The Introduction of Truth Predicates into First-Order Languages

Abstract

This paper is a shortened and slightly changed version of my 1976 paper. In the present paper I will only deal with the question in which way it might be possible to extend first-order languages to languages with truth predicates.¹ The problems of the Liar paradox and of the introduction of truth predicates have often been treated and different solutions have been proposed. But such proposals are not very useful unless they are developed within a precise theory of language and, what is more important, within a theory of language extensions. It is astonishing that there were for a long time no serious systematic attempts to answer the questions: what type of language extension should the introduction of a truth predicate be regarded as, and under which conditions can such a predicate be introduced in a unique way.² Only if one tries to answer these questions is it possible to find a complete and adequate solution to the problems under discussion. But if one does try to do it then in my opinion it is not too difficult to give what looks like an intuitively acceptable solution.³

I would like to thank M. Pätzold and D. Segal for helping with the English.