##  [Gödel's Second Incompleteness Theorem](/godels-second-incompleteness-theorem) 

  ##  [Gödel's Second Incompleteness Theorem](https://mathlogic.quantumdictionary.io/godels-second-incompleteness-theorem-0) 

  

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- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The theorem stating that no consistent, effectively axiomatized formal theory that is capable of representing enough arithmetic can prove its own consistency, when consistency is formalized within the theory itself; informally, a theory cannot certify its own freedom from contradiction by means available inside it.