>Software is an axiomatic system. Human behavior is NOT.

I am not aware of any system of law that covers all possible human behavior. Common law systems theoretically could because part of the determination of what is covered is up to the courts, thus when you have a new human behavior it is uncertain if it is covered or not until you take it to court, but in a Napoleonic system the coverage of the law must be explicitly stated.

Thus Napoleonic systems would try for consistent but not complete.

I assume you refer to his results regarding axiomatic systems for arithmetic on natural numbers? If a law attempts to capture this, then, sure, it's problematic. But I don't that's very common.

From what I've seen, formal methods for legal systems would take the "facts" of a case as given (assumptions), and deduce legal consequences of those.