# G\"{o}del's incompleteness theorem and the Anti-Mechanist Argument: revisited

## TL;DR

This paper revisits G"{o}del's incompleteness theorem and its implications for the Anti-Mechanist Argument, clarifying misunderstandings and discussing recent developments in the philosophical and mathematical debates.

## Contribution

It provides supplementary explanations and classifications of misunderstandings related to G"{o}del's theorem in the context of Anti-Mechanist Arguments, building on Krajewski's work.

## Key findings

- Clarification of misunderstandings about G"{o}del's theorem
- Analysis of G"{o}del's Disjunctive Thesis and Undemonstrability of Consistency
- Discussion of recent advances affecting these issues

## Abstract

This is a paper for a special issue of the journal "Studia Semiotyczne" devoted to Stanislaw Krajewski's paper [30]. This paper gives some supplementary notes to Krajewski's [30] on the Anti-Mechanist Arguments based on G\"{o}del's incompleteness theorem. In Section 3, we give some additional explanations to Section 4-6 in Krajewski's [30] and classify some misunderstandings of G\"{o}del's incompleteness theorem related to Anti-Mechanist Arguments. In Section 4 and 5, we give a more detailed discussion of G\"{o}del's Disjunctive Thesis, G\"{o}del's Undemonstrability of Consistency Thesis and the definability of natural numbers as in Section 7-8 in Krajewski's [30], describing how recent advances bear on these issues.