Abstract

Tarski showed how to give satisfactory theories of truth for a wide variety of languages, but he required that the theory of truth for a language be formulated in an essentially richer metalanguage. Since there is no human language essentially richer than a natural language and since we would like to develop consistent theories of truth for natural languages, we would like to learn how to formulate a theory of truth for a language within that very language. ;Toward this end, I consider a class of formalized languages called partially interpreted languages, derived from the work of Carnap, in which sentences are classified as definitely true, definitely false, and intermediate. I give a condition of adequacy, analogus to Tarski's Convension T, requiring that is true be definitely true iff is definitely true , and show that it is possible to give, effectively and explicity, a theory of truth that meets the condition. Theories of truth that meet the condition are shown to have various pleasant properties. The construction depends heavily upon the work of Saul Kripke. ;In addition to the work of Tarski and Kripke, the "naive semantics" of Gupta and Herzberger is discussed. Of the paradoxes other than the liar, only Montague's paradox about necessity is discussed in any detail. To solve this paradox, I recommend a provability interpretation of modal logic of the type studied by Solovay. Prospects for extending Solovay's results into quantified modal logic are discussed. ;The work is entirely concerned with formal languages, although it is hoped that the tools developed can be usefully applied to natural languages.