A specific indefinite presupposes that someone has in mind an individual who has the property denoted by its descriptive content. Having an individual in mind means that the agent knows who the referent is, and thus it affects the information state of the agent, but not the others. The asymmetric information, shared by all participants in a conversation, cannot be represented when the common ground has only one information state. Thus a common ground must have multiple information states, each for each participant in a conversation. The information state of the agent who has an individual in mind must be differentiated from the others' by being structured into sub-information-states so that each sub-information-state associates the specific indefinite with a different unique individual. It then conveys the information that the agent has some individual in mind, but that it is not known yet who it is. This analysis thus requires a new dynamic semantics which is partially representational and partially denotational. This leads to a new analysis of proper names. Specific indefinites tend to have widest scope, which is explained by claiming that specific indefinites trigger presuppositions. Presuppositions are assumed to have various scopes with respect to operators in a sentence, and the strongest reading is preferred on rational and economic basis. It is shown that stronger readings roughly correspond to wider scopes. This book will be of interest to scholars who work on indefinite NPs, presuppositions, anaphora in belief contexts, and dynamic semantics in general.