ABSTRACT

Where L is a first-order language, let its simple indexical extension LI be the language obtained from L by adding the demonstrative r that', construed (for the present at least) as an indexical term functioning syntactically in precisely the same way as an individual constant. Then there is a well-known problem about how the familiar Tarskian methods for constructing a truth-theory for L need to be modified or extended so as to yield a truth-theory for LI. The problem arises as a particularly urgent one within a Davidsonian framework, which assumes that, underlying a natural language like English, there exists a formal language ('Base English') in which every surface sentence of English finds at least one paraphrase (a 'base paraphrase'); surface sentences are further supposed linked to their base paraphrases by a series of meaningpreserving Chomsky an transformations, and the task of constructing a theory of meaning for English identified with that of finding a recursive truth-theory for Base English meeting appropriate constraints. For the manifest presence in English of indexical elements renders it extremely plaUSible that Base English will need to extend first-order resources at least to the point of being a simple indexical extension of a first-order language. Thus, on Davidsonian assumptions, the problem of the extension of Tarskian methods from first-order languages to their indexical extensions is one not merely of a technical interest, but one that poses key questions for the theory of meaning for natural languages.