Home Spencer-Brown, Luhmann and Klein on Symmetry
Article
Licensed
Unlicensed Requires Authentication

Spencer-Brown, Luhmann and Klein on Symmetry

  • Jean-Sébastien Guy

    Jean-Sébastien Guy, who sadly passed away in November 2022, was Associate Professor at the Department of Sociology and Social Anthropology at Dalhousie University, Halifax, Canada. He had written on systems theory, relational sociology, globalization and the metric/nonmetric distinction. He had published in Cybernetics and Human Knowing, European Journal of Social Theory, Systems Research and Behavioral Science and Technological Forecasting and Social Change. His latest book was Theory Beyond Structure and Agency: Introducing the Metric/Nonmetric Distinction (with Palgrave Macmillan).

Published/Copyright: June 9, 2023
Become an author with De Gruyter Brill

Abstract

This article discusses the concept of symmetry as Felix Klein developed it in his works on geometry as a measure of invariance. The objective is to generalize from Klein’s model and principles to be able to apply the concept of symmetry to the study of social structures or social formations in sociology. To achieve this goal, the article goes on to consider how the concept of symmetry bears on the Laws of Form of George Spencer-Brown and on Niklas Luhmann’s theory of functional differentiation. Both of them are reinterpreted in terms of symmetry breaking.

About the author

Jean-Sébastien Guy († 2022)

Jean-Sébastien Guy, who sadly passed away in November 2022, was Associate Professor at the Department of Sociology and Social Anthropology at Dalhousie University, Halifax, Canada. He had written on systems theory, relational sociology, globalization and the metric/nonmetric distinction. He had published in Cybernetics and Human Knowing, European Journal of Social Theory, Systems Research and Behavioral Science and Technological Forecasting and Social Change. His latest book was Theory Beyond Structure and Agency: Introducing the Metric/Nonmetric Distinction (with Palgrave Macmillan).

References

Aczel, Amir D. (2009): Nicolas Bourbaki, histoire d’un génie des mathématiques qui n’a jamais existé. Paris: JC Lattès.Search in Google Scholar

Barbosa de Almeida, Mauro W. (1990): Symmetry and Entropy: Mathematical Structures in the Works of Lévi-Strauss. Current Anthropology 31, 367–385.10.1086/203850Search in Google Scholar

Baecker, Dirk (ed.) (1999): Problems of Form. Stanford: Stanford University Press.10.1515/9781503617698Search in Google Scholar

Baecker, Dirk (2005): Form und Formen der Kommunikation. Frankfurt a.M.: Suhrkamp.10.1007/978-3-322-80488-4_3Search in Google Scholar

Birkhoff, Garrett/Bennett, M. K. (1988): Felix Klein and his “Erlanger Programm”, in: William Aspray/Philip Kitcher (eds.), Minnesota Studies in the Philosophy of Science, Vol. XI: History and Philosophy of Modern Mathematics. Minneapolis: University of Minnesota Press, 145–176.Search in Google Scholar

Boltanski, Luc (1975): La constitution du champ de la bande dessinée. Actes de la recherche en sciences sociales 1 (1), 37–59.10.3406/arss.1975.2448Search in Google Scholar

Bourdieu, Pierre (1984): Homo Academicus. Stanford: Stanford University Press.Search in Google Scholar

Bourdieu, Pierre (1987): Legitimation and Structured Interests in Weber’s Sociology of Religion, in: Scott Lash/Sam Whimster (eds.), Max Weber, Rationality and Modernity. London: Allen & Unwin, 119–136.Search in Google Scholar

Bourdieu, Pierre (1992): Les règles de l’art. Paris: Seuil.Search in Google Scholar

Bourdieu, Pierre (2015): Sociologie générale, vol. 1. Paris: Seuil.Search in Google Scholar

Bourdieu, Pierre/Wacquant, Loïc (1992): Invitation to Reflexive Sociology. Cambridge: Polity.Search in Google Scholar

Cassirer, Ernst (1923): Substance and Function, and Einstein’s Theory of Relativity. Chicago: Open Court.Search in Google Scholar

Cassirer, Ernst (1944): The Concept of Group and the Theory of Perception. Philosophy and Phenomenological Research 5, 1–36.10.2307/2102891Search in Google Scholar

DeLanda, Manuel (2002): Intensive Science and Virtual Philosophy. New York: Continuum.Search in Google Scholar

