 ##  [Incompleteness Phenomenon](/incompleteness-phenomenon) 

  ##  [Incompleteness Phenomenon](https://mathlogic.quantumdictionary.io/incompleteness-phenomenon-0) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

The widespread occurrence across sufficiently expressive formal systems that there exist true statements about intended structures which are not provable within those systems; encapsulates results like Gödel's incompleteness theorems and related limitations on formalization.