Dynamic semantics has two key components: state and nondeterminism. The former allows expressions to introduce discourse referents, and the latter allows indefinites to be analyzed as nondeterministic analogs of proper names. This talk motivates a picture in which state and nondeterminism are analyzed as linguistic side effects, and formalizes this in terms of the category-theoretic notion of a monad. In contrast with standard dynamic semantics, the semantics I propose is dynamic down to the morpheme, has no use for an operation of dynamic conjunction, and explains a wide variety of exceptional scope phenomena (encompassing both familiar and novel data) without stipulation. Because of the inherent modularity of the monadic approach, it is straightforward to extend the theory to handle phenomena like conventional implicature (à la Potts) and focus. In addition, the monadic perspective suggests a fundamental connection between dynamic and static alternatives-based analyses of indefinites, while offering a clear accounting of how they differ.