Does Four-Dimensionalism Explain Coincidence?

For those who think the statue and the piece of copper that compose it are distinct objects that coincide, there is a burden of explanation. After all, common sense says that different ordinary objects cannot occupy the same space at the same time. A common argument in favor of fourdimensionalism (or ‘perdurantism’ or ‘temporal parts theory’) is that it provides the resources for a superior explanation of this coincidence. This, however, is mistaken. Any explanatory work done by the four-dimensionalist notion of absolute parthood rests ultimately on notions equally available to the three-dimensionalist. Thus, a neutral explanation of coincidence is at least as good while avoiding commitment to temporal parts. Does Four-Dimensionalism Explain Coincidence?* Four-dimensionalism (or ‘perdurantism’ or ‘temporal parts theory’) views objects as stretched out in time as well as in space; it says objects have temporal parts much as they have spatial parts. Besides the spatial part of me that stretches from my right knee to my hip, I also have the temporal part of me that stretches from my third to my fourth birthday. Besides the extreme-most point of my nose, there is the current instantaneous stage of me. Threedimensionalism (or ‘endurantism’) denies such parts, saying that objects exist wholly at every moment of their existence. We won’t worry about how to improve our characterization of the two views, for the present issue doesn’t trade on such niceties. The question is whether fourdimensionalism can better explain coincidence.1 The statue and the piece of copper of which it is composed have different temporal properties: the piece of copper existed yesterday, but not the statue since the artist shaped it just this morning. Because they have different properties, the statue must, following Leibniz’s Law, be distinct from the piece of copper. But this means we have two objects occupying the same space at the same time, which common sense tells us is impossible! Many deny some step in the reasoning just given and insist that the statue and the piece of copper are identical. Those who don’t are left with a “puzzle of coincidence”. A surprising number of threeand fourdimensionalists agree that four-dimensionalism better explains this coincidence.2 According to * Many thanks to David Christensen, Matti Eklund, and an anonymous referee for helpful comments. 1 Four-dimensionalism is not supposed to have a superior explanation of how distinct objects could have the exact same location (or matter) at all times. Because most four-dimensionalists deny this possibility, I will not discuss this related puzzle. 2 The main arguments I will examine come from Heller, Sider, and Hawley, but agreement with these arguments is widespread. Gilmore, a three-dimensionalist, seems to agree with Heller’s argument in his “Time Travel, Coinciding Objects, and Persistence”. Merricks thinks that four-dimensionalism “initially seems to provide an elegant way” of explaining coincidence; the reason he thinks it only initially seems to explain coincidence is, it appears, not because of some lack of explanation for cases of objects that coincide at a time, but rather because the solution doesn’t generalize to explain objects that coincide at all times (Objects and Persons, p. 44). Thomson, who