What Do Four-dimensionalism and Three-dimensionalism Disagree about?

Abstract

Four-dimensionalism and three-dimensionalism are two rival theories of persistence. They give contrasting pictures of persistence of material objects, but it is still under dispute what is the proper formulation of their difference. In this paper, I aim to propose a new formulation of it, in light of which each theory can be properly understood. To this end, first I set three theoretical desiderata for a desirable formulation of the difference between two theories. Next, I consider three representative formulations, which I call respectively, ‘the temporal part formulation,’ ‘the temporal instantiation formulation,’ and ‘the spatiotemporal location formulation.’ I argue that they fail to meet the desiderata in some way or other. The temporal part formulation fails to meet all of three. The temporal instantiation formulation, properly understood, captures important aspects of the distinction, but fails to meet at least one desideratum. The spatiotemporal location formulation fares the best among the three formulations, but still has some deficiencies. Third, I argue that an appropriate combination of the temporal instantiation formulation and the spatiotemporal location formulation is even better and meets all the desiderata. Finally, I draw some implications from the previous discussion for the incompatibility of four-dimensionalism and presentism.