Bergen Logic Seminar: CIRCULARITY AND TRUTH

Abstract. We show that extending any FOL language with quantification over all sentences – of the extended language – does not increase expressive power, in particular, does not lead to any paradoxes. Further extension with sentential operators, by a form of definitional extension, does not lead to any pradoxes, either. This allows to extend conservatively every FOL theory with truth operator axiomatized by the single sentence ∀φ(Tφ ↔ φ).