 Carnap (1946, 1947) worked out an intensional semantics for necessity and possibility operators for different example languages, and for the modal logic S5 that C.I. Lewis (1944) had previously discussed (see the supplement  Semantics (Section 1)  for the details). He also started exploring areas that are presently of special interest, such as “hyperintensional” semantics (see, e.g., Yablo 2014): In the context of addressing the paradox of analysis, he found that a stronger or finer-grained notion of synonymy was needed than identity of intension, i.e., L-equivalence, and he defined a relation called “intensionally isomorphic to” for that purpose. In response to critiques by Benson Mates and Leonard Linsky (1949), who pointed out instances of apparent synonymity that were not intensionally isomorphic by Carnap’s definition, Carnap replied that this just showed that the ordinary-language conception of “synonymity” is vague, and that actually it conceals a number, perhaps a range, of explicanda; for certain purposes, he agreed, a still stronger (or finer-grained) conception of intensionality (and thus synonymity) might be required (Carnap 1949). 