 To generate the correct analysis, we need to invoke three distinct worlds: the actual world \(w_1\), where the Titanic hit an iceberg, a counterfactual world \(w_2\) where it did not, and another counterfactual world \(w_3\) where all survivors of the voyage in \(w_2\) died. So double-indexing and 2D matrices cannot fully capture the compositional semantics of modal sentences: we will need an infinite sequence of possible world indices. For further work on multiple-indexed semantics, see (Ninan 2010; Yalcin 2015).