Collapse, Plurals and Sets
Vol 18, No 3 (2014) • Principia: an international journal of epistemology
Autor: Eduardo Alejandro Barrio
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.
Texto Completo: https://periodicos.ufsc.br/index.php/principia/article/view/1808-1711.2014v18n3p419/29902
Palavras-Chave: Pluralities,absolute generality,sets,hierarch
"Principia: an international journal of epistemology" was founded in 1997 and regularly publishes articles, discussions and review. The journal aims to publish original scholarly work especially in epistemology area , with an emphasis on material of general interest to academic philosophers. Originally published only in print version (ISSN: 1414-4247), in 2005 the journal began to be published also in online version (ISSN: 1808-1711). Since 1999 are published three issues per year: in April, August and December. Qualis CAPES: A2