Volume 11 · Number 3 · Pages 489–497

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Cybernetics, Reflexivity and Second-Order Science

Louis H. Kauffman

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Context: Second-order cybernetics and its implications have been understood within the cybernetics community for some time. These implications are important for understanding the structure of scientific endeavor, and for researchers in other fields to see the reflexive nature of scientific research. This article is about the role of context in the creation and exploration of our experience. Problem: The purpose of this article is to point out the fundamental nature of the circularity in cybernetics and in scientific work in general. I give a point of view on the nature of objective knowledge by placing it in the context of reflexivity and eigenform. Method: The approach to the topic is based on logical analysis of the nature of circularity. Mathematics and cybernetics are both fundamentally concerned with the structure of distinctions, but there can be no definition of a distinction without circularity, since such a definition would itself be a distinction. The article proceeds by explicating the structure of reflexive domains D where the transformations of the domain are in one-to-one correspondence with the domain itself. Results: I show that every element of a reflexive domain has a fixed point. This means that eigenforms arise naturally in reflexive domains. Furthermore, a reflexive domain is itself an eigenform (at a higher level. This supports the context of a second-order science that would study domains of science as part of a larger cybernetic landscape. Implications: The value of the article is in its concise reformulation of the scientific endeavor as a search for eigenforms in reflexive domains. This new view of science is promising in that it includes the former worlds of apparent objectivity and it embraces those newer worlds of science where the theories and theorists become active participants in the ongoing process of creating knowledge. Constructivist content: I argue that the perspective of reflexive domains constitutes a new way to think about the practice of science, with observers deeply imbedded, and objectivity understood as the mutual search for eigenforms.

Key words: Cybernetics, distinction, circularity, reflexivity, reflexive domain, eigenform.


Kauffman L. H. (2016) Cybernetics, reflexivity and second-order science. Constructivist Foundations 11(3): 489–497. http://constructivist.info/11/3/489

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Barendregt H. P. (1985) The lambda calculus. Its syntax and semantic. North Holland, Amsterdam. << Google Scholar

Butler J. (2005) The question of social transformation. In: Butler J. (2005) Undoing gender. Routledge, London: 204–231. << Google Scholar

Davies P. C. W & Brown J. R. (1986) The ghost in the atom. Cambridge University Press, Cambridge. << Google Scholar

Einstein A. & Infeld L. (1966) The evolution of physics: From early concepts to relativity and quanta. Cambridge University Press, Cambridge. Originally published in 1938. << Google Scholar

Foerster H. von (1981) Objects: Tokens for (eigen-) behaviors. In: Foerster H. von, Observing systems. Intersystems, Seaside CA: 274–285 Available at http://cepa.info/1270

Foerster H. von (2003) Objects: Tokens for (eigen-) behaviors. In: Foerster H. von Understanding understanding. Springer, New York: 261–271. Originally published in 1976 Available at http://cepa.info/1270

Foerster H. von (2003) Understanding understanding: Essays on cybernetics and cognition. Springer, New York. << Google Scholar

Forsythe K. (1986) Cathedrals in the mind: The architecture of the metaphor in understanding learning. In: Trappl R. (eds.) Cybernetics and systems ’86. Reidel, Dordrecht: 285–292. << Google Scholar

Forsythe K. (1987) Isopher: Poiesis of Experience. Working Paper No. 87–2. Center for Systems Research, University of Alberta, Edmonton. << Google Scholar

Foucault M. (1994) The order of things. Vintage, London. French original published as: Foucault M. (1966) Les mots et les choses. Gallimard, Paris. << Google Scholar

Foucault M. (2005) Was ist Aufklärung? In: Foucault M. (2005) Dits et Ecrits. Schriften Band 4. Suhrkamp, Frankfurt am Main: 837–848. French original published as: Foucault M. (1984) Qu’est-ce que les lumières? Magazin littéraire 207: 35–39. << Google Scholar

Foucault M. (2007) What is critique? In: Lotringer Silvère (ed.) The politics of truth. Semiotext(e), Los Angeles: 41–81. French original published as: Foucault M. (1990) Qu’est-ce que la critique? Bulletin de la Société française de Philosophie 84(2): 35–63. (Lecture held in 1978). << Google Scholar

Harrison R. (1998) Transcendental arguments. In: Craig E. (ed.) Routledge encyclopedia of philosophy.Volume 9. Routledge, London: 452–454. << Google Scholar

Hegel G. W. F. (1986) Differenz des Fichte’schen und Schelling’schen Systems der Philosophie. In: Hegel G. W. F. Jenaer Schriften 1801–1807. Werke 2. Suhrkamp, Frankfurt am Main: 15–51. << Google Scholar

Heisenberg W. (1963) Physics and philosophy. Allen and Unwin, London. << Google Scholar

