The author says (and I agree) that the process of judging cannot be easily performed completely by a computer, and goes on arguing for better retrieval systems for legal texts -- so Gödel would probably just shrug.
Actually, I think laws (at least in the Civil Law sense; I'm not too familiar with Case Law) could be adequately represented in some formal logic language if the value judgements are made explicit so that the semantics of the law language specifies the meaning of most operators explicitly but leaves the judging-operator up to human judgment.
Case law is very rarely discrete; the point of case law is that the law is not and should not be mechanically applied.
Case law arises from the chancery courts of England, where the primary goal of the court was to do what was "fair", rather than simply what the law said.
