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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| 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 |
| 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. |
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