Research Project by Dr. Philipp Steinkrüger

“Analyse und Aporie in der antiken Philosophie”

In my current research project, I investigate how ancient philosophers were influenced by the method of mathematical or regressive analysis. It has been noted that the success of this method in the mathematical sciences did not go unobserved in the philosophical circles of the time. Plato and Aristotle both mention the method; and later philosophers regularly refer to it as essential to the discovery of first principles. The thought that philosopher were eager to employ this method to discover principles relevant to philosophical problems suggests itself. It appears, however, that at least one of the requirements for the successful employment of regressive analysis is not satisfied in the philosophical realm, at least not for philosophers like Plato and Aristotle. For regressive analysis requires that we be already acquainted with some principles and that these principles are accepted as true and as not in need of proof themselves. Yet, Plato and Aristotle did not think that they were already in possession of such principles. Thus, if regressive analysis is to play a role outside mathematics, and in particular in philosophy, the method must be modified or supplemented by other methods. One candidate for such a supplementing method I will investigate in this project is the so-called aporetic method, which was employed by Plato and Aristotle and which is seen by both as central to the task of finding first principles.