Intensionality of the Godel’s Second Incompleteness Theorem
The difference between the First and Second Godel’ s theorem is discussed in perspective of possible rehabilitation of the Hilbert Program. The essence of the difference lies in the fact that if the First theorem is extensional, then the Second theorem is intensional. The formalization of the consistency concept used in the proof of the Second Theorem is reconsidered, particularly, the other ways of expressing the consistency property that are not subject to this theorem. In this paper, we investigate what can be considered a formal expression of a meaningful concept of consistency. The formalization of the consistency concept, used in the proof of the Second Theorem, is contested with the presentation of other ways of expressing the consistency property, for which the second theorem does not hold. It is investigated what can be considered a formal expression of the concept of consistency.