Why do states recognize an obligation to observe the rules of international law? Existing accounts of international legal obligation suffer from the problem of 'interiority'. They first ground obligation in some internal feature of the international legal system - such as consent, fairness or dialogue - but when these turn out to be insufficient, they fall back on assumptions about the legitimacy of the international legal system itself, for which they cannot account. The roots of this problem ultimately lie in flawed conceptions of politics that underlie these accounts. To overcome this problem, this article proposes an alternative, 'interstitial' understanding of politics that locates politics at the intersections of idiographic, purposive, ethical and instrumental forms of reason and action. This understanding of politics enables us to rethink the nature of institutional rationality, and in turn the bases of international legal obligation. Furthermore, it provides us with a conceptual framework that illuminates the relationship between historically grounded modes of politics and the legitimacy of particular institutional forms, including the modern system of international law. This argument is illustrated through an explanation of the sacral logic of obligation that undergirded the international legal system in the Age of Absolutism.