TITLE:
Consequences of a Godel’s Misjudgment
AUTHORS:
Giuseppe Raguní
KEYWORDS:
Semantic Completeness, Syntactic Incompleteness, Categoricity, Arithmetic, Second-Order Languages, Paradoxes
JOURNAL NAME:
Open Access Library Journal,
Vol.2 No.9,
September
15,
2015
ABSTRACT:
The fundamental aim of the paper is to
correct a harmful way to interpret a Godel’s erroneous remark at the Congress
of Konigsberg in 1930. Although the Godel’s
fault is rather venial, its misreading has
produced and continues to produce dangerous fruits, so 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
questions about the
semantic completeness. In particular, it is
highlighted that a non-formal theory may be semantically complete despite using
a language semantically incomplete. Finally, an alternative interpretation for the Godel’s unfortunate comment is proposed.