31 August 2016


The fascinating 'Legal Sets' by Jeremy N. Sheff proposes that
legal reasoning and analysis are best understood as being primarily concerned, not with rules or propositions, but with sets. The distinction is important to the work of lawyers, judges, and legal scholars, but is not currently well understood. This Article develops a formal model of the role of sets in a common-law system defined by a recursive relationship between cases and rules. In doing so it demonstrates how conceiving of legal doctrines as a universe of discourse comprising (sometimes nested or overlapping) sets of cases can clarify the logical structure of many so-called “hard cases,” and help organize the available options for resolving them according to their form. This set-theoretic model can also help to cut through ambiguities and clarify debates in other areas of legal theory—such as in the distinction between rules and standards, in the study of interpretation, and in the theory of precedent. Finally, it suggests that recurring substantive concerns in legal theory—particularly the problem of discretion—are actually emergent structural properties of a system that is composed of “sets all the way down.”
Sheff comments
The model developed in this paper will be useful to legal educators and law students, as a guide to the types of analytical moves that are part of “thinking like a lawyer.” And the tools of set theory are also of use to the practicing lawyer or judge—who must navigate and deploy the strategies discussed herein as part of the practice of their profession. But these insights may be intuitively grasped without resort to the formal architecture of symbolic logic. The key payoff of the set-theoretic model I will develop here engages legal theory, where heated substantive debates often leave important formal ambiguities unexamined. Not only can the set- theoretic model help cut through those ambiguities, it shows how some of these substantive debates are actually over inescapable structural features of law. 
The Article proceeds in four stages. Part I provides a brief overview of na├»ve set theory for those unfamiliar with it, introducing the terminology and concepts that will be deployed in the analysis that follows; those who feel comfortable with the concepts and notation systems of set theory and predicate logic may skim or skip this section. Parts II and III build the scaffolding of a set-theoretic model of law, and as I have warned they require some patience to see through. Part II demonstrates how the tools of set theory can be deployed to analyze the relationship between rules and cases, and to show how more complex legal doctrines build on set-theoretic concepts. Part III demonstrates more complex interactions of rules and cases, focusing on “hard cases” in which multiple applicable legal rules appear to contradict one another. This Part provides a more thorough description of the aforementioned strategies legal actors can use to negotiate such doctrinal conflicts at various levels of formal structure. Part IV discusses some implications and limitations of a set-theoretic understanding of legal doctrine, including its interaction with other aspects of legal theory. In particular, it shows how a set-theoretic understanding of legal practice cuts through ambiguities in the debate over the relative merits of rules and standards, in general jurisprudence and associated theories of interpretation, and in the theory of precedent.