Kants Konzeption der geometrischen Darstellung: Zum mathematischen Gebrauch der Anschauung

The crucial role played by intuition in Kant’s theory of geometry has been widely discussed. Largely unacknowledged, however, is the fact that Kant here introduces a far-reaching concept: the construction (or Darstellung) of concepts in intuition. ‘Darstellung’, for Kant, refers to the practical use the geometer makes of intuition: starting with a concept like ‘triangle’, he/she (1) constructs a figure in order to (2) reflect on the act and the rule of construction, such that (3) this figure delineates the general concept and exhibits some of its properties (e. g. the sum of the inner angles equals two right angles). In this reflective use of intuition, the single figure does not represent in the manner of an arbitrary sign; rather, it allows us to grasp the general concept by engaging with a singular instance of it.ISSN:0022-8877ISSN:1613-113