Sichelman on The Mathematical Structure of the Law @tedsichelman @USanDiegoLaw

Ted M. Sichelman, University of San Diego School of Law, has published The Mathematical Structure of the Law. Here is the abstract.

Scientific “law” and human-made law (“social law”) are both “laws” in a very 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 formalism of Wesley Hohfeld and related work, this article proposes a novel, mathematical model of legal entitlements. This model allows for physical and mathematical properties—such as entropy, indeterminacy, temperature, and modularity—to be adapted to provide for quantitative measures of the properties of legal systems. Moreover, previous logical models exhibit an important feature: if all relevant information is known, legal actors hold determinate sets of legal entitlements. Although theorists have modeled legal entitlements under conditions of incomplete information, which can effectively lead to indeterminacy, this article proposes a model in which—even with complete information—legal entitlements can exhibit indeterminacy. Unlike classical indeterminacy, which is of a stochastic nature, this sort of “inherent” indeterminacy is akin to—and can be readily modeled by—the notion of “indeterminacy” in quantum mechanical formalism. These results have important implications for the nature of legal rules, legal artificial intelligence, game theory and the law, and the ontology of rule-based systems more generally. Of particular note, the formalism suggests a novel approach to the quantum measurement problem, which proposes that measurement is a “second-order” physical process—fundamentally different from ordinary, “first-order” physical processes.

Download the article from SSRN at the link.