And indeed Kaplan says the following in ‘Afterthoughts:’
“... we should say that context provides whatever parameters are needed. [Footnote: This, rather than saying that context is the needed parameter, which seems more natural for the pretheoretical notion of a context of use, in which each parameter has an interpretation as a natural feature of a certain region of the world.]” (p. 591, emphases in the original).
In so far as I remember, this interpretation seems to be, in any case, at least consistent with the formal system in “Demonstratives” (p. 543). Or am I wrong here?