Truth as translation, part A (Convention T, Liar paradox)

According to Tarski's Convention T, the adequacy of a truth definition is ( implicitly) defined relatively to a translation mapping from the object lan guage to the metalanguage; the translation mapping itself is left unspecifi ed. This paper restates Convention T in a form in which the relativity to t ranslation is made explicit. The notion of an interpreted language is intro duced, and a corresponding notion of a translation between interpreted lang uages is defined. The latter definition is state both in an algebraic versi on, and in an equivalent possible worlds version. It is a consequence of ou r definition that translation is indeterminate in certain cases. Finally, w e give an application of our revised version of Convention T and show that interpreted languages exist, which allow for vicious self-reference but whi ch nevertheless contain their own truth predicate. This is possible if only truth is based on a nonstandard translation mapping by which, e.g., the Li ar sentence is translated to its own negation. in this part of the paper th is existence result is proved only for languages without quantifiers; in Pa rt B the result will be extended to first-order languages.