Collapse, Plurals and Sets

This paper raises the question under what circumstances a plurality forms a set. My main point is that not always all things form sets. A provocative way of presenting my position is that, as a result of my approach, there are more pluralities than sets. Another way of presenting the same thesis cla...

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Bibliographic Details
Published in:Principia 2014-12, Vol.18 (3), p.419-438
Main Author: Barrio, Eduardo Alejandro
Format: Article
Language:English
Subjects:
absolute generality
Economic models
hierarchies
Multiculturalism & pluralism
Pluralities
Set theory
sets
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Summary:This paper raises the question under what circumstances a plurality forms a set. My main point is that not always all things form sets. A provocative way of presenting my position is that, as a result of my approach, there are more pluralities than sets. Another way of presenting the same thesis claims that there are ways of talking about objects that do not always collapse into sets. My argument is related to expressive powers of formal languages. Assuming classical logic, I show that if all plurality form a set and the quantifiers are absolutely general, then one gets a trivial theory. So, by reductio, one has to abandon one of the premiss. Then, I argue against the collapse of the pluralities into sets. What I am advocating is that the thesis of collapse limits important applications of the plural logic in model theory, when it is assumed that the quantifiers are absolutely general.
ISSN:1414-4247
1808-1711
DOI:10.5007/1808-1711.2014v18n3p419