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Temporal Parts and Time Travel

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Abstract

This paper argues that, in light of certain scenarios involving time travel, Sider’s definition of ‘instantaneous temporal part’ cannot be accepted in conjunction with a semantic thesis that perdurantists often assume. I examine a rejoinder from Sider, as well as Thomson’s alternative definition of ‘instantaneous temporal part’, and show how neither helps. Given this, we should give up on the perdurantist semantic thesis. I end by recommending that, once we no longer accept such semantics, we should accept a new set of definitions, which are superior in certain respects to Sider’s original set.

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Notes

  1. Sider has an alternative definition, using temporally relativised mereological relations rather than the atemporal relations given in (1). This is Sider’s irenic effort to placate endurantists who don’t accept atemporal mereological notions. As the definitions are equivalent for the perdurantist, whichever version you use won’t make any difference. So, in the name of simplicity, I stick solely to the atemporal version.

  2. There is no contradiction in that for it is not as if he is standing and not standing. Whereas sitting usually implies that one does not stand, this is not so when a time machine is involved.

  3. Freak-Marty should, however, be a temporal part of Marty (see n5 below) for if Marty had not time travelled then Freak-Marty would have been a temporal part of Marty—albeit a non-instantaneous temporal part that existed at two different instants, that was composed of Past-Marty (existing at one instant) and Future-Marty (existing at another). So Freak-Marty would be composed of those two objects, and be a temporal part of Marty at the discontinuous interval that was composed of the two instants that Past- and Future-Marty existed at. I see no reason to change what is said in the time travel case, so Freak-Marty should still be a temporal part of Marty. So, when time travelling, Freak-Marty is a temporal part that exists for but an instant, but isn’t what has been called an ‘instantaneous temporal part’. That there’s a temporal part that exists for an instant and yet is not an ‘instantaneous temporal part’ is nothing more than a terminological faux pas. Given (2) we are interested in the temporal parts that account for perduring wholes falling under certain predicates. In non-time travel cases such things are instantaneous, hence the labelling of them as ‘instantaneous temporal parts’. But this second problem shows that not every temporal part that exists for an instant explains why perduring wholes fall under predicates like ‘_ is sitting’ etc. hence the faux pas. Perhaps a new term should be coined (‘interesting temporal part’; such that the predicates an object falls under at a given time depends upon its interesting temporal parts, and we then try and find a definition for ‘interesting temporal part’) but in keeping with the terms used in the literature on perdurantism, I retain ‘instantaneous temporal part’ even though it is somewhat misleading.

  4. Following Cameron [2008, p. 5]: P is true directly in virtue of Q being true = df (i) P is true in virtue of Q being true; (ii) there is no proposition R such that P is true in virtue of R and R is true in virtue of Q.

  5. I use ‘directly in virtue of’ instead of ‘in virtue of’ to fend off the second problem from Sect. 1.2. It is not just in virtue of an object’s instantaneous temporal part at time t that it is exactly located where it is at t, but also in virtue of any temporal part that has that instantaneous temporal part as a part. But it will only be directly in virtue of its instantaneous temporal part. As Freak-Marty is a temporal part of Marty (see n3 above), if we used ‘in virtue of’ instead of ‘directly in virtue of’ then Freak-Marty would count as an instantaneous temporal part of Marty. The revision to ‘directly in virtue of’ gets us (8), which avoids having to say that, and so allows us to still avoid the second problem.

  6. An anonymous referee pointed out that the first two conjuncts of (8) aren’t redundant if we consider a case where (a la Penelope Maddy (1990, pp. 58–60)) x’s singleton is exactly located where x is located. In that case, as the singleton’s location is presumably what it is directly in virtue of the location of its member, the perduring whole ends up being an instantaneous temporal part of the singleton. That’s about as wrong as could be. This would be avoided if we retained the two conjuncts from (8) which (9) drops (as the perdurer is not a part of the singleton, nor do they usually exist at but one instant). However, dropping the conjuncts isn’t integral to what follows, and is only effected to make the following exposition clearer. I don’t think anything hangs on this. If I’m wrong and something does hang on it, then an alternative would be to add a conjunct demanding that x and y must be in the same ontological categories (so events can only have events as instantaneous temporal parts; objects can only have objects as instantaneous temporal parts etc.). In doing so, we’d rule out this counterexample.

  7. Following Sider’s lead we can also produce a definition in terms of temporally relativised mereology as an irenic gesture for the benefit of the endurantist (see n1 above): x is an instantaneous temporal part of y at time t = df (i) x is a part of y at time t; (ii) x exists at and only at t.

  8. With thanks to an anonymous referee for pressing me on the fact that these pieces of terminology were only terms of art. That referee also raised concerns about a similar organism composed of x 1, x 2, x 3, y 1, y 2, y 3, z 1, z 2 and z 3, but where those things did not compose X, Y and Z (so it had no persisting parts whatsoever). My definitions say it perdures, but the anonymous referee had worries about this. As such an object would have the same mereological simples as the standard perduring object, would probably be classified as being four-dimensional, and appears to be exactly located at an extended region of spacetime, then I doubt endurantists would want to say that it endured, and I imagine most perdurantists would be fine saying it perdured. So I’m happy for my definition to entail that it perdures.

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Acknowledgments

With thanks to Ross Cameron, Katherine Hawley, Robin Le Poidevin, Joseph Melia, Jon Robson, Jonathan Tallant and Duncan Watson. I must extend special thanks to the two anonymous referees from this journal, whose comments were invaluable.

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Effingham, N. Temporal Parts and Time Travel. Erkenn 74, 225–240 (2011). https://doi.org/10.1007/s10670-010-9231-5

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