Classical Negation Strikes Back: Why Priest’s Attack on Classical Negation Can’t Succeed

Abstract

Dialetheism is the view that some true sentences have a true negation as well. Defending dialetheism, Graham Priest argues that the correct account of negation should allow for true contradictions (sentences of the form $\alpha$ and $\lnot \alpha$) without entailing triviality. A negation doing precisely that is said to have ‘surplus content’. Now, to defend that the correct account of negation does have surplus content, Priest advances arguments to hold that classical Boolean negation (which rules out surplus content) does not even make sense without begging the question against the dialetheist. We shall argue that Priest’s arguments may be turned upon themselves, and that he may also be accused of begging the question against the classical logician. We then advance an argument to the effect that Priest’s account of negation falls short of satisfying his own desiderata on a correct account of a negation: a theory of negation that attempts to represent contradictions cannot coherently allow surplus content, and vice-versa, a negation allowing for surplus content bans contradiction.