The many senses of completeness
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Manuscrito (Online) |
Texto Completo: | https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8644947 |
Resumo: | In this paper I study the variants of the notion of completeness Husserl presented in “Ideen I” and two lectures he gave in Göttingen in 1901. Introduced primarily in connection with the problem of imaginary numbers, this notion found eventually a place in the answer Husserl provided for the philosophically more important problem of the logico-epistemological foundation of formal knowledge in science. I also try to explain why Husserl said that there was an evident correlation between his and Hilbert’s notion of completeness introduced in connection with the axiomatisation of geometry and the theory of real numbers when, as many commentators have already observed, these two notions are independent. I show in this paper that if a system of axioms is complete in Husserl’s sense, then its formal domain, the manifold of formal objects it determines, does not admit any extension. This is precisely the idea behind Hilbert’s notion of completeness in question. Therefore, the correlation Husserl noted indeed exists. But, in order to see it, we must consider the formal domain determined by a formal theory, not its models. |
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The many senses of completenessHusserl. Sense of completenessIn this paper I study the variants of the notion of completeness Husserl presented in “Ideen I” and two lectures he gave in Göttingen in 1901. Introduced primarily in connection with the problem of imaginary numbers, this notion found eventually a place in the answer Husserl provided for the philosophically more important problem of the logico-epistemological foundation of formal knowledge in science. I also try to explain why Husserl said that there was an evident correlation between his and Hilbert’s notion of completeness introduced in connection with the axiomatisation of geometry and the theory of real numbers when, as many commentators have already observed, these two notions are independent. I show in this paper that if a system of axioms is complete in Husserl’s sense, then its formal domain, the manifold of formal objects it determines, does not admit any extension. This is precisely the idea behind Hilbert’s notion of completeness in question. Therefore, the correlation Husserl noted indeed exists. But, in order to see it, we must consider the formal domain determined by a formal theory, not its models.Universidade Estadual de Campinas2016-04-13info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8644947Manuscrito: Revista Internacional de Filosofia; v. 23 n. 2 (2000): out.; 41-60Manuscrito: International Journal of Philosophy; Vol. 23 No. 2 (2000): Oct.; 41-60Manuscrito: Revista Internacional de Filosofía; Vol. 23 Núm. 2 (2000): out.; 41-602317-630Xreponame:Manuscrito (Online)instname:Universidade Estadual de Campinas (UNICAMP)instacron:UNICAMPporhttps://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8644947/12379Copyright (c) 2000 Manuscritoinfo:eu-repo/semantics/openAccessSilva, Jairo José da2022-05-11T16:36:05Zoai:ojs.periodicos.sbu.unicamp.br:article/8644947Revistahttps://periodicos.sbu.unicamp.br/ojs/index.php/manuscritoPUBhttps://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/oaimwrigley@cle.unicamp.br|| dascal@spinoza.tau.ac.il||publicacoes@cle.unicamp.br2317-630X0100-6045opendoar:2022-05-11T16:36:05Manuscrito (Online) - Universidade Estadual de Campinas (UNICAMP)false |
dc.title.none.fl_str_mv |
The many senses of completeness |
title |
The many senses of completeness |
spellingShingle |
The many senses of completeness Silva, Jairo José da Husserl. Sense of completeness |
title_short |
The many senses of completeness |
title_full |
The many senses of completeness |
title_fullStr |
The many senses of completeness |
title_full_unstemmed |
The many senses of completeness |
title_sort |
The many senses of completeness |
author |
Silva, Jairo José da |
author_facet |
Silva, Jairo José da |
author_role |
author |
dc.contributor.author.fl_str_mv |
Silva, Jairo José da |
dc.subject.por.fl_str_mv |
Husserl. Sense of completeness |
topic |
Husserl. Sense of completeness |
description |
In this paper I study the variants of the notion of completeness Husserl presented in “Ideen I” and two lectures he gave in Göttingen in 1901. Introduced primarily in connection with the problem of imaginary numbers, this notion found eventually a place in the answer Husserl provided for the philosophically more important problem of the logico-epistemological foundation of formal knowledge in science. I also try to explain why Husserl said that there was an evident correlation between his and Hilbert’s notion of completeness introduced in connection with the axiomatisation of geometry and the theory of real numbers when, as many commentators have already observed, these two notions are independent. I show in this paper that if a system of axioms is complete in Husserl’s sense, then its formal domain, the manifold of formal objects it determines, does not admit any extension. This is precisely the idea behind Hilbert’s notion of completeness in question. Therefore, the correlation Husserl noted indeed exists. But, in order to see it, we must consider the formal domain determined by a formal theory, not its models. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-04-13 |
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://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8644947 |
url |
https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8644947 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8644947/12379 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2000 Manuscrito info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2000 Manuscrito |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Universidade Estadual de Campinas |
publisher.none.fl_str_mv |
Universidade Estadual de Campinas |
dc.source.none.fl_str_mv |
Manuscrito: Revista Internacional de Filosofia; v. 23 n. 2 (2000): out.; 41-60 Manuscrito: International Journal of Philosophy; Vol. 23 No. 2 (2000): Oct.; 41-60 Manuscrito: Revista Internacional de Filosofía; Vol. 23 Núm. 2 (2000): out.; 41-60 2317-630X reponame:Manuscrito (Online) instname:Universidade Estadual de Campinas (UNICAMP) instacron:UNICAMP |
instname_str |
Universidade Estadual de Campinas (UNICAMP) |
instacron_str |
UNICAMP |
institution |
UNICAMP |
reponame_str |
Manuscrito (Online) |
collection |
Manuscrito (Online) |
repository.name.fl_str_mv |
Manuscrito (Online) - Universidade Estadual de Campinas (UNICAMP) |
repository.mail.fl_str_mv |
mwrigley@cle.unicamp.br|| dascal@spinoza.tau.ac.il||publicacoes@cle.unicamp.br |
_version_ |
1800216566612099072 |