ABSTRACT
Note that the addition of constant symbols to the language introduces fur ther complications. In counterpart semantics, it is far from straightforward to interpret constant symbols, because we need to give an interpretation of these symbols across possible worlds that respects the counterpart relations in some appropriate sense. Variables on the other hand simply denote “objects” in the domain of a given world. In the case of traditional semantics this asymmetry appears in a similar fashion if one allows constant symbols to be non-rigid, as has been done e.g., in [5]. Then, variables denote transcendental entities, whereas constants denote something like individual concepts, i.e. functions from possible worlds to a domain. Facing this dilemma, one solution is to completely move to a higher-order setting, where constants and variables can be of various higher types, e.g., type-0 constants denote objects, type-1 con stants individual concepts etc. (cf. [3]). In this paper, we will follow a different approach, treating constants and variables in the same way, but assuming a more sophisticated notion of a modal individual and identity-at-a-world.
