Despite pervasive variation in the content of laws, legal theorists and anthropologists have argued that laws share certain abstract features and even speculated that law may be a human universal. In the present report, we evaluate this thesis through an experiment administered in 11 different countries. Are there cross-cultural principles of law? In a between-subjects design, participants (N = 3,054) 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. Confirming our preregistered 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 concept of law which defy people’s grasp of how legal systems function in practice.