Vague Objects and the Problem of the Many

Abstract

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.

This is a preview of subscription content, access via your institution.

Notes

  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.

References

  1. Akiba K (2000) Vagueness as a Modality. Philosophical Quarterly 50: 359–70.

    Article  Google Scholar 

  2. Akiba K (2004) Vagueness in the World. Noûs 38: 407–429.

    Article  Google Scholar 

  3. Barnes EJ (2010) Ontic Vagueness: A Guide for the Perplexed. Noûs 44: 601–27.

    Article  Google Scholar 

  4. Barnes EJ, Williams JRG (2009) Vague Parts and Vague Identity. Pacific Philosophical Quarterly 90: 176–87.

    Article  Google Scholar 

  5. Barnes EJ, Williams JRG (2011) A Theory of Metaphysical Indeterminacy. Oxford Studies in Metaphysics 6: 103–48.

    Article  Google Scholar 

  6. Fine K (1975) Vagueness, Truth and Logic. Synthese 30: 265–300.

    Article  Google Scholar 

  7. Geach P (1962) Reference and Generality. Cornell University Press, Ithaca, NY.

    Google Scholar 

  8. Heller M (1990) The Ontology of Physical Objects: Four-Dimensional Hunks of Matter. Cambridge University Press, Cambridge.

    Book  Google Scholar 

  9. Hudson H (2001) A Materialist Metaphysics of the Human Person. Cornell University Press, Ithaca, NY.

    Google Scholar 

  10. Koslicki K (2008) The Structure of Objects. Oxford University Press, Oxford.

    Book  Google Scholar 

  11. Lewis D (1993) Many, but Almost One. In: Bacon J (ed) Ontology, Causality and Mind: Essays in Honour of D. M. Armstrong. Cambridge University Press, Cambridge.

    Google Scholar 

  12. Lowe EJ (1995) The Problem of the Many and the Vagueness of Constitution. Analysis 55: 179–82.

    Article  Google Scholar 

  13. Markosian N (1998) Brutal Composition. Philosophical Studies 92: 211–49.

    Article  Google Scholar 

  14. McGee V, McLaughlin B (2000) The Lessons of the Many. Philosophical Topics 28: 129–51.

    Article  Google Scholar 

  15. McKinnon N (2002) Supervaluations and the Problem of the Many. Philosophical Quarterly 52: 320–39.

    Article  Google Scholar 

  16. Morreau M (2002) What Vague Objects Are Like. Journal of Philosophy 99: 333–361.

    Article  Google Scholar 

  17. Parsons T (2000) Indeterminate Identity. Oxford University Press, Oxford.

    Book  Google Scholar 

  18. Rosen G, Smith NJJ (2004) Worldly Indeterminacy: A Rough Guide. In: Jackson F, Priest G (eds) Lewisian Themes. Oxford University Press, Oxford.

    Google Scholar 

  19. Sattig T (2010) Many as One. Oxford Studies in Metaphysics 5: 145–178.

    Google Scholar 

  20. Schaffer J (2009) On What Grounds What. In: Chalmers D, Manley D, Wasserman R (eds) Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press, Oxford.

    Google Scholar 

  21. Sider T (2001) Maximality and Intrinsic Properties. Philosophy and Phenomenological Research 63: 357–64.

    Article  Google Scholar 

  22. Sider T (2003) Maximality and Microphysical Supervenience. Philosophy and Phenomenological Research 66: 139–49.

    Article  Google Scholar 

  23. Smith NJJ (2005) A Plea For Things That Are Not Quite All There: Or, Is There a Problem about Vague Composition and Vague Existence? Journal of Philosophy 102: 381–421.

    Google Scholar 

  24. Unger P (1980) The Problem of the Many. Midwest Studies in Philosophy 5: 411–67.

    Article  Google Scholar 

  25. van Fraassen B (1966) Singular Terms, Truth-Value Gaps, and Free Logic. Journal of Philosophy 63: 481–95.

    Article  Google Scholar 

  26. Weatherson B (2009) The Problem of the Many. In: Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/problem-of-many/.

  27. Weatherson B (2003) Many Many Problems. The Philosophical Quarterly 53: 481– 501.

    Article  Google Scholar 

  28. Williams JRG (2008) Ontic Vagueness and Metaphysical Indeterminacy. Philosophy Compass 3: 763–788.

    Article  Google Scholar 

  29. Williamson T (2003) Vagueness in Reality. In: Loux MJ, Zimmerman DM (eds) Oxford Handbook of Metaphysics. Oxford University Press, Oxford.

    Google Scholar 

Download references

Acknowledgments

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.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Thomas Sattig.

About this article

Cite this article

Sattig, T. Vague Objects and the Problem of the Many. Int Ontology Metaphysics 14, 211–223 (2013). https://doi.org/10.1007/s12133-013-0122-5

Download citation

Keywords

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