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This paper generalises an argument for probabilism due to Lindley . I extend the argument to a number of non-classical logical settings whose truth-values, seen here as ideal aims for belief, are in the set
, and where logical consequence
is given the “no-drop” characterization. First I will show that, in each of these settings, an agent’s credence can only avoid accuracy-domination if its canonical transform is a (possibly non-classical) probability function. In other words, if an agent values accuracy as the fundamental epistemic virtue, it is a necessary requirement for rationality that her credence have some probabilistic structure. Then I show that for a certain class of reasonable measures of inaccuracy, having such a probabilistic structure is sufficient to avoid accuracy-domination in these non-classical settings.
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