This paper does not attempt to present a semantic theory of a natural language, but rather to characterize the form of such a theory. A semantic theory of a natural language is part of a linguistic description of that language. Our problem, on the other hand, is part of the general theory of language, fully on a par with the problem of characterizing the structure of grammars of natural languages. A characterization of the abstract form of a semantic theory is given by a metatheory which answers such questions as these: What is the domain of a semantic theory? What are the descriptive and explanatory goals of a semantic theory? What mechanisms are employed in pursuit of these goals? What are the empirical and methodological constraints upon a semantic theory?