Degree of belief is expected truth value

In Sebastiano Moruzzi & Richard Dietz (eds.), Cuts and Clouds. Vaguenesss, its Nature and its Logic. Oxford University Press 491--506 (2009)
A number of authors have noted that vagueness engenders degrees of belief, but that these degrees of belief do not behave like subjective probabilities. So should we countenance two different kinds of degree of belief: the kind arising from vagueness, and the familiar kind arising from uncertainty, which obey the laws of probability? I argue that we cannot coherently countenance two different kinds of degree of belief. Instead, I present a framework in which there is a single notion of degree of belief, which in certain circumstances behaves like a subjective probability assignment and in other circumstances does not. The core idea is that one’s degree of belief in a proposition P is one’s expectation of P’s degree of truth.
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