I don't know if I've misread some people here, but it's silly to insist that the law be a formal system. It's impossible. Common Law uses judicial precedent to fill in ambiguities as they turn into actual disputes. If you had to formally define everything, then a) it would run into the various Incompleteness Theorems in logic (like Goedel's) and the Principle of Explosion, so it would go hilariously wrong b) No law would ever get passed, as people would spend years trying and failing to recursively define every term.
Appropriately enough, Gödel had this very problem when getting US citizenship, where he tried to argue that the law had a logical problem:
"On December 5, 1947, Einstein and Morgenstern accompanied Gödel to his U.S. citizenship exam, where they acted as witnesses. Gödel had confided in them that he had discovered an inconsistency in the U.S. Constitution that could allow the U.S. to become a dictatorship; this has since been dubbed Gödel's Loophole. Einstein and Morgenstern were concerned that their friend's unpredictable behavior might jeopardize his application. The judge turned out to be Phillip Forman, who knew Einstein and had administered the oath at Einstein's own citizenship hearing. Everything went smoothly until Forman happened to ask Gödel if he thought a dictatorship like the Nazi regime could happen in the U.S. Gödel then started to explain his discovery to Forman. Forman understood what was going on, cut Gödel off, and moved the hearing on to other questions and a routine conclusion"
