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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Notes
The concept of non-localized potential can also be described by the physical science concept of a ‘phase space’, but one that excludes space and time coordinates.
Rosen distinguished between true models in a scientific sense and simulations, in that true models must reflect natural entailment. In that case, given the syntheses here, a true model is one that considers realized and contextual causes.
In previous work by this author a clockwise arrow was drawn to indicate our ability to infer causality; but in the light of the analytical framework described here, it seems more appropriate to remove it.
The diagram is reversed from Louie’s presentation to correspond with how the holon diagram is drawn in Fig. 4.
The terms ‘inverse’ and ‘complement’ have other mathematical definitions; hence the term ‘natural inverse’ or ‘natural complement’ are used here to refer to the case where natural structures are represented as functors on a contextual category that entails functions.
The implicit identity holons for the m, r, and p functions are redundant with the closed M-R holon elements from which they are produced; thus showing them in summary form would not add anything to the diagram.
References
Bateson G (1979) Mind and nature: a necessary unity. Bantam, Toronto
Hameroff S, Penrose R (1996) Conscious events as orchestrated space-time selections. Conscious Stud 2(1):36–53
Hutchinson GE (1953) The niche: an abstractly inhabited hyper-volume. Proc Acad Natl Sci 105(4):1–12
Kineman JJ (2007) Modeling relations in nature and eco-informatics: a practical application of Rosennean complexity. Chem Biodivers 4(10):2436–2457
Kineman JJ (2008) Fundamentals of relational complexity theory. In: Allen J, Wilby J (eds) Proceedings of the 52nd annual meeting of the international society for the system sciences, Toronto, 2008
Kineman JJ (2009a) Relational self-similar space-time cosmology revisited. In: Allen J, Wilby J (eds) Proceedings of the 54th annual meeting of the international society for the systems science, Waterloo, 2010
Kineman JJ (2009b) Relational theory and ecological niche modeling. In: Allen J, Wilby J (eds) Proceedings of the 53rd annual meeting of the international society for the systems sciences, Brisbane, 2009
Kineman JJ, Kumar KA (2007) Primary natural relationship: Bateson, Rosen, and the Vedas. Kybernetes 36(7/8):1055–1069
Kineman JJ, Banathy BA, Rosen J (2007) The atomistic structure of relationship. In: Allen J, Wilby J (eds) Proceedings of the 51st annual meeting of the international society for the systems sciences, Tokyo, 2007
Koestler A (1967) The ghost in the machine. Hutchinson, UK
Koestler A (1978) Janus: a summing up. Hutchinson, UK
Louie A (2009) More than life itself: a synthetic continuation in relational biology. Ontos Verlag, Frankfurt
Maturana HR, Varela FJ (1980) Autopoieses and cognition: the realization of the living. Reidel Publishing, Dordrecht
Mehta R (1970) Call of the Upanishads. Motilal Banarsidass Publishers Private Limited, Delhi
Muller M (ed) (1884) The Upanishads, part 2 of 2, vol 15. Sacred books of the East. Oxford University Press, Oxford
Odling-Smee FJ, Laland KN, Feldman MW (2003) Niche construction: the neglected process in evolution. Princeton University Press, Princeton
Rosen R (1971) The polarity between structure and function. Dialogue discussion paper. Center for the Study of Democratic Institutions. Special Collections, Box 77, Davidson Library. University of California, Santa Barbara
Rosen R (1978) Fundamentals of measurement and representation of natural systems. North-Holland series in general research systems. North-Holland, New York
Rosen R (1985) Anticipatory systems: philosophical, mathematical, and methodological foundations. Pergamon Press, New York
Rosen R (1991) Life itself: a comprehensive inquiry into the nature, origin, and fabrication of life. Complexity in ecological systems series. Columbia University Press, New York
Rosen R (1999) Essays on life itself. Complexity in ecological systems series. Columbia University Press, New York
Rosen J, Kineman JJ (2004) Anticipatory systems and time: a new look at Rosennean complexity. In: Allen J, Wilby J (eds) Proceedings of the 48th annual meeting of the international society for the system sciences, Asilomar, 2004
Acknowledgments
I wish to acknowledge those on two sides of the planet who contributed insights, support, patience, and encouragement over the many years it required to develop and complete this work. The list of those I have to thank is too daunting to reproduce: I hope the result itself rewards their faith.
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Kineman, J.J. Relational Science: A Synthesis. Axiomathes 21, 393–437 (2011). https://doi.org/10.1007/s10516-011-9154-z
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DOI: https://doi.org/10.1007/s10516-011-9154-z