Notes on w-inconsistent Theories of Truth in Second-Order Languages

Autores
Barrio, Eduardo Alejandro; Picollo, Lavinia María
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
It is widely accepted that a theory of truth for arithmetic should be consistent, but ω-consistency is less frequently required. This paper argues that ω-consistency is a highly desirable feature for such theories. The point has already been made for first-order languages, though the evidence is not entirely conclusive. We show that in the second-order case the consequence of adopting ω-inconsistent truth theories for arithmetic is unsatisfiability. In order to bring out this point, well known ω-inconsistent theories of truth are considered: the revision theory of nearly stable truth T# and the classical theory of symmetric truth FS. Briefly, we present some conceptual problems with ω-inconsistent theories, and demonstrate some technical results that support our criticisms of such theories.
Fil: Barrio, Eduardo Alejandro. Universidad de Buenos Aires. Facultad de Filosofía y Letras. Instituto de Filosofía "Dr. Alejandro Korn"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Picollo, Lavinia María. Universidad de Buenos Aires. Facultad de Filosofía y Letras. Instituto de Filosofía "Dr. Alejandro Korn"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Truth
Second Order Arithmetic
Omega Inconsistency
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:11336/3658
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Notes on w-inconsistent Theories of Truth in Second-Order LanguagesBarrio, Eduardo AlejandroPicollo, Lavinia MaríaTruthSecond Order ArithmeticOmega Inconsistencyhttps://purl.org/becyt/ford/6.3https://purl.org/becyt/ford/6It is widely accepted that a theory of truth for arithmetic should be consistent, but ω-consistency is less frequently required. This paper argues that ω-consistency is a highly desirable feature for such theories. The point has already been made for first-order languages, though the evidence is not entirely conclusive. We show that in the second-order case the consequence of adopting ω-inconsistent truth theories for arithmetic is unsatisfiability. In order to bring out this point, well known ω-inconsistent theories of truth are considered: the revision theory of nearly stable truth T# and the classical theory of symmetric truth FS. Briefly, we present some conceptual problems with ω-inconsistent theories, and demonstrate some technical results that support our criticisms of such theories.Fil: Barrio, Eduardo Alejandro. Universidad de Buenos Aires. Facultad de Filosofía y Letras. Instituto de Filosofía "Dr. Alejandro Korn"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Picollo, Lavinia María. Universidad de Buenos Aires. Facultad de Filosofía y Letras. Instituto de Filosofía "Dr. Alejandro Korn"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaCambridge University Press2013-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/3658Barrio, Eduardo Alejandro; Picollo, Lavinia María; Notes on w-inconsistent Theories of Truth in Second-Order Languages; Cambridge University Press; Review of Symbolic Logic; VI; 4; 12-2013; 733-7411755-0203enginfo:eu-repo/semantics/altIdentifier/url/http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9082404info:eu-repo/semantics/altIdentifier/doi/10.1017/S1755020313000269info:eu-repo/semantics/altIdentifier/issn/1755-0203info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:26:11Zoai:ri.conicet.gov.ar:11336/3658instacron: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 14:26:12.182CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Notes on w-inconsistent Theories of Truth in Second-Order Languages
title Notes on w-inconsistent Theories of Truth in Second-Order Languages
spellingShingle Notes on w-inconsistent Theories of Truth in Second-Order Languages
Barrio, Eduardo Alejandro
Truth
Second Order Arithmetic
Omega Inconsistency
title_short Notes on w-inconsistent Theories of Truth in Second-Order Languages
title_full Notes on w-inconsistent Theories of Truth in Second-Order Languages
title_fullStr Notes on w-inconsistent Theories of Truth in Second-Order Languages
title_full_unstemmed Notes on w-inconsistent Theories of Truth in Second-Order Languages
title_sort Notes on w-inconsistent Theories of Truth in Second-Order Languages
dc.creator.none.fl_str_mv Barrio, Eduardo Alejandro
Picollo, Lavinia María
author Barrio, Eduardo Alejandro
author_facet Barrio, Eduardo Alejandro
Picollo, Lavinia María
author_role author
author2 Picollo, Lavinia María
author2_role author
dc.subject.none.fl_str_mv Truth
Second Order Arithmetic
Omega Inconsistency
topic Truth
Second Order Arithmetic
Omega Inconsistency
purl_subject.fl_str_mv https://purl.org/becyt/ford/6.3
https://purl.org/becyt/ford/6
dc.description.none.fl_txt_mv It is widely accepted that a theory of truth for arithmetic should be consistent, but ω-consistency is less frequently required. This paper argues that ω-consistency is a highly desirable feature for such theories. The point has already been made for first-order languages, though the evidence is not entirely conclusive. We show that in the second-order case the consequence of adopting ω-inconsistent truth theories for arithmetic is unsatisfiability. In order to bring out this point, well known ω-inconsistent theories of truth are considered: the revision theory of nearly stable truth T# and the classical theory of symmetric truth FS. Briefly, we present some conceptual problems with ω-inconsistent theories, and demonstrate some technical results that support our criticisms of such theories.
Fil: Barrio, Eduardo Alejandro. Universidad de Buenos Aires. Facultad de Filosofía y Letras. Instituto de Filosofía "Dr. Alejandro Korn"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Picollo, Lavinia María. Universidad de Buenos Aires. Facultad de Filosofía y Letras. Instituto de Filosofía "Dr. Alejandro Korn"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description It is widely accepted that a theory of truth for arithmetic should be consistent, but ω-consistency is less frequently required. This paper argues that ω-consistency is a highly desirable feature for such theories. The point has already been made for first-order languages, though the evidence is not entirely conclusive. We show that in the second-order case the consequence of adopting ω-inconsistent truth theories for arithmetic is unsatisfiability. In order to bring out this point, well known ω-inconsistent theories of truth are considered: the revision theory of nearly stable truth T# and the classical theory of symmetric truth FS. Briefly, we present some conceptual problems with ω-inconsistent theories, and demonstrate some technical results that support our criticisms of such theories.
publishDate 2013
dc.date.none.fl_str_mv 2013-12
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/11336/3658
Barrio, Eduardo Alejandro; Picollo, Lavinia María; Notes on w-inconsistent Theories of Truth in Second-Order Languages; Cambridge University Press; Review of Symbolic Logic; VI; 4; 12-2013; 733-741
1755-0203
url http://hdl.handle.net/11336/3658
identifier_str_mv Barrio, Eduardo Alejandro; Picollo, Lavinia María; Notes on w-inconsistent Theories of Truth in Second-Order Languages; Cambridge University Press; Review of Symbolic Logic; VI; 4; 12-2013; 733-741
1755-0203
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9082404
info:eu-repo/semantics/altIdentifier/doi/10.1017/S1755020313000269
info:eu-repo/semantics/altIdentifier/issn/1755-0203
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 Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
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 13.22299

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