Truth Theory and Translation

In the 1930s and -40s A. Tarski has defined what it means to call a sentence of a formal language (the "object language") "true"; the language, in which the truth definition is carried out, is called "metalanguage". Tarski could show that his truth definition was not applicable to languages that contain sentences, which speak about themselves. An example is the sentence "This sentence is not true.": this very sentence says about itself that it is not true. We call such a sentence self-referent. Intuitively, this sentence is true if and only if it is not true. Formally, this means that the Tarskian concept of truth cannot be defined for languages containing such a sentence. Extreme examples of such languages are such which are their own metalanguages. Therefore, Tarski suggested to abandon any kind of self-reference in language when dealing with truth definitions. Starting in the 1970s, some logicians introduced new ways to define truth which axe even applicable to sentences of the kind above. E.g. "This sentence is not true." has been analysed as neither true nor false. To show that a new truth theory does not lead to inconsistencies, if confronted with self-referent sentences, is generally no easy task; moreover, one has to give clear semantical intuitions of why truth should be defined differently than done by Tarski. Recently, we have introduced a new way to define truth (see Leitgeb [l]): its basic idea is that a sentence j of the metalanguage claiming the truth of a sentence Y of the object language should be the translation of Y in the metalanguage. This concept is a development of the Tarskian concept of truth, but in a different direction. Of course, to carry out this definition, we also had to define what we mean by the translation of a sentence. We could show that this concept of truth as translation is even applicable to languages, which are their own metalanguages. The aim of our project is continue the work on this new notion of truth. In the first half of the project we want to deal with some important technical questions. In the second half we intend to give some typical applications. If the project is carried out successfully, this will have consequences for our understanding of truth, self-reference and even aspects of natural language.

The central problem of logical truth theories is to give a very extensive definition of a "truth predicate" for sentences, which avoids the socalled semantical paradoxes (like that of the liar) and on the other side allows harmless circularities which may have semantical content (in Tarskis classical solution these are also eliminated by a very strict separation between object- and metalanguage). In the first part of this research project, Dr. Hannes Leitgeb investigated several proposals and worked them out on a high technical level. The main idea was to interpret a sentence of the metalanguage which claims that a sentence in the object language is true as a translation of this sentence in the object language. These investigations have been published in leading scientific journals of this field. In the second part of this research project Dr. Martin Amerbauer tried to connect axiomatic truth theories with systems of modal logic, but could not finish his investigations in time.