 What to make of this argument? First, the truth conditions for negation employed here are contentious. An alternative view has it that \(\neg A\) is true iff \(A\) is false, and \(\neg A\) is false iff \(A\) is true—and in the semantics of many paraconsistent logics (for instance, the logic of First Degree Entailment), truth and falsity may overlap. Such an account preserves our intuition that negation is the operator which (truth-functionally) switches truth and falsity. It also preserves our intuition on contradictoriness, in the form: \(A\) and \(B\) are contradictories iff, if \(A\) is true, \(B\) is false, and if \(A\) is false, \(B\) is true. What has to go, on this proposal, is the assumption that truth and falsity are exclusive in all cases: there exist dialetheias, that is, sentences falling simultaneously under both categories.