Leibniz, Kant and the modern concept of symmetry

The paper analyses the significance of the modern concept of symmetry" for the understanding of the concept of intuition" in Kant's philosophy of geometry. A symmetry transformation or automorphism is a structure preserving mapping of the space into itself that leaves all relevant structure intact so that the result is always like the original, in all relevant respects. Hermann Weyl was the first to show that this idea can be drawn on Leibniz's definition of similarity: two figures are similar if they are only distinguishable through the simultaneous perception of them (comperceptio): an automorphism carries a figure into one that in Leibniz's words is indiscernible from it if each of the two figures is considered by itself'". The author argues that, under the light of this definition, Leibniz's notion of comperceptio" turns out to play a similar role for the notion of intuition" in Kant's philosophy of space and time. Both cases are about the difference between conceptual definition and intuitive exhibition", as Weyl puts it. This result has on the one hand an exegetical significance: it frees Kant's notion of intuition" from every vague reference to the visualisation" of geometrical figures; on the other hand a theoretical one: it makes easy to compare Kant's philosophy of space and time with modern developments of sciences, in which as Weyl first showed, the concept of symmetry plays a fundamental role. © 2011 Walter de Gruyter.