Collapse, Plurals and Sets

Autores
Barrio, Eduardo Alejandro
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fil: Barrio, Eduardo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
COLLAPSE
ABSOLUTE GENERALITY
PARADOXES
PLURALITIES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/46515

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spelling Collapse, Plurals and SetsBarrio, Eduardo AlejandroCOLLAPSEABSOLUTE GENERALITYPARADOXESPLURALITIEShttps://purl.org/becyt/ford/6.3https://purl.org/becyt/ford/6This 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.Fil: Barrio, Eduardo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaUniversidade Federal de Santa Catarina2014-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/46515Barrio, Eduardo Alejandro; Collapse, Plurals and Sets; Universidade Federal de Santa Catarina; Principia; 18; 3; 12-2014; 419-4381808-17111414-4247CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.5007/1808-1711.2014v18n3p419info:eu-repo/semantics/altIdentifier/url/https://periodicos.ufsc.br/index.php/principia/article/view/1808-1711.2014v18n3p419info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:40:50Zoai:ri.conicet.gov.ar:11336/46515instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:40:50.959CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Collapse, Plurals and Sets
title Collapse, Plurals and Sets
spellingShingle Collapse, Plurals and Sets
Barrio, Eduardo Alejandro
COLLAPSE
ABSOLUTE GENERALITY
PARADOXES
PLURALITIES
title_short Collapse, Plurals and Sets
title_full Collapse, Plurals and Sets
title_fullStr Collapse, Plurals and Sets
title_full_unstemmed Collapse, Plurals and Sets
title_sort Collapse, Plurals and Sets
dc.creator.none.fl_str_mv Barrio, Eduardo Alejandro
author Barrio, Eduardo Alejandro
author_facet Barrio, Eduardo Alejandro
author_role author
dc.subject.none.fl_str_mv COLLAPSE
ABSOLUTE GENERALITY
PARADOXES
PLURALITIES
topic COLLAPSE
ABSOLUTE GENERALITY
PARADOXES
PLURALITIES
purl_subject.fl_str_mv https://purl.org/becyt/ford/6.3
https://purl.org/becyt/ford/6
dc.description.none.fl_txt_mv 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.
Fil: Barrio, Eduardo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description 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.
publishDate 2014
dc.date.none.fl_str_mv 2014-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/46515
Barrio, Eduardo Alejandro; Collapse, Plurals and Sets; Universidade Federal de Santa Catarina; Principia; 18; 3; 12-2014; 419-438
1808-1711
1414-4247
CONICET Digital
CONICET
url http://hdl.handle.net/11336/46515
identifier_str_mv Barrio, Eduardo Alejandro; Collapse, Plurals and Sets; Universidade Federal de Santa Catarina; Principia; 18; 3; 12-2014; 419-438
1808-1711
1414-4247
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.5007/1808-1711.2014v18n3p419
info:eu-repo/semantics/altIdentifier/url/https://periodicos.ufsc.br/index.php/principia/article/view/1808-1711.2014v18n3p419
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Universidade Federal de Santa Catarina
publisher.none.fl_str_mv Universidade Federal de Santa Catarina
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432