  One can recognize in \(L\)-truth a version of necessary truth using possible world semantics. There is no accessibility relation, so what is being captured is more like S5 than like other modal logics. But it is not S5 semantics either, since there is a fixed set of state-descriptions determined by the language itself. (If \(P\) is any propositional atom, some state-description will contain \(P\), and so \(\Diamond P\) will be validated.) Nonetheless, it is a clear anticipation of possible world semantics. But what concerns us here is how Carnap treats designating terms in such a setting. Consider predicates \(P\) and \(Q\). For Carnap these are intensionally equivalent if \(\forall x(Px \equiv Qx)\) is an \(L\)-truth, that is, in each state-description \(P\) and \(Q\) have the same extension. Without being quite explicit about it, Carnap is proposing that the intension of a predicate is an assignment of an extension for it to each state-description—intensional identity means identity of extension across all state-descriptions and not just at the actual one. Thus the predicate ‘\(H\)’, human, and the predicate ‘\(FB\)’, featherless biped, have the same extension—in the actual state-description they apply to the same beings—but they do not have the same intension since there are other state-descriptions in which their extensions can differ. In a similar way one can model individual expressions, “The extension of an individual expression is the individual to which it refers.” Thus, ‘Scott’ and ‘the author of Waverly’ have the same extension (in the actual state-description). Carnap proposes calling the intension of an individual expression an individual concept, and such a thing picks out, in each state-description, the individual to which it refers in that state description. Then ‘Scott’ and ‘the author of Waverly’ have different intensions because, as most of us would happily say, they could have been different, that is, there are state-descriptions in which they are different. (I am ignoring the problems of non-designation in this example.)