The "experiment of reason" in Kant and Hegel

Ever since Descartes' exposition of methodical doubt, the concept of a transcendental experiment ("Experiment der Vernunft") has constituted a major concern of philosophy. Since, however, the nature of philosophical inquiry differs fundamentally from scientific experimentation, it is necessary to modify the experimental approach to suit the specific needs of the former. Given this premise, the responses of Kant and Hegel are compared and contrasted to show these specifications.