I argue that expressions that denote sets of alternatives interact with their semantic contexts by taking scope. My account relies only on two freely-applying type-shifters: the first is Karttunen’s (1977) proto-question operator, aka Partee’s (1986) IDENT, and the second can be factored out of extant approaches to the semantics of questions in the tradition of Karttunen (1977). These type-shifters form a decomposition of LIFT, the familiar function mapping values into scope-takers. Exceptional scope of alternative-generating expressions arises via (snowballing) scopal pied-piping.
With an empirical focus on English indefinites, I argue that this approach to alternatives improves on standard alternative-semantic architectures that use point-wise composition to subvert islands (and, more generally, on in situ approaches to indefinites). Specifically, unlike grammars based on point-wise composition, scope-based alternative management is thoroughly categorematic, does not under-generate readings when multiple indefinites occur on an island, and is readily compatible with standard treatments of binding. I explore two generalizations of the basic theory: one is oriented around assignment-relative sets of alternatives, and the other incorporates a dynamic perspective on assignment functions. The upshot is that dynamic semantics can be seen as a strict extension of alternative semantics, with the initial results (including island insensitivity for alternative generators) preserved.