T-Equivalences for Positive Sentences

Although disquotational truth theories are often criticized as unduly weak, in fact some of them turn out to be very rich in arithmetical content. Halbach's theory PUTB, based on positive substitutions of the uniform disquotation schema, belongs to this category. However, local (sentential) disquotation does not produce such a strong theory. Answering a question asked by Halbach (2009), I show that a disquotational truth theory, which takes as axioms all positive substitutions of the sentential truth schema, together with all instances of induction in the language with the truth predicate, is conservative over its syntactical base.