Abstract

A synthesis of the two primary theory structures in Robert Rosen’s relational complexity, relational entailment mapping based on category theory as described by Rosen and Louie, and relational holism based on modeling relations, as described by Kineman, provides an integral foundation for relational complexity theory as a natural science and analytical method. Previous incompatibilities between these theory structures are resolved by re-interpreting Aristotle’s four causes, identifying final and formal causes as relations with context. Category theory is applied to introduce contextual entailment algebra needed to complete the synthesis. The modeling relation is represented as a recursive four-cause hierarchy, which is a unit of both whole and part analysis that relates realized and contextual domains of nature as complementary inverse entailments between structure and function. Context is a non-localized domain of distributed potentials for existence, as contrasted with the realized domain of localized interactive and measurable events. Synthesis is achieved by giving modeling relations an algebraic form in category theory and by expanding relational analysis to include contextual entailments. The revised form of analysis is applied and demonstrated to examine Rosen’s M-R diagram, showing that structure–function relations imply adaptive interaction with the environment, and that contextual relations imply three forms of the M-R entailment corresponding with the generally known three forms of life; Archaea, Bacteria, and Eukaryota, which can be represented by their holon diagrams. The result of this synthesis is a consistent foundation for relational science that should have important implications in many disciplines.