 Many authors, including Armendt (1993), Christensen (1996, 2004), Hellman (1997), Howson and Urbach (1993), and more recently, Briggs (2009) and Mahtani (2015),  have endorsed and elaborated upon the idea that violation of the probability axioms amounts to a kind of inconsistency. For example, Armendt (1993) tells us that it involves an inconsistency that is revealed by the fact that degrees of belief guide action, and that Dutch Book vulnerability amounts to giving conflicting evaluations to the same option(s). He calls this “divided-mind” inconsistency, which he says is a flaw of rationality. This fits the typical sort of case where an agent violates additivity, and sometimes applies to violations of the other axioms, but incoherence does not always entail having two different evaluations of the same option. Although degrees of belief often serve as guides to action, they need not be tied to an evaluation of options at all. However, it is a fundamental assumption of most versions of the DBA that credences do have such a role, as in the theories of Ramsey and de Finetti, so it is of interest that even with this assumption, incoherence need not involve giving conflicting evaluations (Vineberg 2001). Consider for instance a person who is less than fully confident of Fermat’s Last Theorem, perhaps because they don’t know that it has been proven. On at least some ways of understanding propositions, this need not entail attaching two different judgments to the same proposition. One could also violate coherence by only attaching a probability of less than one to a single proposition that is a logical truth, or one could avoid different evaluations by having the same level of confidence in every proposition. These examples aside, even the additivity axiom is problematic on Armendt’s interpretation, for it requires, for mutually exclusive propositions \(p\) and \(q\), that joint bets on \(p\) and on \(q\) amount to the same option as a bet on \(p\) or \(q\). This in turn presumes that values are additive, which goes beyond simply having degrees of confidence in \(p, q\), and their disjunction, although Armendt (1993) suggests that the assumption is generally met and appropriate for the purposes of the DBA.