Horkheimer M. (1975) Critical and traditional theory. In: Horkheimer M., Critical theory. Selected essays. Edited by M. O’Connell. Continuum Press, New York: 188–243. German original published as: Horkheimer M. (1937) Kritische und traditionelle Theorie. Zeitschrift für Sozialforschung. Reprinted in: Gesammelte Schriften. Volume 4: Schriften 1936–41. Fischer, Frankfurt am Main: 162–216. << Google Scholar

Kant I. (1781/1787) Kritik der reinen Vernunft. J. F. Hartknoch, Riga. << Google Scholar

Kant I. (2007) Critique of pure reason. Penguin, London. << Google Scholar

Kauffman L. H. & Buliga M. (2014) Chemlambda, universality and self-multiplication. In: Sayama H., Rieffel J., Risi S., Doursat R. & Lipson H. (eds). Artificial life 14. Proceedings of the 14th International Conference on the Synthesis and Simulation of Living Systems. MIT Press, Cambridge MA: 490–497. << Google Scholar

Kauffman L. H. (1987) Self-reference and recursive forms. Journal of Social and Biological Structures 10(1): 53–72 Available at http://cepa.info/1816

Kauffman L. H. (2001) The mathematics of Charles Sanders Peirce. Cybernetics & Human Knowing 8(1–2): 79–110 Available at http://cepa.info/1823

Kauffman L. H. (2003) Eigenforms – Objects as tokens for eigenbehaviors. Cybernetics & Human Knowing 10(3–4): 73–90 Available at http://cepa.info/1817

Kauffman L. H. (2004) Virtual logic: Fragments of the void – Selecta. Cybernetics & Human Knowing 11(1): 99–107. << Google Scholar

Kauffman L. H. (2005) EigenForm. Kybernetes 34(1/2): 129–150 Available at http://cepa.info/1271

Kauffman L. H. (2009) Reflexivity and eigenform. The shape of process. Constructivist Foundations 4(3): 121–137 Available at http://constructivist.info/4/3/121

Kauffman L. H. (2012) Eigenforms, discrete processes and quantum processes. Journal of Physics: Conference Series 361(1): 012034. Available at http://iopscience.iop.org/article/10.1088/1742–6596/361/1/012034/pdf

Kauffman L. H. (2012) The Russell operator. Constructivist Foundations 7(2): 112–115 Available at 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. Available at http://www.sciencedirect.com/science/article/pii/S0079610715000905

Maturana H. R. & Varela F. J. (1987) The tree of knowledge: The biological roots of human understanding. Shambhala, Boston. << Google Scholar

Maturana H. R. (1987) Everything said is said by an observer. In: Thompson W. I. (ed.) Gaia: A way of knowing. Lindisfarne Press, New York: 65–82. << Google Scholar

Maturana H. R. (1988) Reality: The search for objectivity or the quest for a compelling argument. Irish Journal of Psychology 9(1): 25–82 Available at http://cepa.info/598

Müller K. H. & Riegler A. (2014) Second-order science: A vast and largely unexplored science frontier. Constructivist Foundations 10(1): 7–15 Available at http://constructivist.info/10/1/007

National Science Board (NSF) (2016) Science & engineering indicators 2016. Chapter 7: Science and technology: Public attitudes and understanding. Available at http://www.nsf.gov/statistics/2016/nsb20161/uploads/1/10/chapter-7.pdf

Rorty R. (1991) Objectivity, relativism, and truth: Philosophical papers. Volume 1. Cambridge University Press, Cambridge. << Google Scholar

Russell B. R. (1938) The principles of mathematics. W. W. Norton, New York. Originally published in 1903. << Google Scholar

Sartre J.-P. (2016) What is subjectivity? Verso, New York NY. French original published as: Sartre J.-P. (2013) Qu’est-ce que la subjectivité? Les Prairies ordinaires, Paris. (Lecture held in 1961). << Google Scholar

Scott D. (1971) Continuous lattices. Programming Research Group, Oxford University. Technical Monograph PRG-7. << Google Scholar

Spencer Brown G. (1969) Laws of form. George Allen and Unwin, London Available at http://cepa.info/2382

Thagard P. (1989) Explanatory coherence. Behavioral and Brain Sciences 12: 435–502. << Google Scholar

Umpleby S. A. (2014) Second-order science: Logic, strategies, methods. Constructivist Foundations 10(1): 16–23 Available at http://constructivist.info/10/1/016

Vaihinger H. (1924) The philosophy of “as if”: A system of the theoretical, practical and religious fictions of mankind. Translated by C. K. Ogden. Routledge, and Kegan Paul, London. German original published in 1911. << Google Scholar

Varela F. J. (1979) Principles of biological autonomy. North Holland, New York. << Google Scholar

Wittgenstein L. (1922) Tractatus logico-philosophicus. Harcourt, Brace and Company, New York. Available at http://www.gutenberg.org/ebooks/5740

Wittgenstein L. (1958) Philosophical investigations. MacMillan, New York. Originally published in 1953. << Google Scholar

Wood M., Douglas K. & Sutton R. (2012) Dead and alive: Beliefs in contradictory conspiracy theories. Social Psychological and Personality Science 3: 767–773. << Google Scholar

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