Arithmetic and Intensionality

Abstract

The paper consists of two pats. The first part contains a critical review of "Gödel theorems, possible worlds and intensionality" by W. Krysztofiak. Krysztofiak argues that Gödel's incompleteness theorem and, in particular, the technique of aritmetization of syntax, gives rise to intensionality and intentionality in arithmetic. The author tries to show that these claims are mistaken and based on a simple misunderstanding of the incompleteness theorem and its proof. In the second part the author explains the traditional use (in the sense of Feferman) of the term "intensional" as applied to arithmetical context.