“My task is not to talk (e.g.) about Godel's theorem, but to by-pass it”
Ludwig Wittgenstein.
"Wittgenstein advance a completely trivial and uninteresting misinterpretation"
(
rejecting the label of paradoxical).
Kurt Gödel
Abstract:
Following the debate launched by Floyd and Putnam, it is proposed that, after the demonstration of Gödel, stand pending issues that are not purely philosophical, but regarding how to judge the correctness of the interpretations (Yablo’s paradox is proposed for the heuristic comparison, instead of that of Richard or Epimenides), the mathematical content, and the referential ability (the Frege’s “sense”) of the undecidable sentence.
Previously we try to rebuild a formulation of it, intending to avoid both the ambiguities of the informal versions, as the cryptic aura that surround the gödelian original .
In closing, it is proposed to investigate whether the undecidable sentences form a recursive set. If yes, they can allow to the automation of deductive systems of numeracy, avoiding the truth issues. The core thesis is that the self application of demonstrability is homologous to the division by zero: indefinable and not necessary to the complete sense of aritmetic.
As a post scriptum, the reconstruction of formalism attempted by Gödel is remembered: he was the first in attempt to bypass his own negative results.
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