Towards an evaluation of the normalisation thesis on identity of proofs: the case of church-turing thesis as touchstone

Detalhes bibliográficos
Autor(a) principal: Alves, Tiago de Castro
Data de Publicação: 2021
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Manuscrito (Online)
Texto Completo: https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8664311
Resumo: This article is a methodological discussion of formal approaches to the question of identity of proofs from a philosophical standpoint. First, an introduction to the question of identity of proofs itself is given, followed by a brief reconstruction of the so-called normalisation thesis, proposed by Dag Prawitz in 1971, in which some of its core mathematical and conceptual traits are presented. After that, a comparison between the normalisation thesis and the more well-known Church-Turing thesis on computability is carried out in three main parts: the first dedicated to highlighting some of the analogies between them; the second, their most remarkable differences; and the third, to the possible relations of dependence between the two. Based on these considerations, some concluding remarks concerning the potential of the normalisation thesis and similar approaches to the question of identity of proofs are made in the last section.
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spelling Towards an evaluation of the normalisation thesis on identity of proofs: the case of church-turing thesis as touchstoneHacia una evaluación de la tesis de normalización sobre la identidad de las pruebas: el caso de la tesis de turing de la iglesia como piedra de toquePara uma avaliação da tese de normalização sobre a identidade das provas: o caso da tese da igreja-turing como pedra de toqueNormalisationIdentity of proofsChurch-Turing thesisDerivationNormal formNormalizaciónIdentidad de las pruebasTesis de Church-TuringDerivaciónForma normalNormalizaçãoIdentidade das provasTese de Church-TuringDerivaçãoForma normalThis article is a methodological discussion of formal approaches to the question of identity of proofs from a philosophical standpoint. First, an introduction to the question of identity of proofs itself is given, followed by a brief reconstruction of the so-called normalisation thesis, proposed by Dag Prawitz in 1971, in which some of its core mathematical and conceptual traits are presented. After that, a comparison between the normalisation thesis and the more well-known Church-Turing thesis on computability is carried out in three main parts: the first dedicated to highlighting some of the analogies between them; the second, their most remarkable differences; and the third, to the possible relations of dependence between the two. Based on these considerations, some concluding remarks concerning the potential of the normalisation thesis and similar approaches to the question of identity of proofs are made in the last section.Este artículo es una discusión metodológica de enfoques formales a la cuestión de la identidad de las pruebas desde un punto de vista filosófico. Primero, se da una introducción a la cuestión de la identidad de las pruebas en sí, seguida de una breve reconstrucción de la llamada tesis de la normalización, propuesta por Dag Prawitz en 1971, en la que se presentan algunos de sus rasgos matemáticos y conceptuales centrales. Posteriormente, se realiza una comparación entre la tesis de normalización y la más conocida tesis de Church-Turing sobre computabilidad en tres partes principales: la primera dedicada a resaltar algunas de las analogías entre ellas; el segundo, sus diferencias más notables; y el tercero, a las posibles relaciones de dependencia entre ambos. Con base en estas consideraciones, en la última sección se hacen algunas observaciones finales sobre el potencial de la tesis de normalización y enfoques similares a la cuestión de la identidad de las pruebas.Este artigo é uma discussão metodológica de abordagens formais para a questão da identidade de provas de um ponto de vista filosófico. Primeiramente, é feita uma introdução à questão da identidade das próprias provas, seguida de uma breve reconstrução da chamada tese de normalização, proposta por Dag Prawitz em 1971, na qual alguns de seus traços matemáticos e conceituais centrais são apresentados. Em seguida, uma comparação entre a tese da normalização e a mais conhecida tese de Church-Turing sobre computabilidade é feita em três partes principais: a primeira dedicada a destacar algumas das analogias entre elas; o segundo, suas diferenças mais notáveis; e a terceira, às possíveis relações de dependência entre os dois. Com base nessas considerações, algumas observações finais sobre o potencial da tese de normalização e abordagens semelhantes para a questão da identidade das provas são feitas na última seção.Universidade Estadual de Campinas2021-02-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionTextoTextoinfo:eu-repo/semantics/otherapplication/pdfhttps://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8664311Manuscrito: Revista Internacional de Filosofia; v. 43 n. 3 (2020): jul./set.; 114-163Manuscrito: International Journal of Philosophy; Vol. 43 No. 3 (2020): jul./set.; 114-163Manuscrito: Revista Internacional de Filosofía; Vol. 43 Núm. 3 (2020): jul./set.; 114-1632317-630Xreponame:Manuscrito (Online)instname:Universidade Estadual de Campinas (UNICAMP)instacron:UNICAMPenghttps://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8664311/25955Brazil; ContemporaryBrasil; ContemporáneoBrasil; ContemporâneoCopyright (c) 2020 Manuscrito: Revista Internacional de Filosofiahttps://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessAlves, Tiago de Castro2021-02-15T12:51:01Zoai:ojs.periodicos.sbu.unicamp.br:article/8664311Revistahttps://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:2021-02-15T12:51:01Manuscrito (Online) - Universidade Estadual de Campinas (UNICAMP)false
dc.title.none.fl_str_mv Towards an evaluation of the normalisation thesis on identity of proofs: the case of church-turing thesis as touchstone
Hacia una evaluación de la tesis de normalización sobre la identidad de las pruebas: el caso de la tesis de turing de la iglesia como piedra de toque
Para uma avaliação da tese de normalização sobre a identidade das provas: o caso da tese da igreja-turing como pedra de toque
title Towards an evaluation of the normalisation thesis on identity of proofs: the case of church-turing thesis as touchstone
spellingShingle Towards an evaluation of the normalisation thesis on identity of proofs: the case of church-turing thesis as touchstone
Alves, Tiago de Castro
Normalisation
Identity of proofs
Church-Turing thesis
Derivation
Normal form
Normalización
Identidad de las pruebas
Tesis de Church-Turing
Derivación
Forma normal
Normalização
Identidade das provas
Tese de Church-Turing
Derivação
Forma normal
title_short Towards an evaluation of the normalisation thesis on identity of proofs: the case of church-turing thesis as touchstone
title_full Towards an evaluation of the normalisation thesis on identity of proofs: the case of church-turing thesis as touchstone
title_fullStr Towards an evaluation of the normalisation thesis on identity of proofs: the case of church-turing thesis as touchstone
title_full_unstemmed Towards an evaluation of the normalisation thesis on identity of proofs: the case of church-turing thesis as touchstone
title_sort Towards an evaluation of the normalisation thesis on identity of proofs: the case of church-turing thesis as touchstone
author Alves, Tiago de Castro
author_facet Alves, Tiago de Castro
author_role author
dc.contributor.author.fl_str_mv Alves, Tiago de Castro
dc.subject.por.fl_str_mv Normalisation
Identity of proofs
Church-Turing thesis
Derivation
Normal form
Normalización
Identidad de las pruebas
Tesis de Church-Turing
Derivación
Forma normal
Normalização
Identidade das provas
Tese de Church-Turing
Derivação
Forma normal
topic Normalisation
Identity of proofs
Church-Turing thesis
Derivation
Normal form
Normalización
Identidad de las pruebas
Tesis de Church-Turing
Derivación
Forma normal
Normalização
Identidade das provas
Tese de Church-Turing
Derivação
Forma normal
description This article is a methodological discussion of formal approaches to the question of identity of proofs from a philosophical standpoint. First, an introduction to the question of identity of proofs itself is given, followed by a brief reconstruction of the so-called normalisation thesis, proposed by Dag Prawitz in 1971, in which some of its core mathematical and conceptual traits are presented. After that, a comparison between the normalisation thesis and the more well-known Church-Turing thesis on computability is carried out in three main parts: the first dedicated to highlighting some of the analogies between them; the second, their most remarkable differences; and the third, to the possible relations of dependence between the two. Based on these considerations, some concluding remarks concerning the potential of the normalisation thesis and similar approaches to the question of identity of proofs are made in the last section.
publishDate 2021
dc.date.none.fl_str_mv 2021-02-09
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Texto
Texto
info:eu-repo/semantics/other
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8664311
url https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8664311
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8664311/25955
dc.rights.driver.fl_str_mv Copyright (c) 2020 Manuscrito: Revista Internacional de Filosofia
https://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2020 Manuscrito: Revista Internacional de Filosofia
https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.coverage.none.fl_str_mv Brazil; Contemporary
Brasil; Contemporáneo
Brasil; Contemporâneo
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. 43 n. 3 (2020): jul./set.; 114-163
Manuscrito: International Journal of Philosophy; Vol. 43 No. 3 (2020): jul./set.; 114-163
Manuscrito: Revista Internacional de Filosofía; Vol. 43 Núm. 3 (2020): jul./set.; 114-163
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
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