Peirce and modal logic: delta existential graphs and pragmaticism

Although modern modal logic came about largely after Peirce's death, he anticipated some of its key aspects, including strict implication and possible worlds semantics. He developed the Gamma part of Existential Graphs with broken cuts signifying possible falsity, but later identified the need...

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Detalles Bibliográficos
Autor: Schmidt, Jon Alan
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:Brasil
Institución:Pontifícia Universidade Católica de São Paulo (PUC-SP)
Repositorio:Cognitio (São Paulo. Online)
Idioma:inglés
OAI Identifier:oai:ojs.pkp.sfu.ca:article/60449
Acceso en línea:https://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/60449
Access Level:acceso abierto
Palabra clave:Existential Graphs
Modal logic
Peirce
Possible worlds semantics
Pragmaticism
Grafos existenciais
Lógica modal
Pragmaticismo
Semântica dos mundos possíveis
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spelling Peirce and modal logic: delta existential graphs and pragmaticismPeirce e a lógica modal: grafos existenciais delta e pragmaticismoExistential GraphsModal logicPeircePossible worlds semanticsPragmaticismGrafos existenciaisLógica modalPeircePragmaticismoSemântica dos mundos possíveisAlthough modern modal logic came about largely after Peirce's death, he anticipated some of its key aspects, including strict implication and possible worlds semantics. He developed the Gamma part of Existential Graphs with broken cuts signifying possible falsity, but later identified the need for a Delta part without ever spelling out exactly what he had in mind. An entry in his personal Logic Notebook is a plausible candidate, with heavy lines representing possible states of things where propositions denoted by attached letters would be true, rather than individual subjects to which predicates denoted by attached names are attributed as in the Beta part. New transformation rules implement various commonly employed formal systems of modal logic, which are readily interpreted by defining a possible world as one in which all the relevant laws for the actual world are facts, each world being partially but accurately and adequately described by a closed and consistent model set of propositions. In accordance with pragmaticism, the relevant laws for the actual world are represented as strict implications with real possibilities as their antecedents and conditional necessities as their consequents, corresponding to material implications in every possible world.Embora a lógica modal moderna tenha surgido em grande parte após a morte de Peirce, ele antecipou alguns de seus principais aspectos, incluindo implicação estrita e semântica de mundos possíveis. Ele desenvolveu a parte Gamma dos Gráficos Existenciais com cortes quebrados significando possível falsidade, mas depois identificou a necessidade de uma parte Delta sem nunca soletrar exatamente o que tinha em mente. Uma entrada em seu Caderno de Lógica pessoal é um candidato plausível, com linhas grossas representando possíveis estados de coisas onde proposições denotadas por letras anexadas seriam verdadeiras, em vez de sujeitos individuais aos quais predicados denotados por nomes anexados são atribuídos como na parte Beta. Novas regras de transformação implementam vários sistemas formais comumente empregados de lógica modal, que são prontamente interpretados definindo um mundo possível como aquele em que todas as leis relevantes para o mundo real são fatos, cada mundo sendo parcialmente, mas precisamente e adequadamente descrito por um conjunto de modelos de proposições fechado e consistente. De acordo com o pragmaticismo, as leis relevantes para o mundo real são representadas como implicações estritas com possibilidades reais como seus antecedentes e necessidades condicionais como seus consequentes, correspondendo a implicações materiais em todos os mundos possíveis.Pontifícia Universidade Católica de São Paulo2025-01-31info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/6044910.23925/2316-5278.2025v26i1:e60449Cognitio: Revista de Filosofia; Vol. 26 No. 1 (2025): Cognitio: Revista de Filosofia; e60449Cognitio: Revista de Filosofia; v. 26 n. 1 (2025): Cognitio: Revista de Filosofia; e604492316-52781518-7187reponame:Cognitio (São Paulo. Online)instname:Pontifícia Universidade Católica de São Paulo (PUC-SP)instacron:PUC_SPenghttps://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/60449/46975Copyright (c) 2025 http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessSchmidt, Jon Alan2025-02-01T02:20:25Zoai:ojs.pkp.sfu.ca:article/60449Revistahttps://revistas.pucsp.br/index.php/cognitiofilosofiaPRIhttps://revistas.pucsp.br/index.php/cognitiofilosofia/oairevcognitio@gmail.com2316-52781518-7187opendoar:2025-02-01T02:20:25Cognitio (São Paulo. Online) - Pontifícia Universidade Católica de São Paulo (PUC-SP)false
