Despite the rearguard efforts of Robert Stalnaker and Max Cresswell, by the late 1990s it became widely acknowledged that sets of possible worlds are too coarse-grained to serve as propositions. It is safe to say that among those philosophers who believe in propositions, most think of them as sententially structured entities, composed out of the contents of the words and phrases in the sentences that express them. Fregeans hold that these contents are Fregean senses; Russellians hold that they are objects, properties, and relations.

Yet the 1990s also saw new challenges and approaches to structured propositions. George Bealer and Michael Jubien have independently argued (i) that it is counterintuitive to hold that we believe and assert structured complexes, and (ii) that theories of structured propositions are subject to the same problem that Paul Benacerraf raised for set-theoretic reductions of arithmetic. On one such reduction, the number...