Although this book appeared as early as in 1973 it is still an interesting contribution to the formal study of natural languages. One point of this notice will be to indicate how Cresswell's approach relates to what are currently being proposed as theoretical models for natural languages by linguists working in the tradition of transformational grammars. Logics and Languages is divided into four parts. Parts I and II ('Propositional Languages' and 'Categorial Languages') define a class of formal languages and their semantics which in parts III and IV ('English As A Categorial Language' and 'English As A Natural Language') are used as the basis for a precise description of natural languages. Choosing to discuss CressweU's study from the perspective of its relevance for linguistic research I shall have to leave aside many interesting issues beating on general properties of categorial languages and possible worlds semantics.
Cresswell announces that the purpose of his book "is not to describe a natural language in detail but rather to argue for a certain view of the nature of the entities requiredin semantic analysis" (p. 7). His method is to start with formal languages, whose structures are well-defined, and gradually incorporate devices so that the formal language becomes equal to a natural language in expressive power. Cresswell wants to investigate just how complex formal languages must be in order to act profitably as models for natural languages. He uses a 2~-categorial language with a model theoretic semantics, which he takes to be a philosophically adequate theory of meaning. To let his categorial base obtain an expressive power corresponding to that of natural languages he enriches his system with principles of k-abstraction and kconversion (pp. 85-89). Given this base, CressweU purports to derive 'all of English' by generating a set of k-deep structures, on which the principles of k-conversion operate to rearrange the symbols into a desired order (see Figure 1). Then the k's and the variables are simply deleted and we are left