Abstract

The Catastrophe Theory of Rene Thom and E. C. Zeeman suggests a mathematical interpretation of certain aspects of Hegelian and Marxist dialectics. Specifically, the three 'classical' dialectical principles, (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 catastrophes' 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.