The limits of formal systems are nowhere near being approached by law, which is generally pretty simple but written in obtuse language or full of exceptions that exist purely because of the fact that its very hard to change laws. Legal communication is precisely the opposite of efficient. That being said, some types of law are obviously less amenable to being described in formal language (like laws concerning murder or situations involving complicated human - human interaction). But that is absolutely not true for the average contract , which constitutes most of the legal industry's revenues and time. In that case the only problem is that laws are pointlessly complex. As another example, we'd all be a lot better off if taxes were formulated as a program.
Laws are neither complete nor free of contradictions, and they don't have to. They are the result of a consensus among members of society that has grown over centuries. Democracy is significantly based on trust, transparency and comprehensibility. Legislation is subject to the permanent challenge of finding a balance between regulatory density and manageability. And even if it were socially feasible to rewrite all existing laws, to formalize them, and to massively increase the density of rules: the set of rules will always remain discrete, and it is a naïve assumption to want to fully capture the continuity of human action with a discrete set of rules; there will always remain an unspecified residue that requires human judgment. Striving for a perfect system fails merely because there is no universally accepted definition of a perfect system; and societies in which an attempt was made to realize the utopia of a perfect system were usually totalitarian or became totalitarian in a short time.
