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ON THE ONTOLOGICAL COMMITMENT OF MEREOLOGY

Published online by Cambridge University Press:  01 March 2009

MASSIMILIANO CARRARA*
Affiliation:
Department of Philosophy, University of Padua
ENRICO MARTINO*
Affiliation:
Department of Philosophy, University of Padua
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF PADUA PADOVA, ITALY 35139, E-mail: massimilliano.carrara@unipd.it, enrico.martino@unipd.it
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF PADUA PADOVA, ITALY 35139, E-mail: massimilliano.carrara@unipd.it, enrico.martino@unipd.it

Abstract

In Parts of Classes (1991) and Mathematics Is Megethology (1993) David Lewis defends both the innocence of plural quantification and of mereology. However, he himself claims that the innocence of mereology is different from that of plural reference, where reference to some objects does not require the existence of a single entity picking them out as a whole. In the case of plural quantification “we have many things, in no way do we mention one thing that is the many taken together”. Instead, in the mereological case: “we have many things, we do mention one thing that is the many taken together, but this one thing is nothing different from the many” (Lewis, 1991, p. 87). The aim of the paper is to argue that—for a certain use of mereology, weaker than Lewis’ one—an innocence thesis similar to that of plural reference is defensible. To give a precise account of plural reference, we use the idea of plural choice. We then propose a virtual theory of mereology in which the role of individuals is played by plural choices of atoms.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2009

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References

BIBLIOGRAPHY

Baxter, D. (1988). Identity in the loose and popular sense. Mind, 97, 575582.CrossRefGoogle Scholar
Boolos, G. (1984). To be is to be a value of a variable. (Or to be some values of some variables). Journal of Philosophy, 81, 430449.CrossRefGoogle Scholar
Boolos, G. (1985). Nominalist Platonism. Philosophical Review, 94, 327344.CrossRefGoogle Scholar
Carrara, M., & Martino, E. (2008). On the Alleged Innocence of Mereology. Published online in , University of Padua. Available from: http://paduaresearch.cab.unipd.it/1085/Google Scholar
Copi, I. (1971). The Theory of Logical Types. London, UK: Routledge & Kegan Paul.Google Scholar
Goodman, N. (1977). The Structure of Appearance. Dordrecht, The Netherlands: Reidel Publishing Company.CrossRefGoogle Scholar
Lewis, D. K. (1991). Parts of Classes. Oxford, UK: Oxford University Press.Google Scholar
Lewis, D. K. (1993). Mathematics is megethology. Philosophia Mathematica, 1, 323.CrossRefGoogle Scholar
Martino, E. (2001). Arbitrary reference in mathematical reasoning. Topoi, 20, 6577.CrossRefGoogle Scholar
Martino, E. (2004). Wolves, sheep and logic. In Assenza, E., Chiricò, D., and Perconti, P., editors. Logic, Ontology, and Linguistics. Soveria, Manelli: Rubettino, pp. 75104.Google Scholar
Myhill, J. (1979). A refutation of an unjustified attack on the axiom of reducibility.In Roberts, G. W., editor. Bertrand Russell Memorial Volume. New York, NY: Humanities Press, pp. 8190.Google Scholar