LANGUAGE AND ITS MODELS: IS MODEL THEORY A THEORY OF SEMANTICS?
Tarskian model theory is almost universally understood as a formal counterpart of the preformal notion of semantics, of the “linkage between words and things”. The wide-spread opinion is that to account for the semantics of natural language is to furnish its settheoretic interpretation in a suitable model structure; as exemplified by Montague 1974. The thesis advocated in this paper is that model theory cannot be considered as semantics in this straightforward sense. We try to show that model theory is more adequately understood as shining light on considerations concerning the relation of consequence than on those concerning the relation of expressions to extralinguistic objects; and that it makes little sense to use model theory for the purposes of answering such questions as what is meaning? or when is a sentence true?. The organization of the paper is the following: We start by considering various formal reconstructions of natural languages utilizing standard logic. Section 2 points out that the usual way of explicating the semantics of natural language, namely the way of Tarskian modeltheoretic interpretation, is problematic. In Section 3 we propose a more adequate way: to explicate semantics via the delimitation of the space of possible truth-valuations of sentences, especially in terms of the specification of the relation of consequence (indicating that logic, as an account for consequence, is eo ipso a theory of semantics). Section 4 demonstrates that a plausible way to account for the space of possible truth-valuations is to locate a “basis”, i.e. a class of mutually independent sentences each truth-valuation of which uniquely extends to a truth-valuation of the whole language; and it is noted that some of