Inconsistency as a Touchstone for Coherence Measures

The debate on probabilistic measures of coherence has focused on evaluating sets of consistent propositions. In this paper we draw attention to the largely neglected question of whether such measures concur with intuitions on test cases with inconsistent propositions and whether they satisfy general adequacy constraints on coherence and inconsistency. While it turns out that, for the vast majority of proposals in their original shape, this question must be answered in the negative, we show that it is possible to adapt many of them in order to improve their performance.