Possible world semantics meets metaphysics

Possible world semantics has been gradually fine-grained over the years. First, simple extensional semantics was fine-grained by relativizing it to worlds considered as counterfactual, thus generating standard possible-world semantics, which was later further fine-grained by relativizing it to worlds considered as actual, thus generating two-dimensional semantics. However, worlds considered as actual were only considered with respect to the empirical facts obtained in such worlds. This paper shows that no less of an important role is played by another feature of actual worlds, namely, the criteria of identity that obtain in such worlds.