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ON THE ONTOLOGICAL COMMITMENT OF MEREOLOGY

  • MASSIMILIANO CARRARA (a1) and ENRICO MARTINO (a1)
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.

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*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF PADUA PADOVA, ITALY 35139, E-mail: massimilliano.carrara@unipd.it, enrico.martino@unipd.it
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

G Boolos . (1984). To be is to be a value of a variable. (Or to be some values of some variables). Journal of Philosophy, 81, 430449.

G Boolos . (1985). Nominalist Platonism. Philosophical Review, 94, 327344.

N Goodman . (1977). The Structure of Appearance. Dordrecht, The Netherlands: Reidel Publishing Company.

D. K Lewis . (1993). Mathematics is megethology. Philosophia Mathematica, 1, 323.

E Martino . (2001). Arbitrary reference in mathematical reasoning. Topoi, 20, 6577.

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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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