Paradoxos
Autor: No espaço dos conceitos | Publicado: 2011-12-17T13:11:00-08:00

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Uma das questões que mais intrigam os lógicos são os chamados paradoxos auto-referentes.[1] A lógica moderna se notabiliza como tentativa de respostas a problemas e paradoxos ligados aos fundamentos da matemática. Se alguém diz: Eu tenho 1,70 m de altura” ou “Aquela é a minha casa”, está usando auto-referência. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Vejamos um problema auto-referente:1.&nbsp;&nbsp;&nbsp; Epimênides, o Cretense, dissera: “Todos os cretenses são mentirosos”. Ele estava dizendo a verdade?2.&nbsp;&nbsp;&nbsp; “Esta sentença é falsa” é uma sentença verdadeira ou falsa?3.&nbsp;&nbsp;&nbsp; Numa vila mora um barbeiro que barbeia todos e somente aqueles moradores que não barbeiam a si mesmos. O barbeiro se barbeia?4.&nbsp;&nbsp;&nbsp; Considere o conjunto Z = {X:X ∉ X}. É verdade que Z ∈ Z?Este é o paradoxo da teoria de conjuntos de Bertrand Russell.        [1] Carnielli. W e Epstein. L. Richard. Computabilidade: funções computáveis lógica e os fundamentos da Matemática; tradução. – 2.ed. revista. – São Paulo: Editora. UNESP, 2009.