DeLanda, Manuel (2016): Assemblage Theory. Edinburgh: Edinburgh University Press.10.1515/9781474413640Search in Google Scholar

Green, Adam Isaiah (2008): The Social Organisation of Desire: The Sexual Fields Approach. Sociological Theory 26 (1), 25–50.10.1111/j.1467-9558.2008.00317.xSearch in Google Scholar

Guy, Jean-Sebastien (2019): Theory Beyond Structure and Agency. Cham: Palgrave.10.1007/978-3-030-18983-9Search in Google Scholar

Hénaff, Marcel (1991) : Claude Lévi-Strauss et l’anthropologie structurale. Paris: Belfond.Search in Google Scholar

Ihmig, Karl-Norbert (1999): Ernst Cassirer and the Structural Conception of Objects in Modern Science: The Importance of the “Erlanger Programm”. Science in Context 12, 513–529.10.1017/S0269889700003586Search in Google Scholar

Kline, Morris (1972): Mathematical Thought from Ancient to Modern Times, 3 volumes. Oxford: Oxford University Press.Search in Google Scholar

Latour, Bruno (2013): An Enquiry into Modes of Existence. Cambridge: Harvard University Press.Search in Google Scholar

Lévi-Strauss, Claude (1969): The Elementary Structures of Kinship. Boston: Beacon Press.Search in Google Scholar

Luhmann, Niklas (ed.) (1982): The Differentiation of Society. New York: Columbia University Press.Search in Google Scholar

Luhmann, Niklas (1986): Love as Passion. The Codification of Intimacy. Cambridge: Harvard University Press.Search in Google Scholar

Luhmann, Niklas (1989): Ecological Communication. Chicago: University of Chicago Press.Search in Google Scholar

Luhmann, Niklas (1990): Essays on Self-Reference. New York: Columbia University Press.Search in Google Scholar

Luhmann, Niklas (1995): Social Systems. Stanford: Stanford University Press.Search in Google Scholar

Luhmann, Niklas (2002): Theories of Distinction. Redescribing the Descriptions of Modernity, ed. by W. Rasch. Stanford: Stanford University Press.10.1515/9781503619340Search in Google Scholar

Luhmann, Niklas (2012): Theory of Society, Vol. 1. Stanford: Stanford University Press. Search in Google Scholar

Luhmann, Niklas (2013a): Introduction to Systems Theory, ed. by D. Baecker. Cambridge: Polity.Search in Google Scholar

Luhmann, Niklas (2013b): Theory of Society, Vol. 2. Stanford: Stanford University Press.Search in Google Scholar

Luhmann, Niklas (2017): Trust and Power. Cambridge: Polity.Search in Google Scholar

Piaget, Jean (1967): La psychologie de l’intelligence. Paris: Armand Collin.Search in Google Scholar

Piaget, Jean (1970a): L’épistémologie génétique. Paris: Presses Universitaires de France.Search in Google Scholar

Piaget, Jean (1970b): Structuralism. New York: Basic Books.Search in Google Scholar

Schiemer, Georg (2018): Cassirer and the Structural Turn in Modern Geometry. Journal for the History of Analytical Philosophy 6, 182–212.10.15173/jhap.v6i3.3439Search in Google Scholar

Spencer-Brown, George (1972): Laws of Form. New York: The Julian Press.Search in Google Scholar

Swartz, David (1997): Culture and Power: The Sociology of Pierre Bourdieu. Chicago: University of Chicago Press.10.7208/chicago/9780226161655.001.0001Search in Google Scholar

Vandenberghe, Frédéric (1999): “The Real is Relational”: An Epistemological Analysis of Pierre Bourdieu’s Generative Structuralism. Sociological Theory 17, 32–67.10.1111/0735-2751.00064Search in Google Scholar

Vandenberghe, Frédéric (2001): From Structuralism to Culturalism, Ernst Cassirer’s Philosophy of Symbolic Forms. European Journal of Social Theory 4, 479–497.10.1177/13684310122225271Search in Google Scholar

White, Harrison (2008): Identity and Control: How Social Formations Emerge, 2nd edition. Princeton: Princeton University Press.Search in Google Scholar

Weber, Max (1978): Economy and Society, 2 volumes. Berkeley: University of California Press.Search in Google Scholar

Published Online: 2023-06-09
Published in Print: 2023-06-25

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 23.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/sosys-2023-0004/html?lang=en
Scroll to top button