Game-theoretical semantics of the Hintikka type might be seen as offering a new paradigm for truth-conditional semantics, that is, for defining the concept of truth-in-a-model. The familiar Tarskian approach is to proceed ‘inside out’ by first defining truth-in-a-model for the atomic sentences of a language and then extending the definition to the language as a whole by adding a number of recursive clauses. In the case of formal languages like those of predicate logic the number of recursive clauses will coincide with the number of logical constants; but for more comprehensive languages there may also be recursive clauses of certain non-logical expressions. In general the truth conditions of a complex sentence will always be defined recursively on the basis of the truth conditions of its atomic subformulas.

Game-Theoretical Semantics and Logical Form

categorial complexity is to be replicated recursively by semantic complexity, the range of possible syntactic analyses for a particular fragment of language will depend significantly upon the richness of the chosen semantic theory. For example, within the framework of a Montague-type semantics, which allows a modeltheoretic characterization of intensions, there is the option of taking quantified expressions, such as every woman and some unicorn, as terms. This arises because terms, whether singular or general, can be treated semantically like simple predicates; that is, they can be assigned sets of entities, in this case properties rather than individuals. As a result, terms can be regarded syntactically as expressions which combine with intransitive verb phrases to yield sentences. Such a construction is said to be true just in case the property associated with the verb phrase belongs to the set of properties assigned to the term. In a semantics where intensions cannot be characterized, however, this option may not survive. Thus, standard first-order model theory, lacking as it does a special domain of possible worlds, permits the assimilation of quantified phrases to the category of terms only if the language contains for each term a predicate which uniquely characterizes that term. It might also be noted that such a semantics prevents necessarily and possibly from being represented as logical operators on sentences, because there is no way of characterizing this representation semantically. Given that semantic theory can constrain grammatical analysis in this way, we might wonder whether there is perhaps a preferred semantics which might, in virtue of its

Barry Richards

Papers

Semantic Theory and Grammatical Structure