pp 1–16 | Cite as

Mereological Composition and Plural Quantifier Semantics

  • Manuel Lechthaler
  • Ceth Lightfield


Mereological universalists and nihilists disagree on the conditions for composition. In this paper, we show how this debate is a function of one’s chosen semantics for plural quantifiers. Debating mereologists have failed to appreciate this point because of the complexity of the debate and extraneous theoretical commitments. We eliminate this by framing the debate between universalists and nihilists in a formal model where these two theses about composition are contradictory. The examination of the two theories in the model brings clarity to a debate in which opponents frequently talk past one another. With the two views stated precisely, our investigation reveals the dependence of the mereologists’ ontological commitments on the semantics of plural quantifiers. Though we discuss the debate with respect to a simplified and idealized model, the insights provided will make more complex debates on composition more productive and deflationist criticisms of the debate less substantial.


Composition Mereology Plural logic Ontology 



We would like to thank Zach Weber for discussion and comments on an earlier draft, and several anonymous referees for helpful feedback.


  1. Baxter, D. L. M. (1988). Many-one identity. Philosophical Papers, 17(3), 193–216.CrossRefGoogle Scholar
  2. Black, M. (1952). The identity of Indiscernibles. Mind, 61(242), 153–164.CrossRefGoogle Scholar
  3. Boolos, G. (1984). To be is to be a value of a variable (or to be some values of some variables). The Journal of Philosophy, 81(8), 430–449.CrossRefGoogle Scholar
  4. Boolos, G. (1985). Nominalist Platonism. The Philosophical Review, 94(3), 327–344.CrossRefGoogle Scholar
  5. Bricker, P. (2016). Composition as a Kind of identity. Inquiry, 59(3), 264–294.CrossRefGoogle Scholar
  6. Carmichael, C. (2015). Toward a commonsense answer to the special composition questions. Australasian Journal of Philosophy, 93(3), 475–490.CrossRefGoogle Scholar
  7. Casati, R., & Varzi, A. C. (1999). Parts and places - the structures of spatial representation. Cambridge: MIT Press.Google Scholar
  8. Cotnoir, A. J. (2013). Strange parts: The metaphysics of non-classical mereologies. Philosophy Compass, 8(9), 834–845.CrossRefGoogle Scholar
  9. Cotnoir, A. J. (2014). Composition as identity: Framing the debate. In A. J. Cotnoir & D. L. M. Baxter (Eds.), Composition as identity (pp. 3–23). Oxford: OUP.CrossRefGoogle Scholar
  10. Dorr, C. (2005). What we disagree about when we disagree about ontology. In M. E. Kalderon (Ed.), Fictionalism in metaphysics (pp. 234–286). Oxford: OUP.Google Scholar
  11. Frege, G. (1884). Die Grundlagen der Arithmetik - Eine logisch mathematische Untersuchung über den Begriff der Zahl. Breslau: Verlag von Wilhelm Koebner. (Reprinted and translated by J. L. Austin. 1968. The Foundations of Arithmetic - A logico-mathematical enquiry into the concept of number. Oxford: Basil Blackwell, second revised edition).Google Scholar
  12. Hirsch, E. (2010). Quantifier variance and realism: Essays in Metaontology. Oxford: OUP.Google Scholar
  13. Hossack, K. (2000). Plurals and complexes. British Journal for the Philosophy of Science, 51, 411–443.CrossRefGoogle Scholar
  14. Lewis, D. K. (1986). On the plurality of worlds. Oxford: Basil Blackwell.Google Scholar
  15. Lewis, D. K. (1991). Parts of classes. Oxford: Basil Blackwell.Google Scholar
  16. Lewis, D. K. (1999). Rearrangement of particles: Reply to Lowe. In D. K. Lewis (Ed.), Papers in metaphysics and epistemology (pp. 187–195). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  17. Lowe, E. J. (1989). Kinds of being: A study of individuation, identity and the logic of Sortal terms. Oxford: Blackwell.Google Scholar
