In "Parthood and Identity Across Time," Judith Jarvis Thomson says the following of the 4D thesis that ordinary physical objects have temporal parts: "[According to the 4D thesis,] As I hold the bit of chalk in my hand, new stuff, new chalk keeps constantly coming into existence ex nihilo. That strikes me as obviously false" (213). Now this is not so much an argument as it is making fun of the 4D thesis, but I believe that there is an argument that can be drawn from this remark. For the 4Der is committed to the continuous coming into and going out of existence of temporal parts of things, and when something comes into or goes out of existence, an event, viz. that thing's coming into existence or that thing's going out of existence, occurs. And there is a respectable philosophical thesis, the Principle of Universal Causation, according to which every event, including comings into and goings out of existence, is caused by another event. Kant claimed to have proved this thesis on metaphysical grounds, and quantum physicists (as far as I can tell) now deny it on physical grounds, but surely the Principle of Universal Causation should not be denied on metaphysical grounds alone. But, I submit, this is what the 4Der must do.
Consider a Newtonian world in which a particle, P, travels with constant velocity through points A, B, and C, at times t1, t2, and t3 respectively. According to the 4Der, P has a temporal part, call it P1, that exists only during the interval t1-t2, and another temporal part, call it P2, that exists only during t2-t3. (I won't bother with calculus niceties here. In order to make sure that P1 and P2 do not overlap, we could stipulate that the interval during which P2 exists is open on the left: it comes into existence at t2+e. Alternatively, we could stipulate that the interval during which P1 exists is open on the right. It doesn't matter.) Now at t2, two events occur: P1's going out of existence and P2's coming into existence. (If one thinks that these events are identical, remember the calculus niceties we're ignoring.) Thomson's objection might be stated as follows: how do you (the 4Der) causally explain P2's coming into existence, as well as all those other comings into existence which you say occur all the time? To this question, the 4Der has a pat reply. P2's coming into existence is caused by P1's going out of existence. The 4Der might give the following gloss on Newton's first law: whenever an object x goes out of existence, a new object y comes into existence, having the same velocity as x. (Ceteris paribus, of course.) I think this is a good reply to Thomson's objection.
But suppose that the objector then asks for a causal explanation of P1's going out of existence. At first glance, which is all the glancing I'm going to do in this paper, it seems that the 4Der has no reply. Temporal parts just go out of existence. That's what they do. All the time. It is not comings into existence ex nihilo that are problematic for the 4D view: it is all those goings out of existence in nihilo that need explaining. It seems that the 4Der is committed to denying the Principle of Universal Causation for at least some goings out of existence.
It might seem, however, that this argument, like the ontological argument for the existence of God, is too wild a beast to let out of its cage. For a similar argument might be given to show that events cannot have temporal parts either, something most 3Ders, such as E. J. Lowe, wish to maintain: ". . . It isn't that I don't understand the notion of a temporal part as such - I understand it perfectly well as applied to events or processes - it's just that I deny it's applicability to entities in the category of continuants" ("Lewis on Endurance versus Perdurance," 152). I, at any rate, wish to maintain that events have temporal parts: the first three seconds of the game, the last five minutes of my life, etc. I maintain that the event of P's going from point A to point C, call it E, is composed of the following two events: e1, P's going from A to B; and e2, P's going from B to C.
"Gotcha!" says the 4Der attempting to turn my argument back on me. "What about e3, which is the ceasing to occur of e1; and e4, the beginning to occur of e2? Give me a causal explanation of those events, and don't even think about denying the Principle!" This is a legitimate move, for the beginnings and ends of events are themselves events: the end of a life, for example, is a death. But I'm not in trouble here, for I can identify e3 (or e4, depending on how we've done the calculus niceties) with P's passing through point B, and that event is causally explainable, in accordance with Newton's laws.
This move, however, is thereby available to the 4Der. She identifies P1's going out of existence with P's passing through B, and thus successfully replies to my argument. Touché!
Suppose then that instead of moving from point A to point C during t1-t3, P sits perfectly still. The 4Der is still committed to saying that P1 exists during the interval t1-t2, and P2 exists during t2-t3. In this case, however, there are no other events occurring to identify with the going out of existence of P1 in order to explain it. And I have no problem with this case, for during the interval t1-t3, I maintain, no event has occurred at all, so I have no ceasings to occur and beginnings to occur that I must causally explain if I am to maintain the Principle of Universal Causation.
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