It is possible to wholly exist at multiple spatial locations at the same time. At least, if time travel is possible and objects endure, then such must be the case. To accommodate this possibility requires the introduction of a spatial analog of either relativising properties to times — relativising properties to spatial locations — or of relativising the manner of instantiation to times — relativising the manner of instantiation to spatial locations. It has been suggested, however, that introducing irreducibly spatially relativised or spatially adverbialised properties presents some difficulties for the endurantist. I will consider an objection according to which embracing such spatially relativised properties could lead us to reject mereology altogether in favour of a metaphysics according to which objects are wholly present at every space-time point at which they exist. I argue that although such a view is coherent, there are some good reasons to reject it. Moreover, I argue that the endurantist can introduce spatially relativised or adverbialised properties without conceding that objects lack spatial parts. Such a strategy has the additional advantage that it allows the endurantist not only to explain time travel, but also to reconcile our competing intuitions about cases of fission.
The possibility of travelling back in time to a period in which one’s earlier self or one’s ancestors existed, raises a number of well-worn problems (Grey, 1999; Chambers, 1999; Horwich, 1975 and Sider, 2002). In this paper I am concerned with only one of these: how is it that an [End Page 309] object can travel back in time to meet its earlier self, thus existing at two different spatial locations at one and the same time?
Four-dimensionalists have an easy answer to this question. Or at least, the vast majority of four-dimensionalists, who hold that objects persist by perduring — perdurantists — have an easy answer to this question (Sider, 2001; Balashov, 2000; Heller, 1990; Lewis, 1986). Perdurantists1 hold that persisting objects are four-dimensional space-time worms that are at each time at which they exist, partly present in virtue of having some part — a temporal part — present at that time. Though four-dimensional objects are of course self-identical, no two parts of a four-dimensional whole are strictly identical. So we can explain how I can meet myself in the past, by noting that my younger self and my older self are two different temporal parts of one and the same four-dimensional whole that is me. Thus we can reconcile the intuition that the younger and older selves are both me, with the intuition that they are distinct and have different properties (Lewis, 1976).
Three-dimensionalists or endurantists, however, hold that persisting objects have only three dimensions: they are not extended in time and do not persist by having temporal parts. Rather, three-dimensional objects endure (hence endurantists): they are wholly present whenever they exist (Wiggins, 1968; Baker, 1997; Doepke, 1982; Johnston, 1992). Thus if some enduring object O exists through T, then for every time t and t* in T, O wholly exists at t and t* and is strictly identical to itself at each of these times. For the endurantist, then, my younger self and I are not parts of the persisting object that is me, but rather, my younger self and I are strictly identical. But then the possibility of time travel raises the spectre of the same object wholly existing in two locations at the same time.
In section II, I begin by briefly outlining the manner in which the perdurantist accounts for the possibility of a time travelling self meeting his or her younger self. In section III, I explain how the endurantist will need to make use of spatially relativised properties, and I consider a minor worry that Ted Sider has with this proposal. In...