Solving Multimodal Paradoxes

Autores
Pailos, Federico Matias; Rosenblatt, Lucas Daniel
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Recently, it has been observed that the usual type-theoretic restrictions are not enough to block certain paradoxes involving two or more predicates. In particular, when we have a self-referential language containing modal predicates, new paradoxes might appear even if there are type restrictions for the principles governing those predicates. In this article we consider two type-theoretic solutions to multimodal paradoxes. The first one adds types for each of the modal predicates. We argue that there are a number of problems with most versions of this approach. The second one, which we favour, represents modal notions by using the truth predicate together with the corresponding modal operator. This way of doing things is not only useful because it avoids multimodal paradoxes, but also because it preserves the expressive capacity of the language. As an example of the sort of theory we have in mind, we provide a type-theoretic axiomatization that combines truth with necessity and knowledge.
Fil: Pailos, Federico Matias. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Rosenblatt, Lucas Daniel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Multimodal Paradoxes
Semantic Paradoxes
Truth
Type-Theory
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:11336/36260
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Solving Multimodal ParadoxesPailos, Federico MatiasRosenblatt, Lucas DanielMultimodal ParadoxesSemantic ParadoxesTruthType-Theoryhttps://purl.org/becyt/ford/6.3https://purl.org/becyt/ford/6Recently, it has been observed that the usual type-theoretic restrictions are not enough to block certain paradoxes involving two or more predicates. In particular, when we have a self-referential language containing modal predicates, new paradoxes might appear even if there are type restrictions for the principles governing those predicates. In this article we consider two type-theoretic solutions to multimodal paradoxes. The first one adds types for each of the modal predicates. We argue that there are a number of problems with most versions of this approach. The second one, which we favour, represents modal notions by using the truth predicate together with the corresponding modal operator. This way of doing things is not only useful because it avoids multimodal paradoxes, but also because it preserves the expressive capacity of the language. As an example of the sort of theory we have in mind, we provide a type-theoretic axiomatization that combines truth with necessity and knowledge.Fil: Pailos, Federico Matias. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Rosenblatt, Lucas Daniel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaWiley2014-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/36260Pailos, Federico Matias; Rosenblatt, Lucas Daniel; Solving Multimodal Paradoxes; Wiley; Theoria; 81; 3; 4-2014; 192-2101755-2567CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1111/theo.12052info:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1111/theo.12052/abstractinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:14:19Zoai:ri.conicet.gov.ar:11336/36260instacron: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:34982025-10-15 15:14:19.464CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Solving Multimodal Paradoxes
title Solving Multimodal Paradoxes
spellingShingle Solving Multimodal Paradoxes
Pailos, Federico Matias
Multimodal Paradoxes
Semantic Paradoxes
Truth
Type-Theory
title_short Solving Multimodal Paradoxes
title_full Solving Multimodal Paradoxes
title_fullStr Solving Multimodal Paradoxes
title_full_unstemmed Solving Multimodal Paradoxes
title_sort Solving Multimodal Paradoxes
dc.creator.none.fl_str_mv Pailos, Federico Matias
Rosenblatt, Lucas Daniel
author Pailos, Federico Matias
author_facet Pailos, Federico Matias
Rosenblatt, Lucas Daniel
author_role author
author2 Rosenblatt, Lucas Daniel
author2_role author
dc.subject.none.fl_str_mv Multimodal Paradoxes
Semantic Paradoxes
Truth
Type-Theory
topic Multimodal Paradoxes
Semantic Paradoxes
Truth
Type-Theory
purl_subject.fl_str_mv https://purl.org/becyt/ford/6.3
https://purl.org/becyt/ford/6
dc.description.none.fl_txt_mv Recently, it has been observed that the usual type-theoretic restrictions are not enough to block certain paradoxes involving two or more predicates. In particular, when we have a self-referential language containing modal predicates, new paradoxes might appear even if there are type restrictions for the principles governing those predicates. In this article we consider two type-theoretic solutions to multimodal paradoxes. The first one adds types for each of the modal predicates. We argue that there are a number of problems with most versions of this approach. The second one, which we favour, represents modal notions by using the truth predicate together with the corresponding modal operator. This way of doing things is not only useful because it avoids multimodal paradoxes, but also because it preserves the expressive capacity of the language. As an example of the sort of theory we have in mind, we provide a type-theoretic axiomatization that combines truth with necessity and knowledge.
Fil: Pailos, Federico Matias. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Rosenblatt, Lucas Daniel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description Recently, it has been observed that the usual type-theoretic restrictions are not enough to block certain paradoxes involving two or more predicates. In particular, when we have a self-referential language containing modal predicates, new paradoxes might appear even if there are type restrictions for the principles governing those predicates. In this article we consider two type-theoretic solutions to multimodal paradoxes. The first one adds types for each of the modal predicates. We argue that there are a number of problems with most versions of this approach. The second one, which we favour, represents modal notions by using the truth predicate together with the corresponding modal operator. This way of doing things is not only useful because it avoids multimodal paradoxes, but also because it preserves the expressive capacity of the language. As an example of the sort of theory we have in mind, we provide a type-theoretic axiomatization that combines truth with necessity and knowledge.
publishDate 2014
dc.date.none.fl_str_mv 2014-04
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/11336/36260
Pailos, Federico Matias; Rosenblatt, Lucas Daniel; Solving Multimodal Paradoxes; Wiley; Theoria; 81; 3; 4-2014; 192-210
1755-2567
CONICET Digital
CONICET
url http://hdl.handle.net/11336/36260
identifier_str_mv Pailos, Federico Matias; Rosenblatt, Lucas Daniel; Solving Multimodal Paradoxes; Wiley; Theoria; 81; 3; 4-2014; 192-210
1755-2567
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1111/theo.12052
info:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1111/theo.12052/abstract
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 Wiley
publisher.none.fl_str_mv Wiley
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 12.891075

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