, Volume 194, Issue 7, pp 2645–2666 | Cite as

Multiple reference and vague objects

  • Giovanni Merlo


Kilimanjaro is an example of what some philosophers would call a ‘vague object’: it is only roughly 5895 m tall, its weight is not precise and its boundaries are fuzzy because some particles are neither determinately part of it nor determinately not part of it. It has been suggested that this vagueness arises as a result of semantic indecision: it is because we didn’t make up our mind what the expression “Kilimanjaro” applies to that we can truthfully say such things as “It is indeterminate whether this particle is part of Kilimanjaro”. After reviewing some of the limitations of this approach, I will propose an alternative account, based on a new semantic relation—multiple reference—capable of holding in a one-many pattern between a term and several objects in the domain. I will explain how multiple reference works, what differentiates it from plural reference and how it might be used to accommodate at least some aspects of our ordinary discourse about vague objects.


Vague objects Supervaluationism Plural reference  Multiple reference 



Thanks to Donald Baxter, Philipp Blum, Cian Dorr, Kit Fine, Manuel García-Carpintero, Martin Lipman, Matthew McKeever, Bryan Pickel, Giulia Pravato, Carlos Romero, Sven Rosenkranz, Moritz Schulz, Stewart Shapiro, Achille Varzi, Elia Zardini and two anonymous referees for helpful comments on the ideas in this paper. I am also grateful to the participants of the 65th Eidos Meeting in Ligerz, the LOGOS Seminar in Barcelona, the 8th Arché Graduate Conference in St Andrews, the 1st UNAM-IIFs Philosophy Graduate Conference in Mexico City and the Phlox Research Seminar in Hamburg. The research leading to this paper has received funding from the Swiss National Science Foundation Sinergia Project ‘Grounding - Metaphysics, Science, and Logic’ (Project 147685).


  1. Boolos, G. (1984). To be is to be the value of a variable (or to be some values of some variables). Journal of Philosophy, 81(8), 430–439.CrossRefGoogle Scholar
  2. DeRosset, L. (2015). Analyticity and ontology. Oxford Studies in Metaphysics, 9: 129-170.Google Scholar
  3. Evans, G. (1978). Can there be vague objects? Analysis, 38, 208.CrossRefGoogle Scholar
  4. Fine, K. (1975). Vagueness, truth and logic. Synthese, 54, 235–59.Google Scholar
  5. Hudson, H. (2005). The metaphysics of hyperspace. Oxford: Oxford University Press.CrossRefGoogle Scholar
  6. Jones, N. K. (2011). Williams on supervaluationism and logical revisionism. The Journal of Philosophy, 108(11), 633–641.CrossRefGoogle Scholar
  7. Keefe, R. (2000). Theories of vagueness. Cambridge: Cambridge University Press.Google Scholar
  8. Landman, F. (1989a). Groups, I. Linguistics and Philosophy, 12(5), 559–605.CrossRefGoogle Scholar
  9. Landman, F. (1989b). Groups, II. Linguistics and Philosophy, 12(6), 723–744.CrossRefGoogle Scholar
  10. Lasersohn, P. (1995). Plurality, conjunction and events. Dordrecht: Kluwer.CrossRefGoogle Scholar
  11. Lewis, D. (1983). New work for a theory of Universals. Australasian Journal of Philosophy, 61(4), 343–377.CrossRefGoogle Scholar
  12. Lewis, D. (1999). Many, but almost one. In D. Lewis (Ed.), Papers in metaphysics and epistemology (pp. 164–182). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  13. Linnebo, Ø. (2014). Plural quantification. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy. Retrieved from
  14. McGee, V., & McLaughlin, B. (1994). Distinctions without a difference. The Southern Journal of Philosophy, 33, 203–51.CrossRefGoogle Scholar
  15. McGee, V., & McLaughlin, B. (2000). The lessons of the many. Philosophical Topics, 28(1), 129–151.CrossRefGoogle Scholar
  16. Oliver, A., & Smiley, T. (2008). Is plural denotation collective? Analysis, 68(1), 22–34.CrossRefGoogle Scholar
  17. Oliver, A., & Smiley, T. (2013). Plural logic. Oxford: Oxford University Press.CrossRefGoogle Scholar
  18. Scha, R. (1981). Distributive, collective and cumulative quantification. In J. A. G. Groenendijk, T. M. V. Janssen, & M. B. J. Stokhof (Eds.), Formal methods in the study of language. Amsterdam: Mathematical Center.Google Scholar
  19. Schiffer, S. (2000). Replies. Philosophical Issues, 10, 320–43.Google Scholar
  20. Schwarzschild, R. (1996). Pluralities. Dordrecht: Kluwer.CrossRefGoogle Scholar
  21. Sider, T. (2015). Nothing over and above. Grazer Philosophische Studien, 91, 191–216.Google Scholar
  22. Smith, N. J. J. (2008). Vagueness and degrees of truth. Oxford: Oxford University Press.CrossRefGoogle Scholar
  23. Thomasson, A. L. (2007). Ordinary objects. Oxford: Oxford University Press.CrossRefGoogle Scholar
  24. Unger, P. (1980). The problem of the many. Midwest Studies in Philosophy, 5, 411–468.CrossRefGoogle Scholar
  25. Van Fraassen, B. (1966). Singular terms, truth-value gaps, and free logic. Journal of Philosophy, 63, 481–495.CrossRefGoogle Scholar
  26. Varzi, A. (2001). Vagueness, logic and ontology. The Dialogue. Yearbooks for Philosophical Hermeneutics, 1, 135–154.Google Scholar
  27. Varzi, A. (2007). Supervaluationism and its logics. Mind, 116(2007), 633–676.CrossRefGoogle Scholar
  28. Williams, J. R. G. (2008). Supervaluationism and logical revisionism. The Journal of Philosophy, 105(4), 192–212.CrossRefGoogle Scholar
  29. Williamson, T. (1994). Vagueness. London: Routledge.Google Scholar
  30. Williamson, T. (1997). Imagination, stipulation and vagueness. Philosophical Issues, 8, 215–228.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.University of Hamburg – Phlox Research GroupHamburgGermany

Personalised recommendations