Demonstration in geometry: historical and philosophical perspectives
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Revista Pesquisa Qualitativa (Online) |
Texto Completo: | https://editora.sepq.org.br/rpq/article/view/344 |
Resumo: | In this article, we weave historical-philosophical reflections about demonstration in mathematics, based on works of researchers that discuss the different philosophical perspectives on the topic, more specifically on geometry. We focus first on demonstration and its relationship with intuition and figural representations. Second, we criticize Poincaré’s conception of mathematical demonstration. Third, we reflect, in a non-exhaustive way, on the philosophy of demonstration in geometry, confronting Kant’s conceptions with the axiomatizations of the non-Euclidean geometries. In this text, we do not adopt a single definition that would cover all modes of scientific validation, since we admit the possibility of an evolution of ideas about the validity of a proposition. Not to fall into the symmetrical flaws of the glorification of the Ancients or even being ungrateful to them, we must start from the naive idea that the demonstration has a historical origin and, therefore, maintains a historical character, but we should be more attentive to what characterizes, in its particularity or even its uniqueness, the productions of past and present centuries. Keywords: Philosophy of demonstration; Axiomatization; Induction; Intuition; Representation. |
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Demonstration in geometry: historical and philosophical perspectivesDemonstração em geometria: perspectivas histórica e filosóficaIn this article, we weave historical-philosophical reflections about demonstration in mathematics, based on works of researchers that discuss the different philosophical perspectives on the topic, more specifically on geometry. We focus first on demonstration and its relationship with intuition and figural representations. Second, we criticize Poincaré’s conception of mathematical demonstration. Third, we reflect, in a non-exhaustive way, on the philosophy of demonstration in geometry, confronting Kant’s conceptions with the axiomatizations of the non-Euclidean geometries. In this text, we do not adopt a single definition that would cover all modes of scientific validation, since we admit the possibility of an evolution of ideas about the validity of a proposition. Not to fall into the symmetrical flaws of the glorification of the Ancients or even being ungrateful to them, we must start from the naive idea that the demonstration has a historical origin and, therefore, maintains a historical character, but we should be more attentive to what characterizes, in its particularity or even its uniqueness, the productions of past and present centuries. Keywords: Philosophy of demonstration; Axiomatization; Induction; Intuition; Representation.Tecemos neste artigo reflexões histórico-filosóficas da demonstração em matemática, apoiando-se em trabalhos de pesquisadores em que discutem diferentes perspectivas filosóficas da demonstração em matemática, mais especificamente em geometria. Focamos, em primeiro lugar a demonstração e sua relação com a intuição e as representações figurais. Em um segundo momento, apresentamos uma crítica sobre a concepção de Poincaré sobre a demonstração matemática. Na terceira parte, tecemos reflexões, de modo não exaustiva, sobre a filosofia da demonstração em geometria, confrontando as concepções Kant às axiomatizações das geometrias não-euclidianas. Neste texto, não adotamos uma definição única que cobriria todos os modos de validação cientifica, pois admitimos a possibilidade de uma evolução de ideias sobre a validade de uma proposição. Para não cair nas falhas simétricas da glorificação dos Antigos ou mesmo na ingratidão em relação a eles, devemos partir da ideia não ingênua de que a demonstração tem uma origem histórica e que, portanto, mantém um caráter histórico, mas deveríamos estar mais atentos ao que caracteriza em sua particularidade ou até sua singularidade, as produções dos séculos passados e presentes. Palavras-chave: Filosofia da demonstração; Axiomatização; Indução; Intuição, Representação.Sociedade de Estudos e Pesquisas Qualitativos - SE&PQ2020-10-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://editora.sepq.org.br/rpq/article/view/34410.33361/RPQ.2020.v.8.n.18.344Qualitative Research Journal ; Vol. 8 No. 18 (2020): Special Number: Philosophy of Mathematics; 540-570Revista Pesquisa Qualitativa; v. 8 n. 18 (2020): Edição