Dialectics and catastrophe

  • Martin Zwick

Abstract

The Catastrophe Theory of René Thorn and E. C. Zeeman1 suggests a mathematical interpretation of certain aspects of Hegelian and Marxist dialectics. Specifically, the three ‘classical’ dialectical principles2, (1) the transformation of quantity into quality, (2) the unity and struggle of opposites, and (3) the negation of negation, can be modeled with the seven ‘elementary catastrophes3 given by Thorn, especially the catastrophes known as the ‘cusp’ and the ‘butterfly.’ Far from being empty metaphysics or scholasticism, as critics have argued, the dialectical principles embody genuine insights into a class of phenomena, insights which can now be expressed within a precise mathematical formalism. This fact does not, however, support the claim that these principles, possibly modified or supplemented, constitute the laws of motion for human thought and for natural and social processes — or even just the last of these.

Keywords

Crystallization Steam Rubber Coherence Boiling 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amburgey, T. and D. McQuarie, ‘System Change in Karl Marx’s Model of Socio-economic Formation.’ General Systems 22, 99–103, 1977.Google Scholar
  2. Cornforth, M., Materialism and the Dialectical Method, New York: International, 1975.Google Scholar
  3. Curle, A., Mystics and Militants, London: Tavistock, 1972.Google Scholar
  4. Desan, W., The Marxism of Jean-Paul Sartre, Garden City: Doubleday, 1965.Google Scholar
  5. Dodson, M. M., ‘Darwin’s Law of Natural Selection and Thom’s Theory of Catastrophes.’ Mathematical Biosciences 28, 243–274, 1976.CrossRefGoogle Scholar
  6. Engels, F., Anti-Duhring, New York: International, 1970.Google Scholar
  7. Engels, F., Dialectics of Nature, New York: International, 1973.Google Scholar
  8. Engels, F., Ludwig Feuerbach, New York: International, 1941.Google Scholar
  9. Engels, F., Socialism: Utopian and Scientific. Marx and Engels, Selected Works, New York: International, 1968.Google Scholar
  10. Fowler, D. H., ‘The Reimann-Hugoniot Catastrophe and the Van der Waals Equation’ in C. H. Waddington (ed.), Towards a Theoretical Biology, Vol. 4, Chicago: Aldine-Atherton, 1–7, 1972.Google Scholar
  11. Graham, L. R., Science and Philosophy in the Soviet Union, New York: Vintage, 1971.Google Scholar
  12. Hegel, G. W. F., Science of Logic, W. H. Johnston, and L. G. Struthers (trans.). New York: Macmillan, 1951.Google Scholar
  13. Kirschenmann, P. P., Information and Reflection, New York: Humanities, 1970.CrossRefGoogle Scholar
  14. Kursanov, G., Fundamentals of Dialectical Materialism, Moscow: Progress, 1967.Google Scholar
  15. Marcuse, H., Reason and Revolution, Boston: Beacon, 1960.Google Scholar
  16. Marx, K., A Contribution to the Critique of Political Economy, Chicago: Kerr, 1904.Google Scholar
  17. Marx, K., Capital, Vol. 1–3, New York: International, 1967.Google Scholar
  18. Marx, K. and F. Engels, The German Ideology, New York: International, 1947.Google Scholar
  19. Marx, K. and F. Engels, Manifesto of the Communist Party in Marx and Engels, Selected Works, New York: International, 1968.Google Scholar
  20. McGill, V. U. and W. T. Parry, ‘The Unity of Opposites: A Dialectical Principle.’ Science and Society 12, 418–444, 1948.Google Scholar
  21. Merrill, J., ‘Marxism and Systems Theory: A New Intellectual Convergence?’ unpublished manuscript, March 25, 1977.Google Scholar
  22. Sartre, J. P., Critique of Dialectical Reason, A. Sheridan-Smith (trans.). Honolulu: University of Hawaii, 1977.Google Scholar
  23. Schulman, L. S. and M. Revzen, ‘Phase Transitions as Catastrophes.’ Collective Phenomena 1, 43–47, 1972.Google Scholar
  24. Stalin, J., Dialectical and Historical Materialism, New York: International, 1940.Google Scholar
  25. Thorn, R., Structural Stability and Morphogenesis, Reading: Benjamin, 1975.Google Scholar
  26. Turner, J. H., The Structure of Sociological Theory, Homewood: Dorsey, 1974.Google Scholar
  27. Venable, V., Human Nature, The Marxian View, Cleveland: Meridian, 1966.Google Scholar
  28. Waddington, C. H., ‘A Catastrophe Theory of Evolution.’ Annals of the New York Academy of Sciences 231, 32–42, 1974.CrossRefGoogle Scholar
  29. Wallerstein, L., The Modern World System, New York: Academic, 1974.Google Scholar
  30. Wetter, G. A., Dialectical Materialism, Westport: Greenwood, 1958.Google Scholar
  31. Zeeman, E. C., ‘Catastrophe Theory.’ Scientific American (April): 65–83, 1976.Google Scholar
  32. Zeeman, E. C., Catastrophe Theory: Selected Papers 1972–1977, Reading: Addison-Wesley, 1977.Google Scholar

Copyright information

© R. F. Geyer and J. van der Zouwen 1978

Authors and Affiliations

  • Martin Zwick

There are no affiliations available

Personalised recommendations