On Representing ‘True-in-L’ in L

  • Robert L. Martin
  • Peter W. Woodruff
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 43)


Given Tarski’s familiar treatment of the semantic paradoxes, no formal language can adequately represent its own truth-concept.1 But natural languages do, apparently, express their own truth-concepts and this fact alone has been enough to motivate some to seek alternative treatments of the paradoxes. In this paper we demonstrate that a language construed according to the ‘category’ approach,2 modified in certain respects, can indeed express its own truth-concept.


Concrete Object Philosophical Review Individual Constant Complex Predicate Liar Paradox 
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  1. Fine, K.: 1974, ‘Vagueness, Truth and Logic’, unpublished manuscript.Google Scholar
  2. Kleene, S. C. 1950, Introduction to Metamathematics, Van Nostrand, New York.Google Scholar
  3. Martin, R. L. 1967, ‘Toward a Solution to the Liar Paradox’, The Philosophical Review 76, 279–311.CrossRefGoogle Scholar
  4. Martin, R. L., 1968, ‘On Grelling’s Paradox’, The Philosophical Review 77, 321–331.CrossRefGoogle Scholar
  5. Martin, R. L., 1970, ‘A Category Solution to the Liar’, in R. L. Martin (ed.), The Paradox of the Liar, Yale Univ. Press. London and New Haven, pp. 91–112.Google Scholar
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  7. Tarski, Alfred, 1956, ‘The Concept of Truth in Formalized Languages’, in Logic, Semantics, Metamathematics, Oxford Univ. Press, pp. 152–278.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht-Holland 1976

Authors and Affiliations

  • Robert L. Martin
    • 1
  • Peter W. Woodruff
    • 2
  1. 1.Livingston CollegeRutgers UniversityUSA
  2. 2.University of CaliforniaIrvineUSA

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