over some controversial issues. First, there are exotic counterexamples, e.g., objects enduring according to (3), but having temporal parts according to (4). Similarly, an object might be a temporally extended simple that has no temporal parts. Some authors take exotica of this sort seriously enough to motivate a more fine-grained classification of different ontologies of persistence distinguishing locational endurance and perdurance (where the disagreement boils down to the issue of whether or not objects are temporally extended) from their mereological counterparts (where the disagreement is about possession of temporal parts). See, in particular, Gilmore (2006, 2008), where these distinctions are developed in detail and amply illustrated. We will abstract from the exotic cases below and focus on natural combinations of locational and mereological views.
- 6.
- 7.
Expressed in a given inertial reference frame as \(I = c^{2}\varDelta t^{2} -\varDelta \mathbf{r}^{2}\)
- 8.
The sense in which Minkowski spacetime is partially ordered is the sense in which its points can be ordered by the relation \(R^{+}(q,p) \equiv c^{2}[t(q) - t(p)]^{2} - [\mathbf{r}(q) -\mathbf{r}(p)]^{2} \geq 0 \wedge t(q) - t(p) \geq 0\), which is reflexive, antisymmetric and transitive.
- 9.
- 10.
- 11.
Important refinements will be made in Sect. 2.4.
- 12.
That is, includes at least two timelike separated points.
- 13.
The essential details of the scenario come from Sartori (1996, 185–190), where it is used to illustrate one of the lesser-known ‘paradoxes’ of special relativity, first introduced by Rindler in (1961). My exposition of the case comes from Balashov (2010, 198–200). Thanks to Oxford University Press for permission to use this material.
- 14.
- 15.
See, e.g., Sartori (1996, 184–185).
- 16.
I make no attempt to depict it.
- 17.
Or perhaps a sum. This depends on whether regions are taken to be set-theoretical or mereological notions. We adopt the first strategy, primarily for convenience, not as a matter of principle.
- 18.
For another illustration of the same point, see Gilmore (2006, 210–211)
- 19.
Strictly speaking, o’s path is not a continuous hyper-rectangle but a densely packed ‘multifilament region’. We ignore this complication here.
- 20.
Or so we assume; alternatively, it could be a one-dimensional line or a two-dimensional surface, with the same effect.
- 21.
Amply illustrated in Fig. 2.8 and other figures in this paper.
- 22.
See Gilmore (2006). Gilmore himself takes the case to demonstrate, first and foremost, the need to allow enduring objects to be located, not just at flat time-slices, but at arbitrary maximal spacelike slices of their paths in relativistic spacetime, including curved such slices, a move raising further objections developed by Gibson and Pooley; see Gibson and Pooley (2006, 186). I argue against admitting curved slices as legitimate locations of persisting objects in Minkowski spacetime on independent grounds in Balashov (2008, Section 5; 2010, Section 5.2).
- 23.
Sattig’s neo-Aristotelian ontology, systematically developed in (forthcoming) and a number of earlier papers, regards ordinary objects as ‘double-layered compounds of matter and form.’ The centerpiece of his theory is the thesis that the material and the formal ‘layers’ of ordinary objects ground two different perspectives on them, which generate divergent truth conditions of various claims about objects. Both perspectives – the material (or sortal-abstract) and the formal (or sortal-sensitive) – are equally important, and both are found in ordinary discourse. Some of our thinking about ordinary objects tracks their underlying matter (e.g., when we reflect that two distinct objects cannot occupy the same region of space, or spacetime), while other intuitions track sortal-sensitive ‘careers’ of objects, whose various stages may include materially distinct subjects (e.g., when we re-identify a certain cat composed of a particular mass of matter today with a certain cat composed of a numerically different mass of matter tomorrow). Sattig argues – systematically, rigorously, and persuasively – that the availability of these two perspectives holds key to resolving various problems, including the problem of corner slices/point-shaped chairs (if the latter is a problem). For details, see Sattig (2012; forthcoming, Chapter 8).
- 24.
- 25.
For simplicity, Fig. 2.10 does not represent the first episode of the original scenario, when the initially scattered particles come to compose o in the first place. But similar considerations apply, mutatis mutandis, to such ‘coming into existence’ episodes as well.
- 26.
Cf. Gibson and Pooley (2006, 186–187), who develop a very similar suggestion.
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Acknowledgements
I am very grateful to Cody Gilmore and Thomas Sattig for their comments on the draft of this paper.
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Balashov, Y. (2014). Relativistic Parts and Places: A Note on Corner Slices and Shrinking Chairs. 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_2
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