Volume 12 · Number 3 ·
Pages 246–252
Eigenform and Reflexivity
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Abstract
Purpose: I introduce the concept of eigenform in the context of second-order cybernetics and discuss eigenform and eigenbehavior in the context of reflexivity. The point of eigenform is that it is a concept arising along with the observer at the point where the observer and the observed are apparently the same and yet apparently different. It is this nexus of the observer and the observed that is central to second-order cybernetics. Method: The article is designed as a formal introduction with excursions into the applications and meanings of these constructions. Results: I show how objects in our immediate experience can be seen to be eigenforms and that in this context such objects are a construct of our interactions, linguistic and otherwise experiential. In this way we can investigate scientifically without the need for an assumption of objectivity. Implications: The implications of this research are important for the performance and exploration of science. We can explore our role in that creation and find that what we create is independent of significant subsets of our actions. The practical implications of this study are strongest for the logical understanding of our constructions and actions. The social implications are in accord with the practical implications. We each produce eigenform models of the others and of ourselves.
Key words: Cybernetics, distinction, circularity, reflexivity, reflexive domain, eigenform.
Citation
Kauffman L. H. (2017) Eigenform and reflexivity. Constructivist Foundations 12(3): 246–252. http://constructivist.info/12/3/246
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References
Barbour J. & Pfister H. (eds.) (1995) Mach’s principle: From Newton’s bucket to quantum gravity. Birkhäuser, Boston. ▸︎ Google︎ Scholar
Barendregt H. P. (1984) The lambda calculus: Its syntax and semantics. North Holland, Amsterdam. ▸︎ Google︎ Scholar
Carnap R. (1966) Philosophical foundations of physics. Basic Books, New York. ▸︎ Google︎ Scholar
Casti J. L. (1977) Dynamical systems and their applications: Linear theory. Academic Press, New York. ▸︎ Google︎ Scholar
Descartes R. (1998) Discourse on Method and meditations on first philosophy. Hackett Publishing Company, Indianapolis. Originally published in 1641. ▸︎ Google︎ Scholar
Einstein A. (1956) Out of my later years. Philosophical Library, New York. ▸︎ Google︎ Scholar
Foerster H. von (2003) Understanding understanding: Essays on cybernetics and cognition, Springer, New York. ▸︎ Google︎ Scholar
Hardin G. (1968) The tragedy of the commons. Science 162(3859): 1243–1248. ▸︎ Google︎ Scholar
Hempel C. G. (1966) Philosophy of natural science. Prentice-Hall, Englewood Cliffs. ▸︎ Google︎ Scholar
Hoffrage U. & Marewski J. N. (2015) Unveiling the lady in black: Modeling and aiding intuition. Journal of Applied Research in Memory and Cognition 4: 145–163. ▸︎ Google︎ Scholar
Janssens N. & de Zeeuw G. (2017) Non-observational research. In: Nilsson F., Dunin-Woyseth H. & Janssens N. (eds.) Perspectives on research assessment in architecture, music and the arts. Taylor and Francis, London. ▸︎ Google︎ Scholar
Kahneman D. (2011) Thinking, fast and slow. Penguin Books, London. ▸︎ Google︎ Scholar
Kauffman L. H. (1987) Self-reference and recursive forms. Journal of Social and Biological Structures 10(1): 53–72 http://cepa.info/1816
Kauffman L. H. (2001) The mathematics of Charles Sanders Peirce. cybernetics and Human Knowing 8(1–2): 79–110 http://cepa.info/1823
Kauffman L. H. (2004) Virtual logic: Fragments of the void – Selecta. cybernetics and Human Knowing 11(1): 99–107. ▸︎ Google︎ Scholar
Kauffman L. H. (2005) EigenForm. Kybernetes 34(1/2): 129–150 http://cepa.info/1271
Kauffman L. H. (2009) Reflexivity and eigenform. The shape of process. Constructivist Foundation 4(3): 121–137 http://constructivist.info/4/3/121
Kauffman L. H. (2012) Eigenforms, discrete processes and quantum processes. Journal of Physics: Conference Series 361(1): 012034. ▸︎ Google︎ Scholar
Kauffman L. H. (2012) The Russell operator. Constructivist Foundations 7(2): 112–115 http://constructivist.info/7/2/112
Kauffman L. H. (2015) Self-reference, biologic and the structure of reproduction. Progress in Biophysics and Molecular Biology 10(3): 382–409 http://cepa.info/2844
Lakatos I. & Musgrave A. (eds.) (1968) Problems in the philosophy of science: Proceedings of the International Colloquium in the Philosophy of Science. Volume 3. North-Holland, Amsterdam. ▸︎ Google︎ Scholar
