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Can I be an Instantaneous Stage and yet Persist Through Time?


An alternative to the standard endurance/perdurance accounts of persistence has recently been developed: the stage theory (Sider, T. Four-Dimensionalism: an Ontology of Persistence and Time. Oxford: Oxford University Press, 2001; Hawley, K. How Things Persist. Oxford: Oxford University Press, 2001). According to this theory, a persisting object is identical with an instantaneous stage (temporal part). On the basis of Leibniz’s Law, I argue that stage theorists either have to deny the alleged identity (i.e., give up their central thesis) or hold that stages are both instantaneous and continuants. I subsequently show that, although stage theory is flexible enough to accommodate the latter claim, the cost for accommodating it is an excessive proliferation of persistence concepts.

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  1. One may wonder exactly which instantaneous stage of the perduring aggregate I am identical with. My (!) thinking or uttering “I” takes time. So how is the referent of the indexical “I” – i.e., the referent that is supposed to be identical with an instantaneous stage – picked out? Stage theorists do not say. (However, see Hawley (2001: 57–60) for a somewhat sketchy and non-committal discussion of how language in general may be taken to latch on to a world of instantaneous stages.)

  2. The modal counterpart relation is a relation of similarity, Lewis has told us (Lewis 1968). What does the temporal counterpart relation involve? Sider has no definite view on the matter: “The temporal counterpart relation is the same relation used by the worm theorist [perdurance theorist] to unite the stages of spacetime worms. Also known as the ‘genidentity relation’, the ‘unity relation’, the ‘I-relation’, and so on, it may be analyzed in some way (in the case of persons perhaps in terms of memory or bodily continuity), or taken as primitive; the stage theorist has no particular commitment to any of these alternatives.” (Sider 2001: 194) He does go on to say, though, that the temporal counterpart relation can be intransitive and that it thus allows for fission and fusion (pp. 204–205). Hawley, for her part, invokes unanalyzed “non-supervenient relations” (yielding immanent causation, spatiotemporal continuity, and similarity) in order to “stick” (her term) different instantaneous stages together, making them stages of the “same” (“same” in a loose sense) persisting object (Hawley 2001: ch. 3; see also pp. 62–63). Hawley does not explicitly use Sider’s expression “temporal counterpart”, but this seems to be a mere verbal difference between the two.

  3. Sometimes Leibniz’s Law is put in terms of quantification over properties. I prefer the more general, ontologically neutral, version (cf. Wiggins 2001: 25).

  4. Cf. also Hawley’s discussion of “the sweater” and “the thread” that temporarily coincide (2001: 156–158).

  5. See my (forthcoming) for a discussion of the modal case.

  6. Notice that Sider and Hawley, in effect, accept this intuition when it comes to stages, i.e., stages qua stages (see e.g., the Sider-quote above). But why are stages so special in this respect? Why this, seemingly, arbitrary demarcation?

  7. Arguably, both the endurance and the perdurance accounts of persistence heed to this intuition: the endurance account by saying that a persisting object is wholly present at more than one time; the perdurance account by holding that a persisting object is a four-dimensional aggregate of temporal parts.


  • Hansson Wahlberg, T. “4-D Objects and Disposition Ascriptions”. Philosophical Papers, forthcoming.

  • Hawley, K. 2001. How Things Persist. Oxford: Oxford University Press.

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  • Lewis, D. 1968. “Counterpart Theory and Quantified Modal Logic”. Journal of Philosophy 65: 113–26.

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  • Lewis, D. 1971. “Counterparts of Persons and Their Bodies”. Journal of Philosophy 68: 203–11.

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  • Sider, T. 2001. Four-Dimensionalism: an Ontology of Persistence and Time. Oxford: Oxford University Press.

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  • Wiggins, D. 2001. Sameness and Substance Renewed. Cambridge: Cambridge University Press.

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I thank Heather Dyke, Anna-Sofia Maurin, Nils-Eric Sahlin, Nicholas J.J. Smith, Lena Wahlberg, and the participants of the Lund-Rutgers Conference (Lund, January 2008) for helpful comments on earlier drafts of this paper.

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Correspondence to Tobias Hansson Wahlberg.

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Hansson Wahlberg, T. Can I be an Instantaneous Stage and yet Persist Through Time?. Int Ontology Metaphysics 9, 235–239 (2008).

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  • Persistence
  • Stage theory
  • Temporal counterparts
  • Predication
  • Leibniz’s Law