The Ramban and the Axiomatic Analogy to Torah Law
Law is not usually thought of as an axiomatic system. In fact, there is no reason why a legal system cannot be a chaotic conglomeration of rules, some of which may even contradict each other. It would take some bit of research to come up with real historical examples.
Jewish Law, as codified by the Rambam, is superbly logical and well ordered. One of the great features of the Mishneh Torah is the orderliness, the categories, and logical divisions which aid the student of Torah to understand Halacha – and the place of a particular Halacha within the general system.
The analogy with an Axiomatic System is just that. An analogy draws attention to similarities as well as differences. Jewish Law, as do all legal systems, begins with Basic Laws and then Subsets of Laws. There are different levels and degrees of authority and obligation based on the level of law with which we are dealing.
In Jewish Law, the Deraitot, the Rulings of the Torah itself, form the highest level of legal ruling within the system. There are rules of inference and derivation, just as in math, which in some cases are considered Halachot Le Moshe MiSinai. There are aso a multiplicity of exceptions to the case because of the exigencies of real life. (See Halichot Olam) Such exceptions to the rule breaks down the Axiomatic Analogy.
Finally, the idea of an Axiomatic System of Law is attacked by the Ramban in his Hasagot to the Rambam’s First Shoresh in Sefer HaMitzvot. According to the Ramban, the list of Taryag might be totally different from the Rambam’s enumeration. Further, he hints that the Concept of Taryag itself is not accepted by everyone in the Talmud. The number of Mitzvot Deraita may be larger or smaller than the list enumerated by the Rambam. ( Detailed examination the Ramban’s sources for this argument is a major study.)