Some Lesson About the Law From Self-Referential Problems in Mathematics

We first describe briefly mathematician Kurt Gödel’s brilliant Incompleteness Theorem of 1931, and explore some of its general implications. We then attempt to draw a parallel between axiomatic systems of number theory (or of logic in general) and systems of law, and defend the analogy against anticipated objections. Finally, we reach two types of conclusions. First, failure to distinguish between language and metalanguage in mathematical self-referential problems leads to fallacies that are highly analogous to certain legal fallacies. Second, and perhaps more significantly, Gödel’s theorem strongly suggests that it is impossible to create a legal system that is “complete” in the sense that there is a derivable rule for every fact situation. It follows that criticisms of constitutional systems for failure to determine every answer are unfair: they demand more than any legal system can give. At best they are antilegal in the sense that rejection of such constitutional systems on such a ground would require the rejection of all constitutional systems.