So the problem is not that predicate logic fails to capture the meanings of [7a] and [7b]. The problem is, rather, how to derive [9a] and [9b] from [7a] and [7b] in a principled way. In order to derive these logical forms, we have to assume not only that an indefinite expression buried in a subordinate position ends up having wide scope, but also that it acquires universal force in the process. A theory based on such assumptions might capture the facts, but it would be clearly ad hoc, and would generate a host of false predictions, as well.