Despite pervasive variation in the content of laws, legal theorists and anthropologists have often argued that laws share certain abstract features and even speculated that law may be a human universal. In the present report, we contribute cross-cultural data to this debate: Are there cross-cultural principles of law? Participants in eleven different countries (N = 3054) were asked whether there could be laws that violate certain procedural principles (e.g., laws applied retrospectively or unintelligible laws), and also whether there are any such laws-in a between-subjects design. Confirming our pre-registered prediction, people reported that such laws cannot exist, but also (paradoxically) that there are such laws. These results document cross-culturally and -linguistically robust beliefs about the nature of law which defy people's conception of how legal systems function in practice.