Degree of Belief is Expected Truth Value
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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.