 However, in the Boolean algebra generated from \(W\), no possible-worlds proposition gets a probability of ½ under \(\Pr\). Hájek (1989) in fact showed that there are more distinct conditional probability values than distinct unconditional probability values, for any finite set of possible worlds \(W\) that has at least three worlds with non-zero probability. As pointed out in Égré and Cozic (2011), this result offers a structural analogy with undefinability results in generalized quantifier theory. “Most \(A\)s are \(C\)s” is not definable by applying the unrestricted “most” to first-order definable propositions. Similarly here, we may view the result as showing that in a sentence like “there is a probability of ½ that if \(A\) then \(C\)”, the embedded conditional does not express any proposition.