Summary - In the article I, first of all, analyse some objections to the possibility of a theory of global justice, outlining three fundamental ideas to overcome difficulties. I then discuss two different research programs, identified with the political and cosmopolitical conception of global justice, based on a thesis of Thomas Nagel. I finish proposing a conjecture, centered on the essential tension between the two conceptions, leading to the exploration of alternative political, institutional and legal possibilities within the bonds of a realistic description of space that the world allows us.