Mathematical Individuality in Charles Sanders Peirce
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Cognitio (São Paulo. Online) |
Texto Completo: | https://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/13605 |
Resumo: | Peirce regards mathematics as an informative science capable of really increasing our knowledge. This means that mathematics is not limited to conceptual analysis but possesses a real object of investigation. The core of Peirce’s view of mathematics is that mathematical reasoning is not developed through general concepts alone but deals with an unavoidable element of individuality. The conclusion of a deductive inference can contain information that is not at all present in its premises and can only come into being through concrete work on the part of the mathematician. Peirce describes this work as observation and experimentation on individual diagrams. While the idea of an individual element in mathematics is already present in Kant (and can also be traced back to Aristotle), the different location Peirce assigns it attests to a marked difference in their conceptions, the basis of which lies in the difference between Kant and Peirce in categorial analysis. Peirce’s semiotic approach to mathematics involves a shift from the plane of the object denoted to that of the sign itself. This holds true for geometric as well as algebraic inferences, which Peirce can equate in this respect. In both cases, the individual element of mathematics is thus to be found within the diagram itself with no reference to the object denoted. While the diagram is in any case a token, this cannot explain its essential individuality, to which end the indexical juxtaposition of its parts should be examined. |
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Mathematical Individuality in Charles Sanders PeirceIndividualidade Matemática em Charles Sanders PeirceMatemáticaRaciocínio matemáticoIndividualidadeDiagramaÍndiceMathematicsMathematical reasoningIndividualityDiagramIndexPeirce regards mathematics as an informative science capable of really increasing our knowledge. This means that mathematics is not limited to conceptual analysis but possesses a real object of investigation. The core of Peirce’s view of mathematics is that mathematical reasoning is not developed through general concepts alone but deals with an unavoidable element of individuality. The conclusion of a deductive inference can contain information that is not at all present in its premises and can only come into being through concrete work on the part of the mathematician. Peirce describes this work as observation and experimentation on individual diagrams. While the idea of an individual element in mathematics is already present in Kant (and can also be traced back to Aristotle), the different location Peirce assigns it attests to a marked difference in their conceptions, the basis of which lies in the difference between Kant and Peirce in categorial analysis. Peirce’s semiotic approach to mathematics involves a shift from the plane of the object denoted to that of the sign itself. This holds true for geometric as well as algebraic inferences, which Peirce can equate in this respect. In both cases, the individual element of mathematics is thus to be found within the diagram itself with no reference to the object denoted. While the diagram is in any case a token, this cannot explain its essential individuality, to which end the indexical juxtaposition of its parts should be examined.Peirce considera a matemática uma ciência informativa realmente capaz de aumentar nosso conhecimento. Isso significa que a matemática não é limitada à análise conceitual, mas possui um objeto real de investigação. O coração da visão peirciana da matemática é que o raciocínio matemático não é desenvolvido somente por meio de conceitos gerais, mas lida com um inevitável elemento de individualidade. A conclusão de uma inferência indutiva pode conter informação que não está absolutamente presente nas suas premissas, podendo vir a ser somente por meio de trabalho concreto por parte do matemático. Peirce descreve esse trabalho como observação e experimentação sobre diagramas individuais. Enquanto a idéia de um elemento individual na matemática já está presente em Kant (e pode também ser traçada até Aristóteles), a sua base está na diferença entre Kant e Peirce acerca da análise categorial. A abordagem semiótica peirciana da matemática implica uma mudança, do plano do objeto denotado para o do próprio signo. Isso vale tanto para as inferências geométricas como para as inferências algébricas, que Peirce pode igualar nesse aspecto. Em ambos os casos, o elemento individual da matemática deve ser encontrado dentro do próprio diagrama, sem referência ao objeto denotado. Enquanto o diagrama é em todo caso um token, isso não pode explicar sua individualidade essencial, para cujo fim a justaposição indicial de suas partes deve ser examinada.Pontifícia Universidade Católica de São Paulo2013-02-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/13605Cognitio: Revista de Filosofia; Vol. 6 No. 2 (2005); 201-207Cognitio: Revista de Filosofia; v. 6 n. 2 (2005); 201-2072316-52781518-7187reponame:Cognitio (São Paulo. Online)instname:Pontifícia Universidade Católica de São Paulo (PUC-SP)instacron:PUC_SPenghttps://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/13605/10114Copyright (c) 2013 http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessMarietti, Susanna2024-07-01T13:09:36Zoai:ojs.pkp.sfu.ca:article/13605Revistahttps://revistas.pucsp.br/index.php/cognitiofilosofiaPRIhttps://revistas.pucsp.br/index.php/cognitiofilosofia/oairevcognitio@gmail.com2316-52781518-7187opendoar:2024-07-01T13:09:36Cognitio (São Paulo. Online) - Pontifícia Universidade Católica de São Paulo (PUC-SP)false |
dc.title.none.fl_str_mv |
Mathematical Individuality in Charles Sanders Peirce Individualidade Matemática em Charles Sanders Peirce |
title |
Mathematical Individuality in Charles Sanders Peirce |
spellingShingle |
Mathematical Individuality in Charles Sanders Peirce Marietti, Susanna Matemática Raciocínio matemático Individualidade Diagrama Índice Mathematics Mathematical reasoning Individuality Diagram Index |
title_short |
Mathematical Individuality in Charles Sanders Peirce |
title_full |
Mathematical Individuality in Charles Sanders Peirce |
title_fullStr |
Mathematical Individuality in Charles Sanders Peirce |
title_full_unstemmed |
Mathematical Individuality in Charles Sanders Peirce |
title_sort |
Mathematical Individuality in Charles Sanders Peirce |
author |
Marietti, Susanna |
author_facet |
Marietti, Susanna |
author_role |
author |
dc.contributor.author.fl_str_mv |
Marietti, Susanna |
dc.subject.por.fl_str_mv |
Matemática Raciocínio matemático Individualidade Diagrama Índice Mathematics Mathematical reasoning Individuality Diagram Index |
topic |
Matemática Raciocínio matemático Individualidade Diagrama Índice Mathematics Mathematical reasoning Individuality Diagram Index |
description |
Peirce regards mathematics as an informative science capable of really increasing our knowledge. This means that mathematics is not limited to conceptual analysis but possesses a real object of investigation. The core of Peirce’s view of mathematics is that mathematical reasoning is not developed through general concepts alone but deals with an unavoidable element of individuality. The conclusion of a deductive inference can contain information that is not at all present in its premises and can only come into being through concrete work on the part of the mathematician. Peirce describes this work as observation and experimentation on individual diagrams. While the idea of an individual element in mathematics is already present in Kant (and can also be traced back to Aristotle), the different location Peirce assigns it attests to a marked difference in their conceptions, the basis of which lies in the difference between Kant and Peirce in categorial analysis. Peirce’s semiotic approach to mathematics involves a shift from the plane of the object denoted to that of the sign itself. This holds true for geometric as well as algebraic inferences, which Peirce can equate in this respect. In both cases, the individual element of mathematics is thus to be found within the diagram itself with no reference to the object denoted. While the diagram is in any case a token, this cannot explain its essential individuality, to which end the indexical juxtaposition of its parts should be examined. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013-02-08 |
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/13605 |
url |
https://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/13605 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/13605/10114 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2013 http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2013 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. 6 No. 2 (2005); 201-207 Cognitio: Revista de Filosofia; v. 6 n. 2 (2005); 201-207 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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1803387421281222656 |