On a Gödel's misjudgment

eBook (PDF), 19 Pages
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The fundamental aim of the paper is to correct an harmful way to interpret a Gödel's erroneous remark at the Congress of Königsberg in 1930. Despite the Gödel's fault is rather venial, its misreading has produced and continues to produce dangerous fruits, as to apply the incompleteness Theorems to the full second-order Arithmetic and to deduce the semantic incompleteness of its language by these same Theorems. The first three paragraphs are introductory and serve to define the languages inherently semantic and its properties, to discuss the consequences of the expression order used in a language and some question about the semantic completeness: in particular is highlighted the fact that a non-formal theory may be semantically complete despite using a language semantically incomplete. Finally, an alternative interpretation of the Gödel's unfortunate comment is proposed.
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May 28, 2015
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282.58 KB
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