The first section of this paper deals with the attempts within the framework of transformational grammar to make semantics a systematic part of linguistic description, and outlines the characteristics of the generative semantics position. The second section takes a critical look at generative semantics in its later manifestations, and makes a case against this position on the basis of its treatment of presupposition. The attempt to include presupposition, in a broad sense, in a grammatical system leads to a situation where grammar breaks down. It is possible to redefine grammar in such a way that it can correct tentative assumptions, but this would be the definition of a design criterion for an artificial intelligence (AI) system, in which the aim is to understand the sentence, and grammaticality is at best of secondary importance. A general conclusion is that the demand that grammar should take into account not only well-formedness and semantic acceptability but also all possible aspects of the context of use of a sentence renders the production of a grammar in a normal sense impossible; but it does provide an intelligible and coherent basis for work within the paradigm of artificial intelligence. (AM)