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The qualitative paradox of non-conglomerability. (English) Zbl 1436.60004

Summary: 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.

MSC:

60A05 Axioms; other general questions in probability
03A10 Logic in the philosophy of science
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