The Finitistic Consistency of Heck’s Predicative Fregean System

Detalhes bibliográficos
Autor(a) principal: Cruz-Filipe, L.
Data de Publicação: 2015
Outros Autores: Ferreira, Fernando
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.26/52045
Resumo: Frege’s theory is inconsistent (Russell’s paradox). However, the predicative version of Frege’s system is consistent. This was proved by Richard Heck in 1996 using a model-theoretic argument. In this paper, we give a finitistic proof of this consistency result. As a consequence, Heck’s predicative theory is rather weak (as was suspected).
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spelling The Finitistic Consistency of Heck’s Predicative Fregean SystemconsistencyFregean arithmeticstrict predicativityFrege’s theory is inconsistent (Russell’s paradox). However, the predicative version of Frege’s system is consistent. This was proved by Richard Heck in 1996 using a model-theoretic argument. In this paper, we give a finitistic proof of this consistency result. As a consequence, Heck’s predicative theory is rather weak (as was suspected).Repositório ComumCruz-Filipe, L.Ferreira, Fernando2024-09-11T15:28:49Z20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.26/52045engLuís Cruz-Filipe. Fernando Ferreira. "The Finitistic Consistency of Heck’s Predicative Fregean System." Notre Dame J. Formal Logic 56 (1) 61 - 79, 2015. https://doi.org/10.1215/00294527-2835110https://doi.org/10.1215/00294527-2835110info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-09-15T16:37:25Zoai:comum.rcaap.pt:10400.26/52045Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-09-15T16:37:25Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv The Finitistic Consistency of Heck’s Predicative Fregean System
title The Finitistic Consistency of Heck’s Predicative Fregean System
spellingShingle The Finitistic Consistency of Heck’s Predicative Fregean System
Cruz-Filipe, L.
consistency
Fregean arithmetic
strict predicativity
title_short The Finitistic Consistency of Heck’s Predicative Fregean System
title_full The Finitistic Consistency of Heck’s Predicative Fregean System
title_fullStr The Finitistic Consistency of Heck’s Predicative Fregean System
title_full_unstemmed The Finitistic Consistency of Heck’s Predicative Fregean System
title_sort The Finitistic Consistency of Heck’s Predicative Fregean System
author Cruz-Filipe, L.
author_facet Cruz-Filipe, L.
Ferreira, Fernando
author_role author
author2 Ferreira, Fernando
author2_role author
dc.contributor.none.fl_str_mv Repositório Comum
dc.contributor.author.fl_str_mv Cruz-Filipe, L.
Ferreira, Fernando
dc.subject.por.fl_str_mv consistency
Fregean arithmetic
strict predicativity
topic consistency
Fregean arithmetic
strict predicativity
description Frege’s theory is inconsistent (Russell’s paradox). However, the predicative version of Frege’s system is consistent. This was proved by Richard Heck in 1996 using a model-theoretic argument. In this paper, we give a finitistic proof of this consistency result. As a consequence, Heck’s predicative theory is rather weak (as was suspected).
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-01-01T00:00:00Z
2024-09-11T15:28:49Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.26/52045
url http://hdl.handle.net/10400.26/52045
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Luís Cruz-Filipe. Fernando Ferreira. "The Finitistic Consistency of Heck’s Predicative Fregean System." Notre Dame J. Formal Logic 56 (1) 61 - 79, 2015. https://doi.org/10.1215/00294527-2835110
https://doi.org/10.1215/00294527-2835110
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv mluisa.alvim@gmail.com
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