Vagueness and Ambivalence

What is the proper attitude toward what is expressed by a vague sentence in the face of borderline evidence? Many call this attitude “ambivalence” and distinguish it from uncertainty. It has been argued that Classical Epistemicism and classical probability theory fail to characterize this attitude, and that we must therefore abandon classical logic or classical probabilities in the presence of vagueness. In this paper, I give a characterization of ambivalence assuming a supervaluationist semantics for vague terms that does not revise either. The theory, which I call the theory of Superprobabilities, identifies the proper attitude toward a vague sentence, in the presence of exact borderline evidence, as the set of classical probabilities of the evidence on each member of the set of all precisifications of a vague sentence. I defend the use of sets of probabilities against objections by generalizing the theory of Superprobabilities to a theory of rational betting called Superrationality. I then compare the merits of the theory of Superprobabilities to Classical Epistemicism and nonclassical probabilities theories with respect to the problem of ambivalence.