How hyper are hyperpropositions?

It is an old dispute among logicians and philosophers of language just how finely individuated propositions ought to be. Frege, for one, was torn between two criteria: logical equivalence, which is an exact, but probably also overly crude criterion, and cognitive significance, which is an inexact but arguably on the right track. Possible-world semantics, taking off around 1960, has gotten much technical and philosophical mileage out of the former criterion, but the insight is catching on that propositions need to be more finely individuated than in terms of mathematical mappings. Sophisticated theories of propositions embrace a three-tiered strategy, according to which fine-grained hyperpropositions apply to sentential senses, explicit attitudes, etc.; coarse-grained possible-world propositions apply to states-of-affairs, implicit attitudes, etc., while truth-values make up the third tier. This paper explains the rationale for hyperpropositions and outlines one particular theory maintaining that their right calibration is in terms of near-identity (isomorphism) among abstract procedures. This proposal tallies with the prevalent idea that hyperpropositions are structured meanings.