In logic systems such as classical logic, the **principle of explosion** is the principle that from a contradiction any proposition can be inferred to be true.

To show this, suppose we’ve arrived at a contradictory statement, . Let be any proposition we want to prove. By conjunction elimination, we have , and then by disjunction introduction we have

.

However, since we also have , it follows that is true.

This principle suggests an interesting alternative attitude towards contradiction in systems that exhibit this behavior: contradiction is not undesirable because of any ‘intuitive’ nonsensicalness, but simply because a set of assumptions leading to contradiction gives us *no information*.

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