|Belief degree, degree of belief: subjective assessment of the likelihood of an event. See also belief, probability, probability theory, Bayesianism, Principal Principle, subjective probability.|
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Adams-Conditional/Field: Suppose we add ">" to the general Adams conditional, which can only occur as a main operator, and which obeys the principle that the degree of belief in A > B is always the contingent degree of belief in B given A.
Belief Degree/Field: If we assume that contingent and not contingent belief is represented by conditional or unconditional Q, we obtain that the degree of belief in A > B is equal to Q (B I A).
Adams-Conditional/Field: the normal Adams conditional assuming that belief degrees obey the probability laws captures the "if ... then" better than the probability function of the conditional.
In any case, this only occurs as a main connection:
E.g. "when I try it, I will be added to the team ("If I try out for the yankees, I will make the team").
Then the general Adams conditional seems appropriate for vagueness. If that is so, then the
belief degree of A > B should be:
Q (DA I A).
Probability function/belief degree: Difference: for the probability function, the contingent probability is never higher than the probability of the material conditional.
Williamson/Field: for his argument (1 - 3), this is important: all premisses get the Q value 1 if "if ... then" are read as a general Adams conditional. Then the classic conclusion is not valid in this reading of "if ... then".
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