%0 Journal Article
%T Consequences of a Godel¡¯s Misjudgment
%A Giuseppe Ragun¨ª
%J Open Access Library Journal
%V 2
%N 9
%P 1-12
%@ 2333-9721
%D 2015
%I Open Access Library
%R 10.4236/oalib.1101820
%X 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 <i>full</i> 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 <i>inherently semantic</i> 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.
%K Semantic Completeness
%K Syntactic Incompleteness
%K Categoricity
%K Arithmetic
%K Second-Order Languages
%K Paradoxes
%U http://www.oalib.com/paper/3149400