Truth as translation, part B (Convention T, first-order languages)

This is the second part of a paper dealing with truth and translation. In P art A a revised version of Tarski's Convention T has been presented, which explicitly refers to a translation mapping from the object language to the metalanguage; the vague notion of a translation has been replaced by a prec ise definition. At the end of Part A it has been shown that interpreted lan guages exist, which allow for vicious self-reference but which nevertheless contain their own truth predicate--this is possible if truth is based on a nonstandard translation mapping. However, this result has only been proved for languages without quantifiers. In Part B we now extend the result to f irst-order languages, and we show that this can be done in three different ways. In each case, the addition of a truth predicate to an interpreted lan guage with a high degree of expressiveness leads to changes in the ontology of the language.