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Properties that Four-Dimensional Objects Cannot Have

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Metaphysica

Abstract

The paper argues that four-dimensionalism is incompatible with the existence of “additively cumulative” properties, including mass, volume, and electrical charge. These properties add up over disjoint objects: for example, the mass of a whole composed of two disjoint objects is a sum of the individual masses of the objects. The difficulty with such properties for four-dimensionalism stems from the way this theory makes persistence depend on the existence of disjoint objects at disjoint times. I consider various possible responses to this difficulty and conclude that they all fail.

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Notes

  1. Thus, David Lewis says (1983: 76) that a “person-stage is a physical object, just as a person is … . It does many of the same things that a person does: it talks and walks and thinks, has beliefs and desires, it has a size and shape and location.” Similarly, he claims [1986: 204] that “we are made up of temporal parts, and our temporary intrinsics are properties of these parts, wherein they differ from one another.” A more recent expression of this assumption can be found, for example, in Copeland et al. (2001: 289): “According to the four-dimensionalist, if Descartes has the property of, say, having fought a duel (at t), this is because Descartes has a temporal part (his t-part) that is fighting a duel.”

  2. Conceptual difficulties with perdurantism different from those which I present here are discussed, for example, by Thomson (1983: 205–213), Simons (1987: 123–127), and Lowe (1987, 2002: 50–58).

  3. The objects considered throughout the discussion are all physical objects, unless otherwise indicated.

  4. Note, however, that I am not assuming that the notion of existence at an instant is more fundamental than the notion of existence at a time T which may be longer than an instant.

  5. For a detailed account of the kind of proper parts required by perdurantism, see Sider (2001: Ch. 3, esp. 59ff.).

  6. See Sider (1996: 437–439, 2001: 193–208) and Haslanger (2003: 318–319).

  7. Note that other versions of four-dimensionalism may disagree either by claiming that there are no minimally long temporal parts or stages, or by claiming that minimally long temporal parts or stages are instantaneous.

  8. For a classic statement of this standard four-dimensionalist account, see Lewis (1986: 204).

  9. Among additively cumulative properties we find not only fundamental physical properties such as mass, volume, and electrical charge, but also less fundamental, and not always physical, properties such as sugar content (e.g., of bread) and market value (e.g., of crude oil). It is interesting, but beyond the scope of this paper, to explore the broader notion of a cumulative property arrived at (for the case of mass) if one replaces “M = M 1 + … + M n ” in ACM with “M > M 1, …, M > M n ”. Clearly (assuming M i  > 0 for all 1 ≤ i ≤ n), additive cumulativity is a species of the more general cumulativity.

  10. Terminology: A “perdurantist” is one who maintains perdurantism. A “perdurant” is an object that persists in accordance with the account provided by perdurantism. Its manner of persistence is described as “perdurance.” Persistence in accordance with the three-dimensionalist account is called “endurance.”

  11. In what follows, I use “atomic” as short for “temporally atomic,” i.e., the property of not possessing proper temporal parts. B need not have atomic temporal parts nor instantaneous temporal parts. Instantaneous temporal parts are necessarily atomic for they are without temporal length. But atomic temporal parts are not necessarily instantaneous. Regarding the controversiality of the assumption that some of the temporal parts of B are atomic, see note 13.

  12. The contrary proposal that nonatomic parts possess mass, whereas atomic ones do not, raises problems that are much the same as those associated with option 2.

  13. Zimmerman (1996: 121–122) notes that both Bertrand Russell and C.D. Broad held a “no-instants” theory of perdurance according to which “every temporal part has some temporal extension, but every temporal part also admits of further division into yet “thinner” temporal parts.”

  14. I use the symbol “τ,” and other symbols containing “τ,” to designate lengths of time. The symbol “T” and other symbols containing “T” were used above to designate particular times. An example of a length of time is 7 months. An example of a particular time is 1974.

  15. By “the perdurant corresponding to a persisting object,” I mean that perdurant which the perdurantist account takes to be the whole of the object, rather than any of its proper temporal parts.

  16. Actually, it is not clear that empirical research is at all capable, in principle, of determining whether or not there are noninstantaneous atomic temporal parts. Our ignorance in this respect may therefore have little to do with the state of scientific knowledge.

  17. That the stages are understood to be instantaneous is attested by Sider (1996: 6–7): “… the stage view claims that I am an instantaneous stage that did not exist before today, and will not exist after today.”

References

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Correspondence to Ariel Meirav.

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Meirav, A. Properties that Four-Dimensional Objects Cannot Have. Int Ontology Metaphysics 10, 135–148 (2009). https://doi.org/10.1007/s12133-009-0045-3

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