Especial: Filosofia da Matemática; 540-5702525-82221809-025710.33361/RPQ.v.8.n.18reponame:Revista Pesquisa Qualitativa (Online)instname:Sociedade Brasileira de Estudos e Pesquisa Qualitativos (SE&PQ)instacron:SE&PQenghttps://editora.sepq.org.br/rpq/article/view/344/218Copyright (c) 2020 Revista Pesquisa Qualitativahttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessAg Almouloud, Saddo2022-01-29T23:21:45Zoai:editora.sepq.org.br:article/344Revistahttps://editora.sepq.org.br/index.php/rpq/indexONGhttps://editora.sepq.org.br/index.php/rpq/oai||revista.rpq@gmail.com2525-82221809-0257opendoar:2022-01-29T23:21:45Revista Pesquisa Qualitativa (Online) - Sociedade Brasileira de Estudos e Pesquisa Qualitativos (SE&PQ)false |
dc.title.none.fl_str_mv |
Demonstration in geometry: historical and philosophical perspectives Demonstração em geometria: perspectivas histórica e filosófica |
title |
Demonstration in geometry: historical and philosophical perspectives |
spellingShingle |
Demonstration in geometry: historical and philosophical perspectives Ag Almouloud, Saddo |
title_short |
Demonstration in geometry: historical and philosophical perspectives |
title_full |
Demonstration in geometry: historical and philosophical perspectives |
title_fullStr |
Demonstration in geometry: historical and philosophical perspectives |
title_full_unstemmed |
Demonstration in geometry: historical and philosophical perspectives |
title_sort |
Demonstration in geometry: historical and philosophical perspectives |
author |
Ag Almouloud, Saddo |
author_facet |
Ag Almouloud, Saddo |
author_role |
author |
dc.contributor.author.fl_str_mv |
Ag Almouloud, Saddo |
description |
In this article, we weave historical-philosophical reflections about demonstration in mathematics, based on works of researchers that discuss the different philosophical perspectives on the topic, more specifically on geometry. We focus first on demonstration and its relationship with intuition and figural representations. Second, we criticize Poincaré’s conception of mathematical demonstration. Third, we reflect, in a non-exhaustive way, on the philosophy of demonstration in geometry, confronting Kant’s conceptions with the axiomatizations of the non-Euclidean geometries. In this text, we do not adopt a single definition that would cover all modes of scientific validation, since we admit the possibility of an evolution of ideas about the validity of a proposition. Not to fall into the symmetrical flaws of the glorification of the Ancients or even being ungrateful to them, we must start from the naive idea that the demonstration has a historical origin and, therefore, maintains a historical character, but we should be more attentive to what characterizes, in its particularity or even its uniqueness, the productions of past and present centuries. Keywords: Philosophy of demonstration; Axiomatization; Induction; Intuition; Representation. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-10-07 |
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://editora.sepq.org.br/rpq/article/view/344 10.33361/RPQ.2020.v.8.n.18.344 |
url |
https://editora.sepq.org.br/rpq/article/view/344 |
identifier_str_mv |
10.33361/RPQ.2020.v.8.n.18.344 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://editora.sepq.org.br/rpq/article/view/344/218 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2020 Revista Pesquisa Qualitativa https://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2020 Revista Pesquisa Qualitativa https://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 |
Sociedade de Estudos e Pesquisas Qualitativos - SE&PQ |
publisher.none.fl_str_mv |
Sociedade de Estudos e Pesquisas Qualitativos - SE&PQ |
dc.source.none.fl_str_mv |
Qualitative Research Journal ; Vol. 8 No. 18 (2020): Special Number: Philosophy of Mathematics; 540-570 Revista Pesquisa Qualitativa; v. 8 n. 18 (2020): Edição Especial: Filosofia da Matemática; 540-570 2525-8222 1809-0257 10.33361/RPQ.v.8.n.18 reponame:Revista Pesquisa Qualitativa (Online) instname:Sociedade Brasileira de Estudos e Pesquisa Qualitativos (SE&PQ) instacron:SE&PQ |
instname_str |
Sociedade Brasileira de Estudos e Pesquisa Qualitativos (SE&PQ) |
instacron_str |
SE&PQ |
institution |
SE&PQ |
reponame_str |
Revista Pesquisa Qualitativa (Online) |
collection |
Revista Pesquisa Qualitativa (Online) |
repository.name.fl_str_mv |
Revista Pesquisa Qualitativa (Online) - Sociedade Brasileira de Estudos e Pesquisa Qualitativos (SE&PQ) |
repository.mail.fl_str_mv |
||revista.rpq@gmail.com |
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