The necessity calculus is a familiar adjuvant to the possibility calculus and an uncertain inference tool in its own right. Necessity orderings enjoy a syntactical relationship to some probability orderings similar to that displayed by possibility. In its adjuvant role, necessity may be viewed as bringing possibility closer to achieving the quasi-additive normative desideratum advocated by de Finetti. Nevertheless, there are occasions when one might choose to use possibility without the help of necessity, e.g. when the full range of alternative hypotheses is unknown, or to exploit possibility’s distinctive ability simultaneously to express preference as well as credibility ordering. Such situations arise in uncertain domains like the evaluation of scientific or mathematical hypotheses, where professions of belief may reflect aesthetic, utilitarian, and evidentiary considerations as much as the usual notions of credibility.