Relativity Self-Reference Fundamental Constraints of Complexity in Relative Relations

The relationship between the whole and its parts within a given system is the core relationship underlying both reductionism and complexity. Moving beyond the intuitive conjectures and phenomenological descriptions common in the philosophy of complexity, this paper adopts an axiomatic method based on first principles. Starting from the fundamental constraint of the principle of relativity, it rigorously derives the self-referential structure linking the parts and the whole of a system, and uses the vicious-circle principle to resolve the circular definitions and contradictions arising from self-reference. The laws of complexity derived here follow precisely from this treatment of self-reference. They show that, in addition to interactions among matter, energy, and information, natural systems are subject to a fundamental constraint of relativity relating the local to the whole. This constraint is independent of component types and evolutionary mechanisms, and it provides a unified logical explanation for core phenomena of complex systems, including emergence, chaos, criticality, and hierarchy.