  Carnap’s fundamental idea is that intensions, for whatever entities are being considered, can be given a precise mathematical embodiment as functions on states, while extensions are relative to a single state. This has been further developed by subsequent researchers, of course with modern possible world semantics added to the mix. The Carnap approach is not the only one around, but it does take us quite a bit of the way into the intensional thicket. Even though it does not get us all the way through, it will be the primary version considered here, since it is concrete, intuitive, and natural when it works.