dc.title.none.fl_str_mv Peirce and modal logic: delta existential graphs and pragmaticism
Peirce e a lógica modal: grafos existenciais delta e pragmaticismo
title Peirce and modal logic: delta existential graphs and pragmaticism
spellingShingle Peirce and modal logic: delta existential graphs and pragmaticism
Schmidt, Jon Alan
Existential Graphs
Modal logic
Peirce
Possible worlds semantics
Pragmaticism
Grafos existenciais
Lógica modal
Peirce
Pragmaticismo
Semântica dos mundos possíveis
title_short Peirce and modal logic: delta existential graphs and pragmaticism
title_full Peirce and modal logic: delta existential graphs and pragmaticism
title_fullStr Peirce and modal logic: delta existential graphs and pragmaticism
title_full_unstemmed Peirce and modal logic: delta existential graphs and pragmaticism
title_sort Peirce and modal logic: delta existential graphs and pragmaticism
dc.creator.none.fl_str_mv Schmidt, Jon Alan
author Schmidt, Jon Alan
author_facet Schmidt, Jon Alan
author_role author
dc.subject.por.fl_str_mv Existential Graphs
Modal logic
Peirce
Possible worlds semantics
Pragmaticism
Grafos existenciais
Lógica modal
Peirce
Pragmaticismo
Semântica dos mundos possíveis
topic Existential Graphs
Modal logic
Peirce
Possible worlds semantics
Pragmaticism
Grafos existenciais
Lógica modal
Peirce
Pragmaticismo
Semântica dos mundos possíveis
description Although modern modal logic came about largely after Peirce's death, he anticipated some of its key aspects, including strict implication and possible worlds semantics. He developed the Gamma part of Existential Graphs with broken cuts signifying possible falsity, but later identified the need for a Delta part without ever spelling out exactly what he had in mind. An entry in his personal Logic Notebook is a plausible candidate, with heavy lines representing possible states of things where propositions denoted by attached letters would be true, rather than individual subjects to which predicates denoted by attached names are attributed as in the Beta part. New transformation rules implement various commonly employed formal systems of modal logic, which are readily interpreted by defining a possible world as one in which all the relevant laws for the actual world are facts, each world being partially but accurately and adequately described by a closed and consistent model set of propositions. In accordance with pragmaticism, the relevant laws for the actual world are represented as strict implications with real possibilities as their antecedents and conditional necessities as their consequents, corresponding to material implications in every possible world.
publishDate 2025
dc.date.none.fl_str_mv 2025-01-31
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/60449
10.23925/2316-5278.2025v26i1:e60449
url https://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/60449
identifier_str_mv 10.23925/2316-5278.2025v26i1:e60449
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/60449/46975
dc.rights.driver.fl_str_mv Copyright (c) 2025 http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2025 http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Pontifícia Universidade Católica de São Paulo
publisher.none.fl_str_mv Pontifícia Universidade Católica de São Paulo
dc.source.none.fl_str_mv Cognitio: Revista de Filosofia; Vol. 26 No. 1 (2025): Cognitio: Revista de Filosofia; e60449
Cognitio: Revista de Filosofia; v. 26 n. 1 (2025): Cognitio: Revista de Filosofia; e60449
2316-5278
1518-7187
reponame:Cognitio (São Paulo. Online)
instname:Pontifícia Universidade Católica de São Paulo (PUC-SP)
instacron:PUC_SP
instname_str Pontifícia Universidade Católica de São Paulo (PUC-SP)
instacron_str PUC_SP
institution PUC_SP
reponame_str Cognitio (São Paulo. Online)
collection Cognitio (São Paulo. Online)
repository.name.fl_str_mv Cognitio (São Paulo. Online) - Pontifícia Universidade Católica de São Paulo (PUC-SP)
repository.mail.fl_str_mv revcognitio@gmail.com
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