L&S's theory might be termed a "cognitivized" version of more or less standard truth-conditional semantics - more properly, a series of versions, or T-theories. The authors' strategy is first to present the basic principles; then, beginning with a model that can handle only very simple data, to add more and more structure to accommodate more and more data, and along the way, to entertain departures which are later shown to be inadequate and discarded. Thus we go through PC+ (propositional calculus plus names and predicates), PCset (in which names are singletons), PCprop (in which predicates are properties), PC+DN (in which names are descriptions), VRT (which can handle pronouns and demonstratives), PredC (which can handle quantification), GQ (replacing quantification as done in PredC with generalized quantifiers, and bringing in definite descriptions). After anaphora and tense are introduced, a final version of the theory emerges. This is a formal approach to meaning; L&S's method of imparting it makes it easier to absorb than many textbooks do. Even so, a complete truth derivation for such a sentence as "Every woman loves her car" in GQ, for example, runs to about three typed pages.

The central claim, and at the same time the central problem, with this book - aiming as it does at a cognitive theory - has to do with the concept "interpretivity." A T-theory is interpretive, according to L&S, if the connective "is true iff" yields the same pairings of object-language sentences and metalanguage sentences as the connective "means that." At first they say for example that PC+, PCset and PCprop are all interpretive; later they qualify this, because of ontological commitments. PCset commits us to the existence of sets and PCprop to the existence of Platonic forms: by using these on the right-hand sides of T-theorems, it could be argued, we lose interpretivity. We are saying, for example, that "John sings" means that "the individual named John is a member of the set of singers." We are attributing implicit knowledge of sets to speakers. L&S do not resolve the issue, but suggest that these ontological commitments are not so bad. We cannot formally discuss the meanings of quantifiers, or even develop PC+, without sets. The authors go on to argue that people talk, at least, as if they also assumed the existence of properties & relations. Ultimately, the ontological commitments made by a semantic theory do not clearly provide grounds for accepting or rejecting it.

Since L&S want to make their approach relevant to cognitive science, the problems of coextensive proper nouns and empty proper nouns have to be dealt with; names are assigned "dossiers" which contain what speakers believe about their referents, and dossiers are connected to "concepts." The issue of what a concept is, is not resolved, but by the middle of the book we are assured that "what appears on the right-hand side of an axiom for a proper noun is an individual concept." (Taken literally, of course, this would mean that the meaning of "Socrates jumped over the moon" is "The concept of Socrates jumped over the concept of the moon.")

The book proceeds at an even pace, has good exercises and very good notes, and presents the material clearly. The fundamental papers by Alfred Tarksi and Donald Davidson should ideally be read and discussed before beginning the book.

Ken Miner