Topic: HUMAN SEMANTICS
Strict Identity with No Overlap
By Achille C. Varzi
It is natural to think that a standard, Kripke-style semantics for quantified modal logic (QML) is incompatible with the view that no individual can exist in more than one possible world, a view that seems to require a Lewis-style, counterpart-theoretic semantics instead. Strictly speaking, however, this thought is wrong-headed. A standard semantics regards a modal statement such as ?I might have been fat? as true only if I am in the extension of ?is fat? at some other possible world, whereas counterpart theory regards it as true only if a counterpart of mine is in the extension of ?is fat?. But just as the truth conditions of counterpart theory are in principle compatible with the possibility (rejected by Lewis) that some individuals qualify as their own other-wordly counterparts, the truth conditions of a standard semantics are in principle compatible with the possibility (dismissed by Kripke) that all individuals are world-bound. Here is how.
Source: Online Papers in Philosophy