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 

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