Towards a logic of type-free modality and truth
Hannes Leitgeb · Cambridge University Press eBooks · 2007
. We develop a type-free theory of modality and truth in which modalities are treated syntactically in the same way as truth, i.e., as predicates of sentences. In contrast to Tarski and Montague, we do not conclude from the well-known inconsistency results for the unrestricted truth scheme and for the predicate versions of certain systems of modal logic that truth predicates have to be typed or that modal predicates are to be replaced by sentential operators. Instead we suggest to hold on to an unrestricted syntax while restricting the admissible instances of the truth scheme and the modal axiom schemes and rules. We are going to present a possible worlds semantics and corresponding logical systems for modal predicates in which these restrictions are taken care of. The possible worlds semantics for the reflexive frame that contains exactly one world yields the theory of truth investigated by Leitgeb [14].