Husserl and Hilbert on completeness, still
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/s11229-015-0821-2 http://hdl.handle.net/11449/220407 |
Resumo: | In the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no consensus has been reached. In this paper I approach this question afresh and thoroughly, taking into consideration not only the relevant texts and context, as others have also done before, but, more importantly, Husserl’s philosophy, his intuition-based epistemology in particular. Based on a system of clearly defined concepts that I here present, I reinforce an interpretation—definiteness as a form of syntactic completeness—that has, I believe, some advantages vis-à-vis alternative interpretations. It is in conformity with the available texts; it makes clear that Husserl’s notion of definiteness is indeed close to Hilbert’s notions of completeness; it solves the important problem of imaginaries for which it was created; and last, but not least, it fits naturally into Husserl’s system of concepts and ideas. |
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Husserl and Hilbert on completeness, stillCompletenessDefinitenessHilbertHusserlImaginary elements in mathematicsIn the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no consensus has been reached. In this paper I approach this question afresh and thoroughly, taking into consideration not only the relevant texts and context, as others have also done before, but, more importantly, Husserl’s philosophy, his intuition-based epistemology in particular. Based on a system of clearly defined concepts that I here present, I reinforce an interpretation—definiteness as a form of syntactic completeness—that has, I believe, some advantages vis-à-vis alternative interpretations. It is in conformity with the available texts; it makes clear that Husserl’s notion of definiteness is indeed close to Hilbert’s notions of completeness; it solves the important problem of imaginaries for which it was created; and last, but not least, it fits naturally into Husserl’s system of concepts and ideas.Department of Mathematics University of the State of São Paulo, Av. Quatro, 436, apt. 52University of the State of São Pauloda Silva, Jairo Jose2022-04-28T19:01:24Z2022-04-28T19:01:24Z2016-06-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1925-1947http://dx.doi.org/10.1007/s11229-015-0821-2Synthese, v. 193, n. 6, p. 1925-1947, 2016.1573-09640039-7857http://hdl.handle.net/11449/22040710.1007/s11229-015-0821-22-s2.0-84937061195Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengSyntheseinfo:eu-repo/semantics/openAccess2022-04-28T19:01:24Zoai:repositorio.unesp.br:11449/220407Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462022-04-28T19:01:24Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Husserl and Hilbert on completeness, still |
title |
Husserl and Hilbert on completeness, still |
spellingShingle |
Husserl and Hilbert on completeness, still da Silva, Jairo Jose Completeness Definiteness Hilbert Husserl Imaginary elements in mathematics |
title_short |
Husserl and Hilbert on completeness, still |
title_full |
Husserl and Hilbert on completeness, still |
title_fullStr |
Husserl and Hilbert on completeness, still |
title_full_unstemmed |
Husserl and Hilbert on completeness, still |
title_sort |
Husserl and Hilbert on completeness, still |
author |
da Silva, Jairo Jose |
author_facet |
da Silva, Jairo Jose |
author_role |
author |
dc.contributor.none.fl_str_mv |
University of the State of São Paulo |
dc.contributor.author.fl_str_mv |
da Silva, Jairo Jose |
dc.subject.por.fl_str_mv |
Completeness Definiteness Hilbert Husserl Imaginary elements in mathematics |
topic |
Completeness Definiteness Hilbert Husserl Imaginary elements in mathematics |
description |
In the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no consensus has been reached. In this paper I approach this question afresh and thoroughly, taking into consideration not only the relevant texts and context, as others have also done before, but, more importantly, Husserl’s philosophy, his intuition-based epistemology in particular. Based on a system of clearly defined concepts that I here present, I reinforce an interpretation—definiteness as a form of syntactic completeness—that has, I believe, some advantages vis-à-vis alternative interpretations. It is in conformity with the available texts; it makes clear that Husserl’s notion of definiteness is indeed close to Hilbert’s notions of completeness; it solves the important problem of imaginaries for which it was created; and last, but not least, it fits naturally into Husserl’s system of concepts and ideas. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-06-01 2022-04-28T19:01:24Z 2022-04-28T19:01:24Z |
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://dx.doi.org/10.1007/s11229-015-0821-2 Synthese, v. 193, n. 6, p. 1925-1947, 2016. 1573-0964 0039-7857 http://hdl.handle.net/11449/220407 10.1007/s11229-015-0821-2 2-s2.0-84937061195 |
url |
http://dx.doi.org/10.1007/s11229-015-0821-2 http://hdl.handle.net/11449/220407 |
identifier_str_mv |
Synthese, v. 193, n. 6, p. 1925-1947, 2016. 1573-0964 0039-7857 10.1007/s11229-015-0821-2 2-s2.0-84937061195 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Synthese |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
1925-1947 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
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1803047076433494016 |