## Thursday, July 12, 2018

### Presentism and the mereology of events

According to presentism, non-present events do not exist. Now consider a particular season S of fencing consisting of a dozen fencing meets M1, M2, ..., M12 as well as practices and recovery days on other days. Suppose meet Mi occurs on day Di, and imagine that D1 is today. Then both M1 and S exist, and M1 is a part of S. But according to presentism, the only parts of S that exist are M1 and its parts. But the mereological axiom of weak supplementation says that:

1. If y is a proper part of x, then x has a proper part that does not overlap y.

Letting x = S and y = M1, we get a violation of weak supplementation.

Thus:

1. If weak supplementation is true, presentism is false.

Now, I happen to think that weak supplementation is in general false, so I can’t use this argument as it stands. Still, it seems plausible to me that even if it is false in general, weak supplementation is true for the temporal parts of events (where, roughly, a temporal part is a part that can be delimited solely by temporal boundaries), and that’s all we need for the above argument.

Moreover, here is a very plausible weaker version of weak supplementation for events:

1. If event y is a proper part of event x and x has a temporal duration longer than event y, then x has a proper part that does not overlap y.

But in my case above, the fencing season has a temporal duration longer than the first match, so the fencing season needs to have a proper part that does not overlap the first match, which is false on D1 given presentism. So, (3) requires the rejection of presentism.

Basically, all the problems come from the fact that the presentist has to deny:

1. There is an event that has two non-overlapping temporal parts.

One might object that a presentist will have a version of mereological axioms where the existential quantifier is replaced by “there existed, exists or will exist”. Thus, the weak supplementation axiom might say:

1. If y is a proper part of x, then x had, has or will have a proper part that did not, does not or will not (respectively) overlap y.

I think this is not a move that a presentist will make, as it is a move that in effect makes mereology four-dimensional. For instance, the standard definition of overlap is that x and y overlap if and only if they have a part in common. But the modified version would say that x and y overlap if and only if they had, have or will have a part in common. Now imagine two fir trees, one in Alaska and one in Texas, and suppose that next year the Alaska tree will be transplanted to be right next to the Texan one. And suppose a decade later the two trees grow together in such a way that they have some branch in common. By the tensed version of the definition of overlap, it is now true to say that the tree in Alaska and the tree in Texas overlap. But only a four-dimensionalist will want to say that—that’s exactly the sort of claim the presentist will want to deny.

Moreover, note that (5) doesn’t quite capture the intuitions of weak supplementationist presentists. For it allows for the possibility of an object now having only one proper part, as long as it had another earlier, which is something weak supplementationist presentists will deny.

Perhaps, though, presentists can say that the mereology of events is different from the mereology of objects, and the modification of the axioms is something one only does in the case of events.