Mereological Composition and Plural Quantifier Semantics
- 110 Downloads
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.
KeywordsComposition 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.
- Casati, R., & Varzi, A. C. (1999). Parts and places - the structures of spatial representation. Cambridge: MIT Press.Google Scholar
- 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
- 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
- Hirsch, E. (2010). Quantifier variance and realism: Essays in Metaontology. Oxford: OUP.Google Scholar
- Lewis, D. K. (1986). On the plurality of worlds. Oxford: Basil Blackwell.Google Scholar
- Lewis, D. K. (1991). Parts of classes. Oxford: Basil Blackwell.Google Scholar
- Lowe, E. J. (1989). Kinds of being: A study of individuation, identity and the logic of Sortal terms. Oxford: Blackwell.Google Scholar
- 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
- Nolt, J. (2014). “Free Logic.” In E. N. Zalta (ed) The Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/archives/win2014/entries/logic-free/.
- Quine, W. V. O. (1974). The Roots of Reference. Lasalle: Open Court.Google Scholar
- Quine, W. V. O. (1982). Methods of logic. Cambridge: Harvard University Press.Google Scholar
- Quine, W. V. O. (1986). Philosophy of logic. Cambridge: Harvard University Press.Google Scholar
- Resnik, Michael D. 1988. Second-order logic still wild. The Journal of Philosophy 85 (2). JSTOR: 75–87.Google Scholar
- Shapiro, S. (1991). Foundations without foundationalism: A case for second-order logic. Cambridge: Cambridge University Press.Google Scholar
- 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
- Simons, P. (1987). Parts - a study in ontology. Oxford: OUP.Google Scholar
- Simons, P. (1991). Free part-whole theory. In K. Lambert (Ed.), Philosophical applications of free logic (pp. 285–306). Oxford: OUP.Google Scholar
- 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
- Van Inwagen, P. (1990). Material beings. Ithaca: Cornell University.Google Scholar