Abstract

We introduce and analyze a new axiomatic theory$\mathsf {CD}$of truth. The primitive truth predicate can be applied to sentences containing the truth predicate. The theory is thoroughly classical in the sense that$\mathsf {CD}$is not only formulated in classical logic, but that the axiomatized notion of truth itself is classical: The truth predicate commutes with all quantifiers and connectives, and thus the theory proves that there are no truth value gaps or gluts. To avoid inconsistency, the instances of the T-schema are restricted todeterminatesentences. Determinateness is introduced as a further primitive predicate and axiomatized. The semantics and proof theory of$\mathsf {CD}$are analyzed.