Theorists trying to model natural language have recently sought to explain a range of data by positing covert operators at logical form. For instance, many contemporary semanticists argue that the best way to capture scalar implicatures is through the use of such operators. We take inspiration from this literature by developing a novel operator that can account for a wide range of linguistic effects that until now have not received a uniform treatment. We focus on what we call redundancy effects which occur when attitude verbs and modals imply that certain bodies of information are unsettled about various claims. We explain three pieces of data, among others: diversity inferences, ignorance inferences, and free choice inferences. Our account yields an elegant model of redundancy effects, and has the potential to explain a wide range of puzzles and problems in philosophical semantics.