A story semantics for implication.
Charles B. Daniels · Notre Dame Journal of Formal Logic · 1986
MotivationThis paper results from an interest in stories and in the question of what is "in" and what is not "in" a story.Some stories have texts, some do not.A novel is a text; it is an ordered set of sentences.What is in the story of the novel is what is implied by that set of sentences.But what kind of implication is it that we have here?If, in a story, a geometer discovers a method of trisecting the angle with ruler and compasses alone, that it rained yesterday in Detroit need not be in the story.Yet the impossibility of there being such a method together with the story's assumption that there is such a method does, classically, imply not only that it rained yesterday in Detroit, but that it didn't rain there yesterday as well.In pondering this problem I succumb to a temptation to turn things around to see whether the notion of a story might help to shed some light on implication.It does.What we have is the actual world and a language, or a set of beliefs or pictures, that are true or false of it.Then we have stories described in the same vehicle.Stories can be thought of as sets of these sorts of things closed under implication. 1 The three principal features of stories I shall seize on are: (1) Some of the people, things, and places there are do not figure in some stories, even in stories which contain contradictions.(2) Stories can fail to provide answers to questions.A story in which either John killed Jim or Joe killed Jim may not contain an answer to the question of who, exactly, did kill Jim.In the story of Moby Dick we will not find an answer to the question of whether Hamlet's mother was or was not Antigone's sister.Taking language as our vehicle, a sentence will be true in a story precisely when it is in the story, when it is a member of the set of sentences the story is.This is the way sentences are true for stories.While other aspects of the story semantics to be introduced here will vary in the course of this paper, this valuation, indeed all truth valuations, will remain firmly fixed.I wish to thank an anonymous referee for a number of helpful suggestions.