HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS

Detalhes bibliográficos
Autor(a) principal: VENTURI,GIORGIO
Data de Publicação: 2015
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Manuscrito (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0100-60452015000200005
Resumo: Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.
id UNICAMP-17_6f26a1f8c343efbff98992e30880af55
oai_identifier_str oai:scielo:S0100-60452015000200005
network_acronym_str UNICAMP-17
network_name_str Manuscrito (Online)
repository_id_str
spelling HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICSHilbertAxiomsIntuitionsAxiom of CompletenessFregeReference of axiomsCesar's problemFoundations of geometryProof theoryGrundlagen der GeometrieAbstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.UNICAMP - Universidade Estadual de Campinas, Centro de Lógica, Epistemologia e História da Ciência2015-08-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0100-60452015000200005Manuscrito v.38 n.2 2015reponame:Manuscrito (Online)instname:Universidade Estadual de Campinas (UNICAMP)instacron:UNICAMP10.1590/0100-6045.2015.V38N2.GVinfo:eu-repo/semantics/openAccessVENTURI,GIORGIOeng2016-01-27T00:00:00Zoai:scielo:S0100-60452015000200005Revistahttp://www.scielo.br/scielo.php?script=sci_serial&pid=0100-6045&lng=pt&nrm=isoPUBhttps://old.scielo.br/oai/scielo-oai.phpmwrigley@cle.unicamp.br|| dascal@spinoza.tau.ac.il||publicacoes@cle.unicamp.br2317-630X0100-6045opendoar:2016-01-27T00:00Manuscrito (Online) - Universidade Estadual de Campinas (UNICAMP)false
dc.title.none.fl_str_mv HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS
title HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS
spellingShingle HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS
VENTURI,GIORGIO
Hilbert
Axioms
Intuitions
Axiom of Completeness
Frege
Reference of axioms
Cesar's problem
Foundations of geometry
Proof theory
Grundlagen der Geometrie
title_short HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS
title_full HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS
title_fullStr HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS
title_full_unstemmed HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS
title_sort HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS
author VENTURI,GIORGIO
author_facet VENTURI,GIORGIO
author_role author
dc.contributor.author.fl_str_mv VENTURI,GIORGIO
dc.subject.por.fl_str_mv Hilbert
Axioms
Intuitions
Axiom of Completeness
Frege
Reference of axioms
Cesar's problem
Foundations of geometry
Proof theory
Grundlagen der Geometrie
topic Hilbert
Axioms
Intuitions
Axiom of Completeness
Frege
Reference of axioms
Cesar's problem
Foundations of geometry
Proof theory
Grundlagen der Geometrie
description Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.
publishDate 2015
dc.date.none.fl_str_mv 2015-08-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0100-60452015000200005
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0100-60452015000200005
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/0100-6045.2015.V38N2.GV
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv UNICAMP - Universidade Estadual de Campinas, Centro de Lógica, Epistemologia e História da Ciência
publisher.none.fl_str_mv UNICAMP - Universidade Estadual de Campinas, Centro de Lógica, Epistemologia e História da Ciência
dc.source.none.fl_str_mv Manuscrito v.38 n.2 2015
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_ 1748950064960634880

Registros relacionados