This article redefines arbitrariness not as a normative flaw or a symptom of domination, but as a foundational functional mechanism structuring human systems and interactions. Diverging from critical traditions that conflate arbitrariness with injustice, it posits arbitrariness as a semiotic trait: a property enabling systems - linguistic, legal, or social - to operate effectively while withholding their internal rationale. Building on Ferdinand de Saussure's concept of l'arbitraire du signe, the analysis extends this principle beyond language to demonstrate its cross-domain applicability, particularly in law and social dynamics. The paper introduces the "Motivation -> Constatability -> Contestability" chain, arguing that motivation functions as a crucial interface rendering an act's logic vulnerable to intersubjective contestation. When this chain is broken through mechanisms like "immotivization" or "Conflict Lateralization" (exemplified by "the blur of the wolf drowned in the fish"), acts produce binding effects without exposing their rationale, thus precluding justiciability. This structural opacity, while appearing illogical, is a deliberate design protecting authority from accountability. Drawing on Shannon's entropy model, the paper formalizes arbitrariness as A = H(L|M) (conditional entropy). It thereby proposes a modern theory of arbitrariness as a neutral operator central to control as well as care, an overlooked dimension of interpersonal relations. While primarily developed through human social systems, this framework also illuminates a new pathway for analyzing explainability in advanced artificial intelligence systems.