Dialetheism
Dialetheism is the view that some statements can be both true and false at the same time. It is the opposite of the law of noncontradiction (LNC). Because of this dialetheism is completely opposite of what most philosophers call common sense. Graham Priest defines it as believing there can be true contradictions. Priest gives as an example the liar paradox (or liar's paradox). If someone says "everything I say is a lie", then is the statement true or false? In this paradox it can be both.