On the Infinite in Mereology with Plural Quantification

Review of Symbolic Logic 4 (1):54-62 (2010)
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
Categories (categorize this paper)
Reprint years 2011
DOI 10.1017/S1755020310000158
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 27,636
Through your library
References found in this work BETA
Parts of Classes.David Lewis - 1991 - Blackwell.
Parts: A Study in Ontology.Peter M. Simons - 1987 - Oxford University Press.
Nominalist Platonism.George Boolos - 1985 - Philosophical Review 94 (3):327-344.
Mathematics is Megethology.David Lewis - 1993 - Philosophia Mathematica 1 (1):3-23.
On the Ontological Commitment of Mereology.Massimiliano Carrara & Enrico Martino - 2009 - Review of Symbolic Logic 2 (1):164-174.

View all 8 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles
Plural Quantification.Øystein Linnebo - 2008 - Stanford Encyclopedia of Philosophy.
Plural Logicism.Francesca Boccuni - 2013 - Erkenntnis 78 (5):1051-1067.
On What There Are.Philippe De Rouilhan - 2002 - Proceedings of the Aristotelian Society 102:183 - 200.
The Logic of Finite Order.Simon Hewitt - 2012 - Notre Dame Journal of Formal Logic 53 (3):297-318.
Plural Quantification and Classes.Gabriel Uzquiano - 2003 - Philosophia Mathematica 11 (1):67-81.
Infinity in Ontology and Mind.Nino Cocchiarella - 2008 - Axiomathes 18 (1):1-24.

Monthly downloads

Added to index

2012-05-05

Total downloads

64 ( #81,946 of 2,169,144 )

Recent downloads (6 months)

2 ( #186,285 of 2,169,144 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums