Denis Walter

This chapter investigates the origin of incommensurability within Proclus’ ontology through an analysis of his Commentary on the First Book of Euclid’s Elements and his Commentary on the Parmenides. The central question concerns how incommensurability arises at a specific ontological level and how it corresponds to a distinct mode of cognition. The chapter first situates geometrical entities in an intermediate position between the intelligible and the sensible realms. It then demonstrates that sensible matter cannot serve as the unqualified cause of incommensurability, since it accounts only for imprecision rather than for incommensurability. Likewise, intelligible matter (the soul) alone cannot explain it, as not all objects within the soul exhibit incommensurability. Instead, the chapter argues that incommensurability is an intrinsic property of certain geometrical entities, comparable to their other identifiable features. Ultimately, the essay supports the interpretation that incommensurability is a definable and necessary feature of some geometrical objects.

This book presents a constructive interpretation of Plato’s Parmenides. It offers a close reading of the dialogue’s first part and shows how the second part takes up its problems while unfolding a philosophical project that reaches beyond them. The reader is guided through the exercise as Denis Walter shows how it articulates a complex ontology, addressing the hierarchy of forms, definitions, participation, mathematical structure, and teleology. By organizing the argument around philosophical topics rather than deductions, the study brings into view a coherent ontological framework extending from the One to unlimited multitude. The book offers a clear and philosophically grounded reading of one of Plato’s most demanding texts.

Michael Psellos ist ein Philosoph, der wie kein anderer für die byzantinische Epoche steht. Das Denken dieses Großintellektuellen – der in subtilen Auseinandersetzungen mit antiken und spätantiken Positionen in Theologie, Ontologie und Ethik eine selbständige christliche Philosophie formuliert – findet in diesem Band erstmalig eine monographische Gesamtdarstellung. Die Arbeit liefert durch ihren systematischen Charakter, durch die Einbeziehung bisher nicht interpretierter Texte, durch die Darlegung der bisherigen Forschungsergebnisse und durch die Aufdeckung von Traditioinslinien eine wichtige Grundlage für die weitere Erforschung der byzantinischen Philosophie.

The Byzantine philosopher Michael Psellos describes in his ethics two kinds of virtue: practical and intellectual virtues. Practical virtues are defined as a middle term between two extremes as is known from the Aristotelian tradition. His innovation is to define also a middle regarding the intellectual virtues. He says that the highest object of knowledge is not graspable for the human intellect because it exceeds his powers. Whoever strives to understand the highest object of knowledge, the essence of god, is determined to fail. Thus, the best objects that the human intellect can contemplate are situated below god, in the “middle”. The concept of the middle is thus present twice in Psellos’ ethics: once in the practical virtues and once in the intellectual virtues.

Among the Neoplatonists read by Byzantine thinkers, Plotinus does not rank first. He is surpassed by Proclus, who enjoys a livelier reception. Nevertheless, many Byzantines refer to Plotinus’ Enneads. In this chapter we present the impact he had on the Byzantines from the 5th to the 15th century, namely on John of Scythopolis, John of Damascus, Michael Psellus, Symeon Seth, John Italus, Michael VII. Doukas, Michael of Ephesus, Nicolas of Methone, Nicephorus Blemmydes, Theodorus II. Doukas Laskaris, Georgius, Pachymeres, Maximus Planoudes, Nicephorus Chumnus, Constantinus Akropolites, Theodorus Metochites, Nicephorus Gregoras, Palamas, Georgius Gemistus Plethon, Bessarion, Georgius Gennadius Scholarius, Michael Apostoles. What unites these very different thinkers is that they measure Plotinus, and ancient philosophy in general, by the standard of Christian teaching.