A maximal system is one in which the set of maxims (or premises) from which conclusions can be derived are themselves a posteriori conclusions about the correct application of a metareasoning involving the whole of the system. Individuals’ rights that are themselves derived from our social expectations and cultural values are an example of base maxims in a maximal system. Although the maxims are themselves culturally a posteriori, they operate as the fundamental assumptions, or postulates, upon which the derived conclusions are based. A fundamental maxim inherent to all maximal systems (and possibly the only essential maxim in any such system) is that the system cannot be consistently axiomatized globally with any certainty, thereby making the maximal system's function transcendental in nature.
In a maximal system (such as a system of human rights), it is assumed from the beginning that the maxims (in this case individual rights) are contradictory in their overlap and that the correct application of reasoning within such a system tends to minimize the tension's between the conflicting maxims and maximize the utility of the set of maxims taken collectively, which in turn further minimizes tensions in a systems dynamics feedback loop. This contrasts with an axiomatic system which (when axioms are appropriately chosen) will create a mathematical structure void of any contradiction. The systems dynamics analysis is used in human rights systems because the application of government action on our expectations discovers and creates new maxims which will in turn be acted upon. The fact that this happens in real time means that the symbolic representation of the information, the underlying physical process that is acting on the information, and the information itself cannot be clearly separated.
In a maximal system, the set of maxims taken as a whole has the emergent property that it effectively reduces all inherent tensions that are due to its internal contradiction (if maxims have been properly chosen and correctly acted upon). In the development of a healthy civilization, new and better maxims are created while simultaneously minimizing tensions between existing rights and maximizing personal freedom, and thereby also maximizing economic utility.
In a maximal system, a just government would function to foresee the ways in which each of the actors which it governs will apply their own greedy algorithm to social participation, and thereby collect and redistribute wealth to nudge the collective group of actors toward the global optimum which their individual greedy algorithms might otherwise cause them to fall short of. In such a system, the global optimum is defined in terms of greatest social mobility, information exchange, egalitarian access to necessities, wealth production and distribution, and the least possible armed conflict.