The Theorem of Dual Closure and How it Leads to the Operator Hierarchy

During the construction phase of the new theory introduced in this book, it became apparent that the quest for a foundation of a theoretic framework for analysing natural organisation may profit from the classical approach to mathematics developed by the great Greek mathematician Euclid. His approach allows a consistent framework to be built from the ground up, providing a theoretical model of how nature has constructed increasingly complex types of systems. The theoretic logic could serve as a philosophical instrument that could support the recognition of increasingly complex types of organisation in nature which in turn correspond with the levels indicated by the theoretic logic. Ideally one finds a close match between the abstract model and the observations of natural organisation.