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A probability function is non-conglomerable just in case there is some proposition E and partition (pi ) of the space of possible outcomes such that the probability of E conditional on any member of (pi ) 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.

DOI: 10.1007/s11229-016-1261-3

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