  As has been noted several times earlier, formal intensional logics have been developed with a full hierarchy of higher types, Church,  Montague, Bressan, Tichý for instance. Such logics can be rather formidable, but Carnap’s ideas are often (certainly not always) at the heart of such logics, these ideas are simple, and are sufficient to allow discussion of several common intensional problems. Somehow, based on its sense (intension, meaning) a designating phrase may designate different things under different conditions—in different states. For instance, “the number of the planets” was believed to designate 6 in ancient times (counting Earth). Immediately after the discovery of Uranus in 1781 “the number of the planets” was believed to designate 7. If we take as epistemic states of affairs the universe as conceived by the ancients, and the universe as conceived just after 1781, in one state “the number of the planets” designates 6 and in the other it designates 7. In neither state were people wrong about the concept of planet, but about the state of affairs constituting the universe. If we suppress all issues of how meanings are determined, how meanings in turn pick out references, and all issues of what counts as a possible state of affairs, that is, if we abstract all this away, the common feature of every designating term is that designation may change from state to state—thus it can be formalized by a function from states to objects. This bare-bones approach is quite enough to deal with many otherwise intractable problems.