 A bit of terminology is in need of clarification here. De Finetti identified degrees of belief with betting quotients and termed degrees of belief that are susceptible to a Dutch Book incoherent; those that are not so susceptible he called coherent (de Finetti 1937). ‘Susceptible’ here should be understood in the sense of the above theorem, namely that bets are specifiable corresponding to those degrees of belief that will produce a sure loss to one side. Given the theorem, coherence amounts to satisfaction of the probability axioms, with incoherence involving their violation, and accordingly the terms are often used as a shorthand way of specifying whether the axioms are satisfied. However, both Ramsey and de Finetti understood incoherence to be a kind of inconsistency, and some use the term in this sense. There are various questions about understanding violation of the probability axioms and susceptibility to a Dutch Book as a  kind of inconsistency, as will be discussed, and so here it will be best to use ‘incoherent’ for degrees of belief that violate the probability axioms, and that by the Dutch Book theorem are associated with susceptibility to a sure loss, and leave open whether incoherence understood as such involves a form of inconsistency.