In this paper, I revisit Mattias Kumm's work on a ‘cosmopolitan conception of law’. I make two claims: First, I claim that although some criticism can be resisted by Kumm, under closer methodological scrutiny there are flaws in his theory. Second, I claim that these flaws challenge Kumm's approach when reading the Charter of the United Nations (UN Charter) as a ‘global constitution’. This also has pertinent practical implications for the functioning of the United Nations. This contribution does not take (...) a stance on the nature of law but focuses on this conception in the context of politics and law. In a first section, I recount Kumm's cosmopolitan conception of law. In a second section, I claim that implicit monism in the relationship between national and international law and theoretical idealization pose serious difficulties to the cosmopolitan approach. In a third section, I claim that these flaws pose a challenge to the United Nations when considering the UN Charter as a 'global constitution'. I sum up my findings in a final section and reflect on a future outlook for research on global constitutionalism in political philosophy. (shrink)