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While natural sciences such as physics hold causality for granted as one of the most fundamental principles to make adequate theories of the real world, social sciences, first of all, sociology have not this advantage. Of course, humans are subjected to causality insofar as they are physical entities too, but moreover they are endowed with free will that essentially complicates their behavior and social activity. Unlike causality, logistics should take the same place in social sciences. Conscious beings behave rationally and act logistically as well as they possess some physical experience (including causality) and socially structured knowledge. Thus, free will is restricted not only by causality and other physical laws but also logistics. This paper argues for a logistical approach to the society and models the state as a power hierarchy (mathematical ideal). The state can exist, function, and be stable over time only as a hierarchy. Then sovereignty emerges as a logistical phenomenon whose ‘dynamical magnitude’ is naturally decomposed by the societal strata of the society and the mankind as a whole. Further, any state-based legal system (SLS) can be analyzed in structuralism tradition by means of logical-algebraic modeling. When the states as a set of the self-sufficient (logistically complete) sovereign hierarchies confront in the international law field (ILF) it leads inevitably to incompleteness of the ILF. In sum, the logistical theorem on war can be elicited. [ABSTRACT FROM PUBLISHER]