Dissensus – incompatible theories co-existing for an extended period – has been traditionally viewed as a rare accident or else as a stage in the progression of scientific inquiry that is bound to terminate: on these views, consensus is the stable state to which science tends. Following Miriam Solomon's reconsideration of dissensus as rationally on par with consensus, it is argued that the persistence of dissensus is compatible with the pull towards the resolution of inconsistency. While the social turn in philosophy of science goes some way towards relieving the tension, the key move is to go one step beyond and to distinguish between the social-psychological level, where the pull towards resolution is in force, and the public level, where it does not operate directly and can be counter-balanced by other mechanisms. An added benefit of this approach is to provide a more realistic picture of the scientists' predicament, at both the individual and communal levels, who face not only Nature but public science that stand in need of interpretation. Finally, it is suggested that dissensus enhances the ability of public science to quickly overcome impasses.