Classical Determinate Truth I

Kentaro Fujimoto, Halbach Volker

Research output: Contribution to journalArticle (Academic Journal)peer-review


We introduce and analyze a new axiomatic theory 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 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 to determinate sentences. Determinateness is introduced as a further primitive predicate and axiomatized. The semantics and proof theory of CD are analyzed.
Original languageEnglish
JournalJournal of Symbolic Logic
Early online date5 Jul 2023
Publication statusE-pub ahead of print - 5 Jul 2023

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