The Unexpected Applicability of Paraconsistent Logic: A Chomskyan Route to Dialetheism

Paraconsistent logics are characterized by rejection of ex falso quodlibet, the principle of explosion, which states that from a contradiction, anything can be derived. Strikingly these logics have found a wide range of application, despite the misgivings of philosophers as prominent as Lewis and Putnam. Such applications, I will argue, are of significant philosophical interest. They suggest ways to employ these logics in philosophical and scientific theories. To this end I will sketch out a ‘naturalized semantic dialetheism’ following Priest’s early suggestion that the principles governing human natural language may well be inconsistent. There will be a significant deviation from Priest’s work, namely, the assumption of a broadly Chomskyan picture of semantics. This allows us to explain natural language inconsistency tolerance without commitment to contentious views in formal logic.