Dialetheism

Dialetheism is the view that some statements can be both true and false simultaneously. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called "true contradictions", dialetheia, or nondualisms.

Dialetheism is not a system of formal logic; instead, it is a thesis about truth that influences the construction of a formal logic, often based on pre-existing systems. Introducing dialetheism has various consequences, depending on the theory into which it is introduced. For example, in traditional systems of logic (e.g., classical logic and intuitionistic logic), every statement becomes false if a contradiction is true; this means that such systems become trivialist when dialetheism is included as an axiom. Other logical systems do not explode in this manner when contradictions are introduced; such contradiction-tolerant systems are known as paraconsistent logics.

Graham Priest defines dialetheism as the view that there are true contradictions. JC Beall is another advocate; his position differs from Priest's in advocating constructive (methodological) deflationism regarding the truth predicate.