 ##  [Inconsistency](/inconsistency) 

  ##  [Inconsistency](https://mathlogic.quantumdictionary.io/inconsistency-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

Property of a set of sentences from which a contradiction can be derived under the given consequence relation, or equivalently of a theory that proves both a formula and its negation.