The Mathematical Structure of the Law

Abstract

Scientific “law” and human-made law (“social law”) are both “laws” in a general sense—scientific laws “govern” the workings of the material world and social laws govern the behavior of people. Beyond this superficial resemblance, do social laws partake of the same sorts of mathematical structures as scientific laws? Many theorists have proposed formal, deontic-oriented logical models of legal rights and other entitlements. Here, leveraging the typology of Wesley Hohfeld, this Article proposes a novel, mathematical model of legal entitlements. This model incorporates physical and mathematical properties—such as entropy, indeterminacy, temperature, and modularity—to measure quantitative properties of legal systems. Moreover, this Article proposes a post-classical approach to model ontological legal indeterminacy by adapting the formalism of quantum mechanics. These understandings have important implications for the nature of legal rules, legal AI, game theory and the law, and the ontology of rule-based systems. Of particular note, the formalism suggests a novel approach to the quantum measurement problem, proposing that measurement is a “second-order” physical process, which is fundamentally different from the “first-order” physical processes currently described by quantum mechanics