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The Introduction of Truth Predicates into First-Order Languages

  • Walther Kindt
Part of the Synthese Language Library book series (SLAP, volume 4)

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

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Bibliography

  1. Bell, J. L. and Slomson, A. B. (1974), Models and Ultraproducts, Amsterdam.Google Scholar
  2. Feferman, S. (1976), ‘Comparison of some Type-Free Semantic and Mathematical Theories’, Ms. University of Stanford (to appear in JSL).Google Scholar
  3. Kindt, W. (1972), Eine Abstrakte Theorie von Dialogspielen, Dissertation, University of Freiburg.Google Scholar
  4. Kindt, W. (1976), ‘Über Sprachen mit Wahrheitsprädikat’, Ms. University of Bielefeld, to appear in Ch. Habel and S. Kanngießer (eds.), Sprachdynamik und Sprachstruktur, Tübingen.Google Scholar
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  8. Tarski, A. (1935), ‘Der Wahrheitsbegriff in den formalisierten Sprachen’, Studia Philosophica 1.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1978

Authors and Affiliations

  • Walther Kindt
    • 1
  1. 1.Fakultät für Linguistik und LiteraturwissenschaftUniversität BielefeldDeutschland

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