Historically one can deduce several models of the objectivity of legal discourses. The key concept of the first model is "subjective right", which was conceived as a sort of entitlement, exclusive dominance of the entitled within a definite sphere. The whole social landscape was conceptualized as divided into exclusive spheres of dominance, monads with strictly delineated ("hard and fast lines") borders. The key thesis was a purely Kantian one: the possibility of peaceful and conflictless coexistence of such exclusive entitlements. The Kantian formalism enabled objectivity of law, because law was conceived predominantly in a "rules of a game" fashion. It enabled to achieve any goal a given person would like to without that the law itself had any specific goal.
The second model reflected another more complex and dynamic society. The idea of a non-conflict coexistence was abandoned and the emphasis has shifted from the subjective right to the objective law. The basic function of the latter was to solve the conflicts of social interests on the basis of the political compromises achieved within the political system. The type of objectivity has changed dramatically. Now, it was an objectivity of the "clear sense" of the legal enactment. The political compromises achieved within the political sphere were formulated as legal rules, each possessing a literal sense which enabled uniform interpretation and application. Objectivity now means uniformity of application.
Very soon it has become clear that this ideal is a pure illusion. One need an omniscient God as the legislator to achieve the ideal of a gapless, uncontroversial and politically neutral (with respect to application and interpretation) legal system. Interpretation is context dependent enterprise. That's why a third model of objectivity has occurred. The key concepts here is interpretivism, narrative coherence and argumentation. In a situation of relatively underdetermined legal rules the weight of a better argument raises. This type of objectivity rests on the internalist concept of (best) narrative coherence.