Vague Objects and the Problem of the Many


The problem of the many poses the task of explaining mereological indeterminacy of ordinary objects in a way that sustains our familiar practice of counting these objects. The aim of this essay is to develop a solution to the problem of the many that is based on an account of mereological indeterminacy as having its source in how ordinary objects are, independently of how we represent them. At the center of the account stands a quasi-hylomorphic ontology of ordinary objects as material objects with multiple individual forms.

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  1. 1.

    See Unger (1980) and Geach (1962).

  2. 2.

    I said that the problem of the many poses the task of explaining mereological indeterminacy of ordinary objects in a way that sustains our familiar practice of counting these objects. The solutions to be discussed here embrace this task. Various other known solutions are less ambitious. Unger (1980), for example, draws the conclusion that there are many mountains or none, thereby giving up on our intuitive cardinality claim that there is a single mountain on the plain. Markosian (1998), by contrast, tries to capture this uniqueness claim by arguing that among many largely overlapping pluralities of rocks on the plain, only one such plurality has a fusion. This approach, however, leaves the mountain’s fuzzy boundary in the dark. An account of mereological indeterminacy is not part of the package. To mention a third approach, Lewis (1993) accepts that while each of the aggregates is a mountain, the commonsense claim that there is only one mountain on the plain is preserved, as ordinary speakers don’t count by strict identity, but rather by the weaker relation of massive overlap. This is an attempt to get the uniqueness claim to come out true. But the approach by itself offers no handle on mereological indeterminacy. See Sattig (2010) for criticism along these lines.

  3. 3.

    For classical presentations of supervaluationism, see Fine (1975) and van Fraassen (1966).

  4. 4.

    A standard and plausible assumption in the background is that the predicate “is a part of” is a precise predicate. The mereological indeterminacy is meant to have its exclusive source in the imprecision of “M”, which derives from the imprecision of the sortal mountain associated with “M”. This treatment of ordinary mereological indeterminacy is most prominently endorsed by Lewis (1993).

  5. 5.

    I shall assume that “the set of mountain-candidates” is precise and thereby ignore issues of higher-order vagueness.

  6. 6.

    This solution appears in Lewis (1993), McGee and McLaughlin (2000), Heller (1990), and Lowe 1995).

  7. 7.

    A forceful rendition of the ensuing objection is presented in McKinnon (2002). See Hudson (2001, Ch. 1) and Weatherson (2003, 2009) for overviews of further objections.

  8. 8.

    For constructive discussion of metaphysical indeterminacy, see, inter alia, Akiba (2000, 2004), Barnes (2010), Barnes and Williams (2009, 2011), Morreau (2002), Parsons (2000), Rosen and Smith (2004), Smith (2005), Williams (2008), and Williamson (2003.

  9. 9.

    For a statement of this principle, see Schaffer (2009, p. 361).

  10. 10.

    The picture to be sketched below is developed in more detail and with further applications in (Sattig, forthcoming). For an application of the framework to an argument against vague objects by Weatherson (2003, §4), see (Sattig, forthcoming).

  11. 11.

    If the sortal mountain is semantically imprecise, then different properties of material objects realize the sortal on different precisifications. In particular, different precisifications of the sortal specify different minimal degrees of boundary contrast and hence specify different sets of eligible mountain-boundaries. This semantic indeterminacy will not play a role here. Since I claim that mereological indeterminacy as it occurs in the case of M does not have its source in the semantic imprecision of mountain, I shall assume, for simplicity, that it is always a precise matter which properties realize which sortals, or kinds. Indeterminacy emanating from semantic imprecision of sortals requires a separate treatment. For further details, see (Sattig, forthcoming).

  12. 12.

    See, inter alia, Sider (2001, 2003).

  13. 13.

    See Koslicki (2008) on Aristotelian and neo-Aristotelian hylomorphism about ordinary objects.

  14. 14.

    What follows is a very rough outline of the account. For further details, see (Sattig, forthcoming).

  15. 15.

    It is not even clear that the account applies to all instances of mereological indeterminacy. There may well be mereological cases that are best understood as de dicto.

  16. 16.

    For ease of exposition, I am here treating the properties of being composed of the xs and of having r as a part as complex monadic properties, ignoring individual forms of the xs and of r. Ultimately, the framework should be able to handle relational formal predications of parthood that are sensitive to the individual forms of all of its relata.

  17. 17.

    For another derivative account of mereological indeterminacy de re, developed in the context of a relative-identity solution to the problem of the many, see Sattig (2010).

  18. 18.

    For a more elaborate characterization of the role of these classical–mereological assumptions in the proposed ontology of ordinary objects, see (Sattig, forthcoming).

  19. 19.

    Thanks to Robbie Williams here.


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For comments on the material presented in this essay, I am indebted to Marta Campdelacreu, Aurélien Darbellay, Katherine Hawley, Geert Keil, Kathrin Koslicki, Dan López de Sa, Christian Nimtz, Roy Sorensen, Achille Varzi, Robbie Williams, and audiences at Humboldt University in Berlin, Bielefeld University and the Third PERSP Metaphysics Workshop in València.

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Sattig, T. Vague Objects and the Problem of the Many. Int Ontology Metaphysics 14, 211–223 (2013).

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  • Vagueness
  • Indeterminacy
  • Material objects
  • Problem of the many