  Although the categorical arithmetic is not effectively axiomatizable, the
belief that the incompleteness Theorems can be apply to it is fairly common.
Furthermore, the so-called "essential" (or "inherent") semantic incompleteness
of the second-order Logic that can be deduced by these same Theorems does not
imply the standard semantic incompleteness that can be derived using the
Loewenheim-Skolem or the compactness Theorem. This state of affairs has its
origins in an incorrect and misinterpreted Goedel's comment at the Koenigsberg
congress of 1930 and has consolidated due to different circumstances. This
paper aims to clear up these questions and proposes an alternative
interpretation for the Goedel's statement.

General Mathematics