Once Again on Misinterpretations of Gödel’s Second Incompleteness Theorem

Abstract

A response is given to the paper by A. M. Izmailova (Izmailova A. M. O kritike teoremy K. Gedelya o nepolnote A. V. Bessonovym [On A. V. Bessonov’s criticism of K. Gödel’s incompleteness theorem]. Studencheskii nauchnyi zhurnal “Grani nauki” [Student Scientific Journal "Facets of Science"], 2018, no. 1, p. 7-9. (in Russ.)) allegedly indicating a «serious error» in my analysis of K. Gödel’s second incompleteness theorem. It is shown that her criticism is based on gross logical errors, as well as on a misunderstanding of both the second incompleteness theorem and my results. Such a widespread misinterpretation is based on the inadmissible confusion of the proof of the consistency of formal arithmetic with the proof in it of a formula expressing its consistency. It is argued that Gödel's second theorem is not directly related to the proof of the consistency of formal arithmetic. It is proved that this theorem cannot be used in argumentation against feasibility of D. Hilbert’s finitistic program.