Abstract
Under the eternalist hypothesis that objects or events exist temporally, but independently of being present two different views of persistence are on the market: Persisting objects endure if they are multiply located in (space-)time, and persisting objects perdure if they are singly located by having numerically different temporal parts. In the framework of the special theory of relativity (SR), the metaphysics of persistence is confronted with peculiar difficulties. Things persist by being “wholly present” at more than one time; but what are times within a temporally non-separated spacetime? Things persist by having different temporal parts at different times; but what are the temporal parts of a four-dimensional object in Minkowski spacetime? Recently, several authors have argued that SR favours perdurantism over its endurantist rival. In this paper, I intend to show that the purported arguments are only those against endurantism. The first simply fails, but the second, more convincing one, is such that with a similar strategy we should argue against perdurantism as well: Enduring and perduring entities are hence both in conflict with SR which undermines the eternalist hypothesis.
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- 1.
The spatial analogy is taken to mean treating spacetime like space, i.e., as a timeless entity.
- 2.
In fact, Putnam has shown, if the argument were valid, that with respect to a given spacetime point p all events located at some p′ or other are realized: The realization-relation R – “pRe”: e is realized with respect to p – is universal. But that means that existence with respect to p is coextensive with “existence simpliciter”, which contradicts the classical eternalist view according to which “existence simpliciter” is temporally restrictable by “existence-at-t”.
- 3.
The crucial point of this theory is that tensed sentences like “it is raining now” are indispensible and untranslatable in tenseless ones. So, there are inevitable sentences that vary in truth-value, not depending on a transitory present, as the A-theorists would have it, but from B-time to B-time. From that follows, in contrast to Putnam, that “existence simpliciter” is temporally restrictable in the following sense: Although it does not vary with time what exists simpliciter, in fact it varies with t what exists at t. So, Tooley, for example, is wrong, defending his “dynamic” view of temporal existence, when he describes the eternalist view (similarly to Putnam): “All temporal states of affairs are actual as of all times” (Tooley 1997, 41; see the reply by Mellor 1998, 81).
- 4.
At least in the sense that a perduring entity “fills up” time by having parts, like a spatially extended object “fills up” space by having parts. But note that, also according to the eternalist view, the perduring entity has its temporal parts successively – namely ordered by the earlier-later relation. For temporal succession within a B-theory of time, see Williams (1996).
- 5.
“Pre-existing” is, of course, not conceived of as temporal precedence. But, what else could it mean?
- 6.
But note: This time, “simpliciter” cannot disjunctively analyzed, as the eternalist would have it, in the sense of, to be or to have something “at some time or other”. For an instantaneous temporal part cannot exist (and cannot have some properties) at a time, since, in principle, it cannot be or have something at another time. Only the perduring whole exists at times and has properties at times – namely derivatively by means of its temporal parts.
- 7.
In other words: A perduring entity exists, according to the neutral sense of persistence (see Lewis 1986, 220), at more than one time, so, within the relativistic context, at more than one moment of proper time (if available) or at more than one moment of frame-times. Of course, it exists so derivatively, by means of its temporal parts (see Merricks 1994, 167: “A perduring object […] exists at different times derivatively […]. An enduring object, by contrast, directly and nonderivatively exists at different times”). But according to Balashov, Miller and Gibson/Pooley the perduring whole exists over and above as a four-dimensional whole – analogous to three-dimensional wholes existing in space.
- 8.
- 9.
These are maximal spacelike subregions of a 4D path (worldtube).
- 10.
The distinction between “timelike” and “spacelike” holds also in Putnam’s block-universe that is nevertheless a timeless world in the sense that existence and parthood are non-relative to times. The elements of a sequence of timelike related entities are ordered by a transitive, anti-symmetric and irreflexive relation. But that could be a non-temporal C-series in McTaggart’s sense, the relation not conceived of as the temporal earlier-later relation. It is thus not obvious that “being timelike related” means “being temporally related”.
