 ##  [Principle of Explosion](/principle-explosion) 

  ##  [Principle of Explosion](https://natural.quantumdictionary.io/principle-explosion-0) 

  
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**Natural &amp; Formal Sciences Dictionary**

 
Definition

A rule of classical logic (ex falso quodlibet) stating that once a contradiction is admitted in a deductive system (both P and ¬P), any proposition can be validly inferred from it.

 
 ##  [Principle of Explosion](https://mathlogic.quantumdictionary.io/principle-explosion-1) 

  
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- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

The inference principle, ex contradictione quodlibet, that once a contradiction (both P and ¬P) is present in a deductive system, any proposition Q can be derived; contradictions lead to logical triviality in classical consequence relations.