Conceptions of Intensionality of Mathematical Discourse: The Stages of Self-reference

The article discusses the reasons for the emergence of intensional structures in mathematical discourse with the example of the proof of the Second Gödel Theorem on the incompleteness of arithmetic. It is shown that one of the reasons for intensionality is the conceptual structure, including the transition from strictly mathematical formulations to their interpretation. Three stages of intensionality are analyzed – coding, constructing a predicate of proof, and constructing a self-reference sentence. It is shown that the choice between the alternatives at each stage is the source of intensionality

Keywords: intensionality, Gödel Second Incompleteness Theorem, self-reference, syntax arithmetization, Gödel.