- 11.
Or by being “wholly present” at each frame-time, or by having temporal parts at those frame-times.
- 12.
According to Balashov (2008) those regions are “merely matter-filled” but not exactly occupied by an enduring object – and not occupied by a temporal part of a perduring one, as I want to add.
- 13.
“Presumably I am currently in condition A at least in part because I was in condition B yesterday: In other words, my being in condition B yesterday is a cause of my being in condition A today” (Gilmore 2006, 215).
- 14.
“Exact occupation” of a spacetime region is Gilmore’s formally more precise notion analogous to “being wholly present”.
- 15.
But see the reply in Gibson/Pooley (2006, sec. 5), according to which it is sufficient for the causal relation to hold only partially.
- 16.
As it is said before, perdurantism is not the “doctrine of arbitrary spatiotemporal parts” (Gibson/Pooley 2006, 162). From that “starting point” the subsequent restriction to “instantaneous” parts, subregions with “no temporal extent”, seems to be unmotivated, since the temporal character of persistence is already lost. But, to repeat, eternalism, i.e., the new B-theory is pretended to be a theory about real time and not about a timeless block-universe.
- 17.
Of course, in a certain sense, trivially, everything within the boundaries of a spatiotemporal thing is itself spatiotemporal. But that is not the point: Within the four-dimensional whole some subregions are purely timelike, some are purely spacelike, some flat, some curved, and so on. The perdurantist has to say which parts could be the relativistic analogues of the classical “temporal” parts.
References
Balashov, Yuri. 2000a. Persistence and space-time: Philosophical lessons of the Pole and Barn. The Monist 83: 321–340.
Balashov, Yuri. 2000b. Enduring and perduring objects in Minkowski space-time. Philosophical Studies 99: 129–166.
Balashov, Yuri. 2005. Special relativity, coexistence and temporal parts: A reply to Gilmore. Philosophical Studies 124: 1–40.
Balashov, Yuri. 2008. Persistence and multilocation in spacetime. In The ontology of spacetime II, ed. D. Dieks, 59–81. Amsterdam: Elsevier.
Gibson, Ian, and Oliver Pooley. 2006. Relativistic persistence. In Philosophical Perspectives, Vol. 20, Metaphysics, ed. J. Hawthorne, 157–198, Malden, MA: Blackwell.
Gilmore, Cody S. 2002. Balashov on special relativity, coexistence, and temporal parts. Philosophical Studies 109: 241–263.
Gilmore, Cody S. 2006. Where in the relativistic world are we? In Philosophical Perspectives, Vol. 20, Metaphysics, ed. J. Hawthorne, 199–236, Malden, MA: Blackwell.
Lewis, David. 1976. Survival and identity. In Philosophical papers I, ed. D. Lewis, 55–77. Oxford: OUP (1983).
Lewis, David. 1986. On the plurality of worlds. Oxford: Blackwell.
Mellor, Hugh D. 1998. Real time II. London: Routledge.
Merricks, Trenton. 1994. Endurance and indiscernibility. The Journal of Philosophy 91(4): 165–184.
Miller, Kristie. 2004. Enduring special relativity. Southern Journal of Philosophy 42(3): 349–370.
Putnam, Hilary. 1967. Time and physical geometry. The Journal of Philosophy 64: 240–247.
Sider, Theodore. 2001. Four-dimensionalism. An ontology of persistence and time. Oxford: Clarendon Press.
Tooley, Michael. 1997. Time, tense, and causation. Oxford: Clarendon Press.
Williams, Clifford. 1996. The metaphysics of A- and B-time. The Philosophical Quarterly 46(184): 371–381.
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Friebe, C. (2012). Persistence in Minkowski Space-Time. In: de Regt, H., Hartmann, S., Okasha, S. (eds) EPSA Philosophy of Science: Amsterdam 2009. The European Philosophy of Science Association Proceedings, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2404-4_7
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