On the philosophical relevance of Gödel’s Incompleteness theorems

Gödel’s second incompleteness theorem states that no consistent formal system can prove its own consistency. These results are among the most philosophically important logico-mathematical discoveries ever made. However, there is also ample misunderstanding and confusion surrounding them. The aim of this paper is to review and evaluate various philosophical interpretations of Gödel’s theorems and their consequences, as well as to clarify some confusions.