 Stalnaker (1984) endorses the possible-worlds view of propositions and imports it directly into his discussion of belief content: He contends the content of a belief is specified by the set of “possible worlds” at which that belief is true (see Lewis 1979 for a similar approach). The structure of belief content is thus the structure of set theory. Among the advantages Stalnaker claims for this view is its smooth accommodation of gradual change and of what might, from the point of view of a discrete linguistic structure, be seen as problematically indeterminate belief contents. Developing an example from Dennett (1969), he describes the gradual transition from a child’s learning to say (without really understanding) that “Daddy is a doctor” to having a full, adult appreciation of the fact that her father is a doctor. At some point, Stalnaker suggests, it’s best to say that child “sort of” or “half” believes the proposition in question. It’s not clear how to characterize such gradual shifts by means of a linguistic or quasi-linguistic propositional structure (1984, p. 64–65; see also Schwitzgebel 2001). On Stalnaker’s view, the child’s half-belief is handled by attributing her the capacity to rule out some but not all of the possibilities incompatible with Daddy’s being a doctor: As her knowledge grows, so does her sense of the excluded possibilities.