Sabe-se que Wittgenstein não recebeu bem os resultados de Goedel. Mas, sua crítica foi depois muito rebatida. Francesco Berto, todavia, no artigo cujo resumo está a seguir, argumenta que Wittgenstein propositalmente recusava a distinção entre o nível objeto e o meta-nível e ao mesmo tempo tinha intuições que hoje conferem com propostas de uma aritmética dita paraconsistente.
Quem tiver comentários a fazer, contra ou a favor da ideia, sinta-se à vontade. “The Gödel Paradox and Wittgenstein's Reasons - Philosophia Mathematica By Francesco Berto “An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics match with some intuitions underlying Wittgenstein’s philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any mathematical question. Most problems of teaching are not problems of growth but helping cultivate growth. As far as I know, and this is only from personal experience in teaching, I think about ninety percent of the problem in teaching, or maybe ninety-eight percent, is just to help the students get interested. Noam Chomsky -- Você está recebendo esta mensagem porque se inscreveu no grupo "LOGICA-L" dos Grupos do Google. Para cancelar inscrição nesse grupo e parar de receber e-mails dele, envie um e-mail para [email protected]. Para ver esta discussão na web, acesse https://groups.google.com/a/dimap.ufrn.br/d/msgid/logica-l/17073CA8-8B73-4798-9DA4-0CC4C0F4B5FB%40gmail.com.
