Sometimes, the strategy of proving ~P by showing how P entails absurdity is called "proof by negation". The phrase "proof by contradiction" is then reserved for

Sometimes, the strategy of proving ~P by showing how P entails absurdity is called "proof by negation". The phrase "proof by contradiction" is then reserved for the strategy of proving P by showing how ~P entails absurdity. On that usage, constructivists are happy with all proofs by negation, but not generally happy with proofs by contradiction.