The qualitative paradox of non-conglomerability

A probability function is non-conglomerable just in case there is some proposition E and partition of the space of possible outcomes such that the probability of E conditional on any member of is bounded by two values yet the unconditional probability of E is not bounded by those values. The paradox of non-conglomerability is the counterintuitive-and controversial-claim that a rational agent's subjective probability function can be non-conglomerable. In this paper, I present a qualitative analogue of the paradox. I show that, under antecedently plausible assumptions, an analogue of the paradox arises for rational comparative confidence. As I show, the qualitative paradox raises its own distinctive set of philosophical issues.