  18. Marcus, R. B. (1962). Interpreting quantification. Inquiry, 5(1–4), 252–259.CrossRefGoogle Scholar
  19. Marcus, R. B. (1972). Quantification and ontology. Noûs, 6(3), 240–250.CrossRefGoogle Scholar
  20. Marcus, R. B. (1978). Nominalism and the substitutional quantifier. The Monist, 61(3), 351–362.CrossRefGoogle Scholar
  21. Merricks, T. (2001). Objects and persons. Oxford: OUP.CrossRefGoogle Scholar
  22. Moltmann, F. (1998). Part structures, integrity, and the mass-count distinction. Synthese, 116(1), 75–111.CrossRefGoogle Scholar
  23. Musgrave, A. (2001). Metaphysical realism versus word-magic. In D. Aleksandrowicz & H. Ruß (Eds.), Realismus, Disziplin, Interdisziplinarität (pp. 29–54). Amsterdam: Editions Rodopi.Google Scholar
  24. Nolan, D. (2004). Classes, worlds and Hypergunk. The Monist, 87(3), 303–321.CrossRefGoogle Scholar
  25. Nolt, J. (2014). “Free Logic.” In E. N. Zalta (ed) The Stanford Encyclopedia of Philosophy.
  26. Oliver, A., & Smiley, T. (2013). Plural logic. Oxford: Oxford University Press.CrossRefGoogle Scholar
  27. Quine, W. V. O. (1951). Ontology and ideology. Philosophical Studies, 2(1), 11–15.CrossRefGoogle Scholar
  28. Quine, W. V. O. (1974). The Roots of Reference. Lasalle: Open Court.Google Scholar
  29. Quine, W. V. O. (1982). Methods of logic. Cambridge: Harvard University Press.Google Scholar
  30. Quine, W. V. O. (1986). Philosophy of logic. Cambridge: Harvard University Press.Google Scholar
  31. Rea, M. (1998). In defense of mereological universalism. Philosophy and Phenomenological Research, 58(2), 347–360.CrossRefGoogle Scholar
  32. Rescher, N. (1955). Axioms for the part-whole relation. Philosophical Studies, 6(1), 8–11.CrossRefGoogle Scholar
  33. Resnik, Michael D. 1988. Second-order logic still wild. The Journal of Philosophy 85 (2). JSTOR: 75–87.Google Scholar
  34. Shapiro, S. (1991). Foundations without foundationalism: A case for second-order logic. Cambridge: Cambridge University Press.Google Scholar
  35. Shapiro, S. (2005). Higher-order logic. In S. Shapiro (Ed.), The Oxford handbook of philosophy of mathematics and logic. Oxford: OUP.CrossRefGoogle Scholar
  36. Sider, T. (2001). Four-Dimensionalism: An ontology of persistence and time. Oxford: OUP.CrossRefGoogle Scholar
  37. Sider, T. (2013). Against parthood. In K. Bennett & D. W. Zimmerman (Eds.), Oxford studies in metaphysics (Vol. 8, pp. 237–293). Oxford: OUP.Google Scholar
  38. Simons, P. (1987). Parts - a study in ontology. Oxford: OUP.Google Scholar
  39. Simons, P. (1991). Free part-whole theory. In K. Lambert (Ed.), Philosophical applications of free logic (pp. 285–306). Oxford: OUP.Google Scholar
  40. Thomson, J. J. (1998). The statue and the clay. Noûs, 32(2), 149–173.CrossRefGoogle Scholar
  41. Turner, J. (2013). Existence and many-one identity. The Philosophical Quarterly, 63(250), 313–329.CrossRefGoogle Scholar
  42. Van Cleve, J. (2008). The moon and sixpence. In T. Sider, J. Hawthorne, & D. W. Zimmerman (Eds.), Contemporary debates in metaphysics (pp. 321–340). Oxford: Blackwell.Google Scholar
  43. Van Inwagen, P. (1990). Material beings. Ithaca: Cornell University.Google Scholar
  44. Varzi, A. C. (2000). Mereological commitments. Dialectica, 54(4), 283–305.CrossRefGoogle Scholar
  45. Zimmerman, D. W. (1996). Could extended objects be made out of simple parts? An argument for ‘Atomless gunk’. Philosophy and Phenomenological Research, 56(1), 1–29.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of OtagoDunedinNew Zealand
  2. 2.Department of PhilosophyUniversity of California, DavisDavisUSA

Personalised recommendations