Indefinites, wh-in-situ, and focus all display a characteristic insensitivity to islands. But a unified formal treatment of this island-insensitivity has proved elusive, and the extant piecemeal accounts (e.g., choice functions and alternative semantics) tend to both over- and under- generate, even with respect to their more narrowly construed empirical domains.

This talk argues that a new variety of alternative semantics offers a unified and empirically robust explanation of this data. This is accomplished by decomposing LIFT (e.g., Partee 1987) into two freely applying type-shifters (relevant technical concepts will be introduced, rather than presupposed). These typeshifters, which correspond to the category-theoretic/computer-science notion of a ‘monad’, are implicit in the post-Karttunen literature on questions, but they haven’t been factored out in precisely the way I’ll argue for here. The resulting theory gives a satisfying account of binding (including both in-scope and dynamic varieties), along with selectivity (e.g., multiple indefinites on a single island taking scope in different ways outside the island, Baker-ambiguities of embedded multiple-wh questions, and multiple association with focus). In addition, the proposal has far-reaching consequences for the organization of the lexicon: things that introduce alternatives interact in a modular fashion with things that don’t, without any need for lexical generalizations to the worst case.