Uma abordagem sobre a concepção de proposição da teoria institucionalista de tipos

• Ano de defesa: 2013
• Autor(a) principal: Mundim, Bruno Rigonato
• Orientador(a): Porto, André da Silva
• Banca de defesa: Porto, André da Silva, Velloso, Araceli Rosich Soares, Pereira, Luiz Carlos Pinheiro Dias
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Goiás
• Programa de Pós-Graduação: Programa de Pós-graduação em Filosofia (FAFIL)
• Departamento: Faculdade de Filosofia - FAFIL (RG)
• País: Brasil
• Palavras-chave em Português: Teoria intuicionista de tipos; Martin-Löf; Proposições como conjuntos/tipos
• Palavras-chave em Inglês: Propositions as sets/types; Intuitionistic type theory
• Área do conhecimento CNPq: FILOSOFIA::LOGICA
• Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tede/3337

By means of the Curry-Howard Correspondence Martin-Löf’s intuitionistic type theory claims that to define a proposition by laying down how its canonical proofs are formed is the same as to define a set by laying down how its canonical elements are formed; consequently a proposition can be seen as the set of its proofs. On the other hand, we find in this very same theory a distinction between the notions of set and of type, such that the difference of the latter in relation to the former consists in the fact that to form a type we do not need to present an exhaustive prescription for the formation of its objects; it is sufficient to just have a general notion of what would be an arbitrary object that inhabits such type. Thus we argue that we can extract two distinct notions of propositon from the intuitionistic type theory, one which treats propositions as types and another which treats propositions as sets. Such distinction will have some bearing on discussions concerning hypothetical demonstrations and conjecture’s formation.