Relativistic Objects

Abstract

I offer an argument in defense of four-dimensionalism, the view that objects are temporally, as well as spatially extended. The argument is of the inference-to-thebest-explanation variety and is based on relativistic considerations. It deals with the situation in which one and the same object has different three-dimensional shapes at the same time and proceeds by asking what sort of thing it must be in order to present itself in such different ways in various "perspectives"~associated with moving reference frames! without being different from itself. I argue that the best answer is that the object must be four-dimensional. It will then have differing 3D shapes in different perspectives because such shapes are intrinsic properties of its 3D parts.Three-dimensionalism~3D! is the view that objects persist through time by "enduring," that is, by being wholly present at all times at which they exist. Fourdimensionalism~4D! is the opposite view that objects persist by "perduring," that is, by being temporally, as well as spatially extended, or by having~spatio-!temporal parts. The issue between the 3D and 4D accounts of persistence has become an intensely-debated topic in contemporary metaphysics. 1 The theory of special relativity is credited with introducing the four-dimensional world of events. Does special relativity~SR! also require the four-dimensional ontology of objects? Despite the obvious importance of this question, it has not received due attention. Relativistic considerations are almost entirely absent from the 3D04D debate. And where they are present~mostly in footnotes and parenthetical remarks!, their import is unclear. 2 This paper attempts to remedy the situation by offering an argument, of the inference-to-the-best-explanation variety, for 4D, based on SR. In §1 I prepare the ground for the argument, which I then present in §2. Along the way, I respond to a possible objection suggested by van Inwagen's recent paper~1990!. The ideas of his paper are pre-relativistic, but they can easily~and, I hope, fairly! be extrapolated to the relativistic context. In subsequent sections, I discuss other objections that can be raised against my argument.

Material Constitution is Ad Hoc

“…Only in the former case does my argument operate against Chisholm. 23 Special relativity may also provide a reason to believe that objects have both spatial and temporal parts (Balashov 1999). 24 I have assumed throughout this section that perdurantism does solve both PC and PCO.…”

On the Persistence of Particles

“…For the continuity of worldlines, assumption (b), implies that-with i, j now labelling persisting particles!-each of the n(n − 1)/2 functions dist ij (t) is a continuous function of t, so that d is also continuous. 14 The idea now is that the perdurantist can use d to determine the worldline (q-curve) through the occupied point < t 0 , x 0 , y 0 , z 0 >∈ T . I shall first present the intuitive idea, then discuss how it faces a problem, and finally show how the corollaries to the Heine-Borel theorem solve the problem.…”

“…(ii) for perdurantism: Balashov, (14) Hawley, (1) Lewis (8,15,16) (1986, pp. 202-204), and Sider (2) himself.…”

The Donkey Problem

“…There are two dominant arguments for 4Dism and one recent argument that is drawing a lot of attention. These are ( I here ignore other interesting arguments for 4Dism that have yet to generate a following-arguments such as Balashov's (1999) Argument from Relativity Theory 7 Drawing on work of Hirsch (2002) and Sider (2001, p. 127), it may well be that in the language that includes donkey-talk quantifier phrases like 'there are' will not be synonymous with homophonic phrases in the minimal language that does not include donkey-talk. This so-called ''quantifier variance'' is suggested by the fact that there will be homophonic numerical sentences in the two languages that have different truth values.…”