On the Infinite in Mereology with Plural Quantification

Review of Symbolic Logic 4 (1):54-62 (2011)

Authors
Massimiliano Carrara
University of Padua
Abstract
In 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, ifMPQ 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
Keywords mereology  plural quantification
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Reprint years 2011
DOI 10.1017/s1755020310000158
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Parts: A Study in Ontology.Peter Simons - 1987 - Oxford University Press.
Parts : a Study in Ontology.Peter Simons - 1999 - Revue de Métaphysique et de Morale 2:277-279.
Parts of Classes.David LEWIS - 1991 - Mind 100 (3):394-397.
Parts of Classes.David LEWIS - 1991 - Philosophical Quarterly 43 (172):362-366.

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