Typed and untyped disquotational truth

Cezary Cieśliński

pp. 307-320

in: Theodora Achourioti, Henri Galinon, José Martínez Fernández, Kentaro Fujimoto (eds), Unifying the philosophy of truth, Berlin, Springer, 2015

Abstract

We present an overview of typed and untyped disquotational truth theories with the emphasis on their (non)conservativity over the base theory of syntax. Two types of conservativity are discussed: syntactic and semantic. We observe in particular that TB—one of the most basic disquotational theories—is not semantically conservative over its base; we show also that an untyped disquotational theory PTB is a syntactically conservative extension of Peano Arithmetic.