Online research in philosophy

I examine the issue of persistence over time in the context of the special theory of relativity (SR). The four-dimensional ontology of perduring objects is clearly favored by SR. But it is a different question if and to what extent this ontology is required, and the rival endurantist ontology ruled out, by this theory. In addressing this question, I take the essential idea of endurantism, that objects are wholly present at single moments of time, and argue that it commits one to unacceptable conclusions regarding coexistence, in the context of SR. I then propose and discuss a plausible account of coexistence for perduring objects, which is free of these defects. This leaves the endurantist room for some maneuvers. I consider them and show that they do not really help the endurantist out. She can accommodate the notion of coexistence in the relativistic framework only at the cost of renouncing central endurantist intuitions.

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 (Jackson 1998, p. 138). 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!

Four-dimensionalism, or perdurantism, the view that temporally extended objects persist through time by having (spatio-)temporal parts or stages, includes two varieties, the worm theory and the stage theory. According to the worm theory, perduring objects are four-dimensional wholes occupying determinate regions of spacetime and having temporal parts, or stages, each of them confined to a particular time. The stage theorist, however, claims, not that perduring objects have stages, but that the fundamental entities of the perdurantist ontology are stages. I argue that considerations of special relativity favor the worm theory over the stage theory.

Under the eternalist hypothesis that objects or events exist independently of being present two different views of persistence are on the market: Persisting objects endure if they are multiply located in (space-)time, and persisting objects perdure if they are singly located by having numerically different temporal parts. Recently, several authors (Balashov, Hales/Johnson, Gilmore, Gibson/Pooley) have argued that special relativity (SR) favours perdurantism over its endurantist rival. In my talk, I want to show that in fact the purported arguments are only those against endurantism, and that with similar ones we should argue against perdurantism, as well: Enduring and perduring entities are both in conflict with SR which undermines the eternalist hypothesis. For arguing in favour of perdurantism Yuri Balashov (2000b; 2005), on the one hand, considers spatially unextended (persisting) objects in Minkowski space-time and claims that for the endurantists there are unwelcome consequences from an adequate concept of their coexistence. On the other hand, spacelike extended (persisting) objects are under investigation. Concerning point-like objects, Cody Gilmore (2002) has convincingly shown that Balashov’s arguments fail and, therefore, I will confine me to extended object. My paper has two parts following the two different strategies – namely, concerning the problem of the endurantist “explanatory deficiency” according to Balashov (2000a; 2008), and the problem of criss-crossing hyperplanes according to Gilmore (2006).

How do ordinary objects persist through time and across possible worlds ? How do they manage to have their temporal and modal properties ? These are the questions adressed in this book which is a "guided tour of theories of persistence". The book is divided in two parts. In the first, the two traditional accounts of persistence through time (endurantism and perdurantism) are combined with presentism and eternalism to yield four different views, and their variants. The resulting views are then examined in turn, in order to see which combinations are appealing and which are not. It is argued that the 'worm view' variant of eternalist perdurantism is superior to the other alternatives. In the second part of the book, the same strategy is applied to the combinations of views about persistence across possible worlds (trans-world identity, counterpart theory, modal perdurants) and views about the nature of worlds, mainly modal realism and abstractionism. Not only all the traditional and well-known views, but also some more original ones, are examined and their pros and cons are carefully weighted. Here again, it is argued that perdurance seems to be the best strategy available.

Existing puzzles about coinciding objects can be divided into two types, corresponding to the manner in which they bear upon the endurantism v. perdurantism debate. (Endurantism is the view that material objects lack temporal extent and persist through time by being wholly present at each moment of their careers. Perdurantism is the opposing view that material objects persist by being temporally extended and having different temporal parts located at different times.) Puzzles of the first type, which involve temporary spatial co-location, can be solved simply by abandoning endurantism in favor of perdurantism, whereas those of the second type, which involve career-long spatial co-location, remain equally puzzling on both views. I show that the possibility of backward time travel (either via discontinuous jumps or via closed timelike curves) would give rise to a new type of puzzle. The new puzzles confront perdurantists and can be solved just by shifting to endurantism.

Under the eternalist hypothesis that objects or events exist temporally, but independently of being present two different views of persistence are on the market: Persisting objects endure if they are multiply located in (space-)time, and persisting objects perdure if they are singly located by having numerically different temporal parts. In the framework of the special theory of relativity (SR), the metaphysics of persistence is confronted with peculiar difficulties. Things persist by being “wholly present” at more than one time; but what are times within a temporally non-separated spacetime? Things persist by having different temporal parts at different times; but what are the temporal parts of a four-dimensional object in Minkowski spacetime? Recently, several authors have argued that SR favours perdurantism over its endurantist rival. In this paper, I intend to show that the purported arguments are only those against endurantism. The first simply fails, but the second, more convincing one, is such that with a similar strategy we should argue against perdurantism as well: Enduring and perduring entities are hence both in conflict with SR which undermines the eternalist hypothesis.

There are two main theories about the persistence of objects through time: endurantism and perdurantism. Endurantists hold that objects are three-dimensional, have only spatial parts, and wholly exist at each moment of their existence. Perdurantists hold that objects are four-dimensional, have temporal parts, and only partly exist at each moment of their existence. In this paper we argue that endurantism is poorly suited to describe the persistence of objects in a world governed by Special Relativity, and can accommodate a relativistic world only at a high price, one that we argue is not worth paying. Perdurantism, on the other hand, fits beautifully with our current scientific understanding of the world. Furthermore, we make this argument from implications of the Lorentz transformations, without appeals to geometrical interpretations, dimensional analogies, or auxillary premises like temporal eternalism.

Although considerations based on contemporary space-time theories, such as special and general relativity, seem highly relevant to the debate about persistence, their significance has not been duly appreciated. My goal in the paper is twofold: (1) to reformulate the rival positions in the debate (i.e., endurantism (three-dimensionalism) and perdurantism (four-dimensionalism, the doctrine of temporal parts)) in the framework of special relativistic space-time; and (2) to argue that, when so reformulated, perdurantism exhibits explanatory advantages over endurantism. The argument builds on the fact that four-dimensional entities extended in space as well as time are relativistically invariant in a way three-dimensional entities are not.

Persistence through time is like extension through space. A road has spatial parts in the subregions of the region of space it occupies; likewise, an object that exists in time has temporal parts in the various subregions of the total region of time it occupies. This view — known variously as four dimensionalism, the doctrine of temporal parts, and the theory that objects “perdure” — is opposed to “three dimensionalism”, the doctrine that things “endure”, or are “wholly present”.1 I will attempt to resolve this dispute in favor of four dimensionalism by means of a novel argument based on considerations of vagueness. But before argument in this area can be productive, I believe we must become much clearer than is customary about exactly what the dispute is, for the usual ways of formulating the dispute are flawed, especially where three dimensionalism is concerned.