The Goedel's legacy: revisiting the Logic

TL;DR

This paper critically examines common misconceptions in logic, particularly regarding Gödel's incompleteness theorems, Chaitin's ideas, and the classification of axiomatic theories based on language order.

Contribution

It clarifies misunderstandings about fundamental logical theorems and classifications, providing a more accurate perspective on these core topics.

Findings

Identifies and corrects misconceptions about Gödel's theorems

Analyzes superficial interpretations of Chaitin's work

Reevaluates the classification of axiomatic theories based on language order

Abstract

Some common fallacies about fundamental themes of Logic are exposed: the First and Second incompleteness Theorem interpretations, Chaitin's various superficialities and the usual classification of the axiomatic Theories in function of its language order.