@MISC{Lam12vaguenessand, author = {Barry Lam}, title = {Vagueness and Ambivalence}, year = {2012} }

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Abstract

Abstract: 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 prob-ability 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.