International law suffers from a series of epistemic crises: it is unclear what forms it can take, who can make it, and how it relates to other, largely domestic legal orders. The reason is simple: many of the central concepts were devised over a century ago, for a different world, and have not kept pace. This article suggests that the crises can be met by engaging in two related intellectual operations: positing the possibility of presumptive law and connecting this to the concept of inter-legality