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    Carrara, Massimiliano and Martino, Enrico 2015. Grounding Megethology on Plural Reference. Studia Logica, Vol. 103, Issue. 4, p. 697.


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ON THE INFINITE IN MEREOLOGY WITH PLURAL QUANTIFICATION

  • MASSIMILIANO CARRARA (a1) and ENRICO MARTINO (a1)
  • DOI: http://dx.doi.org/10.1017/S1755020310000158
  • Published online: 17 September 2010
Abstract

In “Mathematics is megethology,” Lewis reconstructs set theory using mereology and plural quantification (MPQ). In his recontruction he assumes from the beginning that there is an infinite plurality of atoms, whose size is equivalent to that of the set theoretical universe. Since this assumption is far beyond the basic axioms of mereology, it might seem that MPQ do not play any role in order to guarantee the existence of a large infinity of objects. However, we intend to demonstrate that mereology and plural quantification are, in some ways, particularly relevant to a certain conception of the infinite. More precisely, though the principles of mereology and plural quantification do not guarantee the existence of an infinite number of objects, nevertheless, once the existence of any infinite object is admitted, they are able to assure the existence of an uncountable infinity of objects. So, if—as Lewis maintains—MPQ were parts of logic, the implausible consequence would follow that, given a countable infinity of individuals, logic would be able to guarantee an uncountable infinity of objects.

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*DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF PADUA, PADOVA, ITALY. E-mail:massimiliano.carrara@unipd.it
DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF PADUA, PADOVA, ITALY. E-mail: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.

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

S. Pollard (1988). Plural quantification and the axiom of choice. Philosophical Studies, 54, 393397.

P. Simons (2000). Parts: A Study in Ontology. Oxford, UK: Oxford University Press.

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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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