On Formally Undecidable Propositions of Law: Legal Indeterminacy and the Implications of Metamathematics

Recent articles in the Critical Legal Studies literature claim that results from mathematical logic show that no system of law can be formalized so that every dispute is determinate. Specifically, it has been suggested that G6del's Incompleteness Theorem and the works of Lbwenheim and Skolem inform the question whether the law compels outcomes of cases. Because those results prove that certain formal systems of mathematics are necessarily indeterminate, they might suggest that analogous claims are true of the law. In their Article, Mr. Greenberg and Professor Brown analyze Gbdel's Incompleteness Theorem in an attempt to determine how, if at all, these proofs apply to the law.

The underlying issue addressed by this Article is whether the law can formally direct outcomes, given specific facts. The authors demonstrate that for any reasonably powerful formalization of the law, a proposition can be constructed that cannot be formally resolved. Like mathematics, any formally constructed model of the law must prove trivial, inconsistent, or incomplete. Legal reasoning cannot be automated, and must ultimately turn on human judgment and intuition.

The ideal of legal formalism is therefore an illusion.