Laura Marongiu

This chapter endeavors to explore the notion of atemporality within selected works belonging to the Platonist tradition. Beyond providing an overview of various facets of atemporality and highlighting their mutual relations, this chapter aims to investigate their role in a range of accounts of the world’s origins. By focusing on the cosmogonical views elaborated by Platonists who deny that the cosmos is generated in time, such as Plotinus, Porphyry, Calcidius, and Proclus, I will dwell on a specific kind of atemporality, namely ‘timeless simultaneity,’ and shed light on its theoretical advantages in explaining the demiurgic creation of the cosmos within a sempiternalist framework. Paradoxical as it may seem, within this perspective, the assertion that the Demiurge creates the cosmos at once does not conflict but, in fact, is fully compatible with the assumption that the cosmos has no temporal beginning, causally depends on a higher cause, and is always in a process of coming to be. As a result, a multi-layered taxonomy of atemporality, and especially the notion of ‘timeless simultaneity,’ enables Platonists adopting a sempiternalist stance to argue consistently that the cosmos is both ungenerated and created all at once, and to effectively explain in what sense it is so.

This book offers a clear account of timelessness together with the discussion of temporality in fundamental physics and cosmology. The multi-disciplinary approach to the problem of time and timelessness shows the remarkable difference between pre-relativistic debates and current developments. This book thoroughly discusses notions of timelessness and time emerging in the most recent literature on Quantum Gravity, String Theory and Cosmology. The contributions explore, among many aspects, the historical-philosophical roots of the notions of temporality and atemporality, the role of mathematics in defining time and temporality with respect to both order relations and causality, approaches to quantum gravity and cosmology that make use of quantum fluids and condensate to approximate space–time in general relativity, time and timelessness in black holes and the problem of cosmological time in bouncing cosmologies. The novelty of this volume lies in the interaction among scientists, philosophers, and historians in exploring the nature of time and timelessness and the origin of these concepts. The book represents a valuable toolkit for researchers and graduate students in physics, cosmology, philosophy and the history of those fields.

In the search for the origins of the quadrivium, several authoritative studies have identified Plato as its most prominent precursor. This paper investigates whether and to what extent this is the case by focusing on logistikê—a discipline concerned with number and calculation—and using it as a test case. Indeed, while Plato depicts logistikê as an epistemologically valuable discipline, later sources either remove it from the classification of mathematics or dismiss it as a subject devoid of theoretical import. By combining a thorough examination of Plato’s treatment of logistikê with an investigation of its development in the later tradition, I aim both to reassess the actual importance of this discipline in the dialogues and to provide a comprehensive explanation of its progressive marginalisation in the later tradition. The test case of logistikê will thus offer an insightful perspective on the evolution of the quadrivium, revealing how the latter developed and consolidated through a prolonged, and often non-linear process of mediation, whose most crucial feature is the discovery of effective strategies for framing important Platonic tenets within Nicomachus’ fundamental model. At the same time, this test case will enable us to clarify the sense in which Plato can be seen as the founder of the quadrivium: while confirming essential thematic continuities between Plato’s reflections on mathematics and the later quadrivium, it illustrates how the quadrivium emerged through a collective exegetical effort carried out by several Platonists over the centuries.

This contribution aims to examine Calcidius’ account of nature in his translation of and commentary on Plato’s Timaeus, with particular emphasis on the status of nature and its role in the cosmological framework. While Calcidius’ uses of natura in the translation are broadly consistent with Plato’s uses of physis, in the commentary he articulates a more robust account of nature as a causal agent and a teleological demiurgic principle, closely mirroring the role assigned to the lesser gods in Timaeus 41a–d. Remarkably, although the commentary testifies to an account of nature that goes beyond Plato’s, it does not provide evidence to support the hypothesis that Calcidius elevates nature to the status of a separate level of being. This hypothesis is further weakened by comparing Calcidius’ stance on nature with Neoplatonist hypostatic models. Finally, and most importantly, I will argue that regardless of the sources that may have had an influence on Calcidius, his introduction of nature as a demiurgic principle and causal agent alongside God is part of his own philosophical agenda and represents a crucial exegetical strategy to effectively rethink Plato’ account of cosmogenesis.