Lakatos I. & Musgrave A. (eds.) (1970) Criticism and the growth of knowledge: Proceedings of the International Colloquium in the Philosophy of Science. Volume 4. Cambridge University Press, Cambridge. ▸︎ Google︎ Scholar
Lakatos I. (ed.) (1967) Problems in the philosophy of mathematics: Proceedings of the International Colloquium in the Philosophy of Science. Volume 1. North-Holland, Amsterdam. ▸︎ Google︎ Scholar
Lakatos I. (ed.) (1968) The problem of inductive logic: Proceedings of the International Colloquium in the Philosophy of Science. Volume 2. North-Holland, Amsterdam. ▸︎ Google︎ Scholar
Landsberger H. A. (1958) Hawthorne revisited. The New York State School of Industrial and Labor Relations, New York. ▸︎ Google︎ Scholar
Maturana H. R. & Varela F. J. (1987) The tree of knowledge: The biological roots of human understanding. Shambhala, Boston. ▸︎ Google︎ Scholar
McCulloch W. S. (1988) A heterarchy of values determined by the topology of nervous nets. In: McCulloch W. S., Embodiments of mind. MIT Press, Cambridge: 40–45. Originally published in 1945. ▸︎ Google︎ Scholar
McFarlane T. (2006) The play of distinction. Holos: Forum for a New Worldview 2(2) ▸︎ Google︎ Scholar
Menger K. (1979) Gulliver in the land without one, two, three. In: Menger K., Selected papers in logic and foundations, didactics, economics. Reidel, Dordrecht: 305–314. Originally published in 1959. ▸︎ Google︎ Scholar
Merton R. K. (1948) The self-fulfilling prophecy. The Antioch Review 8(2): 193–210. ▸︎ Google︎ Scholar
Müller A. & Müller K. H. (eds.) (2007) An unfinished revolution? Heinz von Foerster and the Biological Computer Laboratory | BCL. 1958–1976. Edition echoraum, Vienna. ▸︎ Google︎ Scholar
Müller K. H. & Riegler A. (2014) Second-order science: A vast and largely unexplored science frontier. Constructivist Foundations 10(1): 7–15 http://constructivist.info/10/1/007
Nagel E. (1961) The structure of science: Problems in the logic of scientific explanation Harcourt, Brace & World, New York. ▸︎ Google︎ Scholar
Noether E. (1918) Invariante Variationsprobleme. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse 1918: 235–257. ▸︎ Google︎ Scholar
Ostrom E. (2010) Beyond markets and states: Polycentric governance of complex economic systems. American Economic Review 100(3): 641–672. ▸︎ Google︎ Scholar
Popper K. R. (1963) Conjectures and refutations: The growth of scientific knowledge. Hutchinson, London. ▸︎ Google︎ Scholar
Popper K. R. (1975) Objective knowledge: An evolutionary approach. Third edition. Oxford University Press, Oxford. Originally published in 1972. ▸︎ Google︎ Scholar
Reason P. & Bradbury H. (2001) Handbook of action research: Participative inquiry and practice. SAGE, London. ▸︎ Google︎ Scholar
Rosen J. (2008) Symmetry rules: How science and nature are founded on symmetry. Springer, Berlin. ▸︎ Google︎ Scholar
Rosenthal R. (1963) On the social psychology of the psychological experiment: The experimenter’s hypothesis as unintended determinant of experimental results. American Scientist 51(2): 268–283. ▸︎ Google︎ Scholar
Rosenthal R. (1966) Experimenter effects in behavioral research. Appleton-Century-Crofts, New York. ▸︎ Google︎ Scholar
Rostow W. W. (1971) The stages of economic growth: A non-communist manifesto. Second edition. Cambridge University Press, Cambridge. Originally published in 1960. ▸︎ Google︎ Scholar
Rostow W. W. (1978) The world economy: History & prospect. University of Texas Press, Austin. ▸︎ Google︎ Scholar
Sackett D. L. (1979) Bias in analytic research. Journal of Chronic Diseases 32(1–2): 51–63. ▸︎ Google︎ Scholar
Scott D. (1971) Continuous lattices. Programming Research Group, Oxford University. Technical Monograph PRG-7. ▸︎ Google︎ Scholar
Spencer Brown G. (1969) Laws of form. Julian Press, New York http://cepa.info/2382
Stadler R. (2016) The scientific approach to evolution. Creative Space, Seattle. ▸︎ Google︎ Scholar
Susskind L. & Friedman A. (2014) Quantum mechanics. Basic Books, New York. ▸︎ Google︎ Scholar
Umpleby S. A. (2014) Second-order science: Logic, strategies, methods. Constructivist Foundations 10(1): 16–23 http://constructivist.info/10/1/016
Van Bendegem J. P. (2000) How to tell the continuous from the discrete. In: Beets F. & Gillet E. (eds.) Logique en Perspective. Mélanges offerts à Paul Gochet, Ousia, Brussels: 501–511. ▸︎ Google︎ Scholar
Varela F. J. (1979) Principles of biological autonomy. North Holland, New York. ▸︎ Google︎ Scholar
Watson J. (1968) The double helix. Simon & Schuster, New York. ▸︎ Google︎ Scholar
Wittgenstein L. (1922) Tractatus logico-philosophicus. Harcourt, Brace and Company, New York. ▸︎ Google︎ Scholar
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