Mereological Explanation and Time Travel

Abstract

I have previously argued in a paper with Robson that a particular time travel scenario favours perdurantism over endurantism on the grounds that endurantists must give up on the Weak Supplementation Principle. Smith has responded, arguing that the reasons we provided are insufficient to warrant this conclusion. This paper agrees with that conclusion (for slightly different reasons: that even the perdurantist has to give up on the Weak Supplementation Principle) but argues that the old argument can be supplanted with a new one.

Notes

¹For the purpose of example I will assume that it is classical mereology we find favour with. This is solely for the purpose of presentation. You could substitute different systems (for instance, see n. 8 where I suggest the perdurantist might want to give up the atemporal version of Uniqueness) and similar problems would still arise for the principles of those systems.

²Given this definition, the following revision might still not work, for objects could be multi-located when exactly occupying identical regions. For instance, a time travelling boson that superposes with itself will be ‘multi-located’ at exactly the same region (and just as two superposed bosons may compose a further object, there's no reason to think the time travelling boson fails to either). Let us charitably ignore this problem for the sake of this discussion.

³Now we can see why being a presentist-endurantist won't help even if they do accept atemporal mereology. They won't accept (P@T) so their atemporal mereology won't explain the revisions. Indeed, just as the regular endurantist has to make revisions to temporally relativized mereology, the presentist would have to make corresponding revisions to their atemporal mereology. So they'll end up with a system just as complex as the regular endurantist.

⁴Unless the two temporal parts were identical, but then if the ‘tower’ of bricks from scenario (vi) all shared one and the same temporal part there wouldn't be lots of bricks there at that time—as (vi) demands—but just one brick.

⁵Sider wants to retain ‘instantaneous temporal part’ for talking about the object that is the fusion of what I call the instantaneous temporal parts, and instead calls the ‘person-like’ parts ‘person-stages’. But it'll do no harm for me to instead label the person-like parts ‘instantaneous temporal parts’.

⁶Parsons 2007 demurs, arguing that enduring objects are exactly located at but a single spacetime region. But that wouldn't help here, for what is important is that he would agree that perduring objects must likewise be atemporally exactly located at but a single region, again ruling out the possibility of atemporal multi-location.

⁷Whilst I am fixing errors in the original paper, I must note that the claim that given universalism and WSP it follows that if the ys are part of an object x then any object the ys compose is also a part of x[Effingham and Robson 2007: 636] is also false. You need Uniqueness as well, which may well be given up. This is only a minor problem, for one would think the theorem is intuitively plausible in its own right and should be derivable in any sensible mereology, and you would still be left with the other problems the paper describes in any case.

⁸For what it's worth I think the perdurantist should admit defeat, and give up on Uniqueness (other alternatives are surveyed by Eagle [forthcoming: §6]). Note that whilst this means that the perdurantist won't be able to endorse a classical mereology, the mereology they do endorse will still be simpler than the revised system the endurantist endorses as they generally want to give up Uniqueness anyhow.

⁹Many thanks to an anonymous referee for this journal (particularly with §6), Philip Goff, Jon Robson, Michael Rush, Donald Smith and those who attended a presentation of this paper at the University of Birmingham. Thanks also to Cody Gilmore and Anthony Eagle for making their papers available to me.