The following quotation, from Frank Jackson, is the beginning of a typical exposition of the debate between those metaphysicians who believe in temporal parts, and those who do not: The dispute between three-dimensionalism and four-dimensionalism, or more precisely, that part of the dispute we will be concerned with, concerns what persistence, and correllatively, what change, comes to. Three-dimensionalism holds that an object exists at a time by being wholly present at that time, and, accordingly, that it persists if it is (...) wholly present at more than one time. For short, it persists by enduring. Four-dimensionalism holds that an object exists at a time by having a temporal part at that time, and it persists if it has distinct temporal parts at more than one time. For short, it persists by perduring. In the light of these comments, some readers will perhaps find the question that forms the title of this paper a little puzzling. They may have learned to use the terms ‘fourdimensionalism’ ‘perdurantism’ and ‘belief in temporal parts’ interchangeably; or perhaps even to define one in terms of the other. Such a usage, however, is inapposite. We might imagine a Flatland-like world of two spatial dimensions and one temporal, whose philosophers are divided between a theory of persistence on which they persist by having temporal parts, and a theory on which they persist by being wholly located in each of several times. This is just the same issue we face, but at least the label ‘four-dimensionalism’ seems inapposite: the four-dimensionalist Flatlanders believe in only three dimensions! (shrink)

The strongest version of the principle of the Identity of Indiscernibles states that of necessity, there are no distinct things with all their universals in common (where such putative haecceities as being Aristotle do not count as universals: I use 'universal' rather than 'property' here and in what follows for the simple reason that 'universal' is the term of art that most safely excludes haecceities from its instances). It is commonly supposed that Max Black's famous paper 'The identity of indiscernibles' (...) (2) refutes this thesis. (Armstong's [1], chapter 9 is representative here.) Black argues ([2], p. 156) that it is perfectly possible that there be a world consisting solely of two indiscernible spheres at some distance to each other and that this world constitutes a counterexample to the principle above. The strongest version of the bundle theory of substance claims that of necessity, the substances that make up the world are bundles of universals.1 It is commonly supposed that a consequence of Black's defeat of the principle of the Identity of Indiscernibles is that this bundle theory of substance is mistaken. (Again, Armstong's [1] is representative.) I shall argue that Black's thought experiment does not defeat the bundle theory and that, as a result, the bundle theory can be used to salvage the principle of the Identity of Indiscernibles. (shrink)

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. (shrink)

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. (shrink)