We propose a novel way of carrying out Beck's (2006) insight that focus intervention can be studied in the framework of alternative semantics. Our implementation relies on the idea that focus alternatives and ordinary alternatives are alternatives along different dimensions. The interaction of different types of alternatives gives rise to inappropriate quantificational domains of focus-sensitive operators, causing focus intervention.
On the empirical front, this approach has updated the generalization of focus intervention in two ways. First, focus-sensitive operators are no longer taken to be inherent interveners; they become problematic only when they take a set of sets of alternatives as its quantificational domain. On this view, focus intervention is not actually an intervention phenomenon, but a purely quantificational phenomenon. Second, this approach allows for a very general understanding of focus intervention, providing a unified analysis of focus intervention with interrogative wh-phrases, non-interrogative wh-phrases and disjunctive phrases. On the theoretical front, this approach makes Alternative Semantics a more fascinating theory by recognizing that alternatives along different dimensions may interact to give rise to interesting grammatical phenomena.