Gödel’s Incompleteness Theorem and the Anti-Mechanist Argument: Revisited

This is a paper for a special issue of Semiotic Studies devoted to Stanislaw Krajewski’s paper (2020). This paper gives some supplementary notes to Krajewski’s (2020) on the Anti-Mechanist Arguments based on Gödel’s incompleteness theorem. In Section 3, we give some additional explanations to Section 4–6 in Krajewski’s (2020) and classify some misunderstandings of Gödel’s incompleteness theorem related to AntiMechanist Arguments. In Section 4 and 5, we give a more detailed discussion of Gödel’s Disjunctive Thesis, Gödel’s Undemonstrability of Consistency Thesis and the definability of natural numbers as in Section 7–8 in Krajewski’s (2020), describing how recent advances bear on these issues.