Relational Science: A Synthesis |
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Authors: | John J Kineman |
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Institution: | (1) Ecosystem Sciences Division, Cooperative Institute for Research in the Environmental Sciences (CIRES), University of Colorado, UCB-216, Boulder, CO 80309-0216, USA |
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Abstract: | A synthesis of the two primary theory structures in Robert Rosen’s relational complexity, (1) relational entailment mapping
based on category theory as described by Rosen and Louie, and (2) 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 (a ‘holon’) 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 (models) 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. |
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