Suspension of Judgment, Non-additivity, and Additivity of Possibilities

Abstract

In situations where we ignore everything but the space of possibilities, we ought to suspend judgment—that is, remain agnostic—about which of these possibilities is the case. This means that we cannot sum our degrees of belief in different possibilities, something that has been formalised as an axiom of non-additivity. Consistent with this way of representing our ignorance, I defend a doxastic norm that recommends that we should nevertheless follow a certain additivity of possibilities: even if we cannot sum degrees of belief in different possibilities, we should be more confident in larger groups of possibilities. It is thus shown that, in the type of situation considered (in so-called “classical ignorance”, i.e. “behind a thin veil of ignorance”), it is epistemically rational for advocates of suspending judgment to endorse this comparative confidence, while on the other hand it is shown that, even in classical ignorance, no stronger belief—such as a precise uniform probability distribution—is warranted.