From Plato's Timaeus onwards, the world or cosmos has been conceived of as a living, rational organism. Most notably in German Idealism, philosophers still talked of a 'Weltseele' (Schelling) or 'Weltgeist' (Hegel). This volume is the first collection of essays on the origin of the notion of the world soul (anima mundi) in Antiquity and beyond. It contains 14 original contributions by specialists in the field of ancient philosophy, the Platonic tradition and the history of theology. The topics range from the 'obscure' Presocratic Heraclitus, to Plato and his ancient readers in Middle and Neoplatonism (including the Stoics), to the reception of the idea of a world soul in the history of natural science. A general introduction highlights the fundamental steps in the development of the Platonic notion throughout late Antiquity and early Christian philosophy. Accessible to Classicists, historians of philosophy, theologians and invaluable to specialists in ancient philosophy, the book provides an overview of the fascinating discussions surrounding a conception that had a long-lasting effect on the history of Western thought.

'Let me give you a simple example of what I mean, and you will see the rest for yourself.' This is how Plato usually introduces mathematical examples to illustrate important philosophical puzzles. The research presented in this book offers a systematic analysis of these examples and demonstrates their crucial psychagogical function. Providing a toolkit of paradoxical objects that challenge the soul and summon thought, mathematical examples do not convey demonstrative rigor or exact calculations, but instead induce psychic states of aporia and wonder. The gaze of Plato's mathematicians is directed both downwards and upwards: precisely for this reason mathematics have the power to awaken the soul and to lead it towards the Forms.

The Timaeus says that the World Soul has come to be and that it was generated before the world’s body (34b10–35a1). This chapter investigates two interwoven questions, i.e., whether the World Soul’s generation takes place in time and whether its priority with respect to the cosmos’ body should be understood in chronological terms. By addressing these questions, I shall explore how Plato’s account of psychogony is related to the controversial issue of the creation of the cosmos and of time, as well as to the explanation of motion in the pre-cosmic state. In addition, I shall consider the implications for the World Soul’s “creation” in the light of the Phaedrus, where the soul is explicitly described as ungenerated. By taking into account the views of some ancient commentators alongside those of modern scholars, I shall argue that the contradiction between the two dialogues is only apparent. Finally, I shall show that while the literal and the metaphorical reading of the psychogony each have their strengths and weaknesses, the latter is preferable as to the World Soul’s “birth” and especially as to its priority with respect to the cosmos’ body.

The purpose of this paper is to reassess some mathematical examples in Plato’s dialogues which at a first glance may appear to be nothing more than trivial puzzles. In order to provide the necessary background for this analysis, I shall begin by sketching a brief overview of Plato’s mathematical passages and discuss the criteria for aptly selecting them. Second, I shall explain what I mean by ‘mathematical examples,’ and reflect on their function in light of the discussion on παραδείγματα outlined in the Sophist and the Statesman. Against this framework, I shall move to a close examination of specific examples drawn from the Theaetetus (154c–55d), the Republic (523c–24d), and the Phaedo (96d–97b, 100e–101d). By placing these examples in the broader context of pre-Euclidean mathematics, I shall show that their mathematical content is often less elementary than might appear at first sight. Moreover, by placing emphasis on the specific philosophical concerns that motivated their introduction, I shall argue that the examples are not merely nonsensical jokes. Even if their illustrative purpose is not always immediately clear, and even if they can sound playful and bizarre, they in fact fulfil an important function: by virtue of their power to generate wonder or confusion, they serve as exercises and act as a trigger with respect to the difficult philosophical issues they are intended to clarify.