The article deals with a pivotal conceptual distinction used in philosophical discussions about global justice. Cosmopolitans claim that arguing from the perspective of moral cosmopolitanism does not necessarily entail defending a global coercive political authority, or a ‘world-state’, and suggest that ambitious political and economic (social) goals implied in moral cosmopolitanism may be achieved via some kind of non-hierarchical, dispersed and/or decentralized institutional arrangements. I argue that insofar as moral cosmopolitans retain ‘strong’ moral claims, this is an untenable position, and that the goals of cosmopolitan justice, as explicated by its major proponents, require nothing less than a global state-like entity with coercive powers. My background ambition is to supplement some existing works questioning the notion of ‘governance without government’ with an argument that goes right to the conceptual heart of cosmopolitan thought. To embed my central theoretical argument in real-world developments, I draw on some recent scholarship regarding the nature of international organizations, European Union, or transnational democratization. Finally, I suggest that only after curbing moral aspirations in the first place can a more self-consciously moderate position be constructed, one that will carry practical and feasible implications for institutional design. [ABSTRACT FROM PUBLISHER]