6.9.1—
A Nonconventional Analysis?

First, it is by no means clear that the analysis presented by Tarski renders the semantics of languages essentially nonconventional. Tarski says that we "indicate which objects satisfy the simplest sentential functions" (Tarski [1956b] 1985: 56, emphasis added). But in the context in which he is speaking, this "indication" can be interpreted in either of two ways, both of which are plausibly interpreted in conventional terms . On the one hand, one might wish to supply a semantic analysis of an existing formal language (say, Hilbert's geometry). In this case, one is ap-

proaching an existing public language game that is conventionally established. The ability to "indicate" the objects that satisfy the sentential functions in such a language game by no means shows that the relationship of satisfaction is essentially nonconventional. Making the mapping from expressions to interpretations explicit in no way implies that the preexisting system is nonconventional. And indeed the way in which the mapping is indicated in the formal model is itself conventional.

Alternatively, one may be defining a new language game de novo, and hence stipulating its semantic assignments. Here there is no preexisting convention-laden public language game. But in doing this one is necessarily defining a convention for semantic interpretation. Doing so by no means shows there is an independent stratum of meaning or even satisfaction that obtains apart from the conventions established by the theorist. At best, if there is a preexisting set of markers, there are infinite numbers of mappings between that set and sets of objects. And mappings do, indeed, exist independent of mapping conventions. But a mapping, per se, is not a semantic relationship. Nor does the existence of mappings that are independent of conventions establish the existence of semantic relations that are independent of conventions. Semantic assignments are represented by mappings and involve mappings, but mappings are not themselves semantic.