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

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...

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Detalles Bibliográficos
Autor: Alves, Tiago de Castro
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:Brasil
Institución:Universidade Estadual de Campinas (UNICAMP)
Repositorio:Manuscrito (Online)
Idioma:inglés
OAI Identifier:oai:ojs.periodicos.sbu.unicamp.br:article/8664311
Acceso en línea:https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8664311
Access Level:acceso abierto
Palabra clave: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
Descripción
Sumario: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.