Story grammars have been proposed as a means of expressing a theory of stories. Story grammarians claim that stories are a linguistic form in much the same sense that sentences are, and that we can attribute constituent structure to stories in much the same way we attribute it to sentences. Just as sentences and their constituent structure can be characterized by sentence grammars, so stories and their constituent structure can be characterized by a story grammar. However, the analogy between story grammars and sentence grammars is ill conceived. It is based on a category error that assumes stories to be textual entities like sentences. This is demonstrably not the case. Moreover, this confusion is the cause of most of the misunderstandings about story grammars and what they can accomplish. Once this mistake is acknowledged, the possible contribution of story grammars to a theory of stories is considerably diminished. In place of story grammars, I propose the rudiments of a theory, called the theory of story points. Although it lacks some of the aesthetic appeal of story grammars, the theory of story points seems a more promising route to a meaningful theory of stories. The theory is being used as a component of a computer story-understanding system under development at Berkeley. In addition, some very preliminary experiments conducted on the basis of this approach seem to lend it some psychological plausibility.