S. F. Griffin

Plotinus posits the One as the single underlying principle from which everything that exists proceeds. This postulate makes the omnipresence of the One a given. Upon a close inspection, though, the matter is less clear-cut. How can the One be both ‘beyond existence’ and the productive ‘power’ of existence? How can the One be simultaneously nowhere and everywhere? How is the One present in the intelligible and the sensible level of reality? The omnipresence of the One, this chapter demonstrates, is for Plotinus the power of unity, emanating from the One and making everything to be what it is through the ontologically constitutive role of number. Plotinus thus challenges the Stoic view of material omnipresence and magnifies Plato’s conception of the good-making property of unity. He uncovers the relation between omnipresence and numbers, long before it becomes one of the future directions of research on the subject today.

The Handbook of Neoplatonism is an authoritative and comprehensive survey of the most important issues and developments in one of the fastest growing areas of research in ancient philosophy. An international team of scholars situates and re-evaluates Neoplatonism within the history of ancient philosophy and thought, and explore its influence on philosophical and religious schools worldwide. The Handbook of Neoplatonism is a major reference source for all students and scholars in Neoplatonism and ancient philosophy, as well as researchers in the philosophy of religion and the history and philosophy of science.

Chapter six examines the relationship between Plotinus’ concepts of number and multiplicity, and Porphyry’s organization of the Enneads. Porphyry’s thematical arrangement of the Enneads is traditionally considered to be more detrimental than beneficial for understanding Plotinus’ thought. The chapter re-examines this issue and discovers that Porphyry fuses Plotinus’ philosophy with Neopythagorean numerical symbolism to reveal the central organizing theme of Plotinus’ universe. In the Neopythagorean tradition, the number six is considered to be the first perfect number and the hexad is identified as the number of Soul, while the completion of the universe is represented by the number nine, which is “called ‘ennead’ as if it were the ‘henad’ of everything within it, by derivation from the ‘one’.” The individual treatises are consequently grouped in nines, because they enclose the numerical essence of the universe from “henad” to “ennead.” Porphyry’s arrangement of the Enneads encrypts numerically the perfect unity of Plotinus’ universe, for which Ennead VI.6 provides the conceptual blueprint.

This chapter examines the relationship between Plotinus’ concept of the origin of multiplicity as “separation from the One” and Plato’s presentation of the Demiurge’s composition of the universe in the Timaeus. The two terms characterize the “top-down” approach in Ennead VI.6 and the “bottom-up” approach in the Timaeus. The two works achieve the same goal—the explanation of the universe—with the same means—according to number—but from opposite starting points. The missing conceptual link between the two approaches, the chapter discovers, is found in Numenius’ concept of the Three Gods, ordering the universe: the Father, the Maker, and the Creation. The characteristics of Numenius’ First God convey the dichotomy between rest, as being and stability, and motion, as change, in the first principle. The explicit paradox of ontological stability and innate motion in Numenius’ First God is implicitly present in Plotinus’ explanation of the origin of the universe as “separation.” This chapter concludes that Plotinus induces the concept of multiplicity as a measurement of the ontological distance from the One. It also opens the possibility for stronger Neopythagorean influences.

This chapter analyzes Plotinus’ refutation of the Aristotle’s criticism of Plato’s view of number in the Parmenides. By rejecting any quantitative value of number in the intelligible realm, Plotinus specifically focuses on Aristotle’s inability to understand the Monad and the Indefinite Dyad as the principles of creation and order of the intelligible. The chapter shows that Plotinus not only follows the steps of his Platonic and Neopythagorean predecessors in defence of Plato’s position, but cleverly uses Aristotle’s own ideas in arguing that number in the intelligible is activity and a property of primary substance. The result is an original and ontologically elaborate theory of substantial number which offers a new and more successful defence of Plato’s “true numbers” against Aristotle’s criticism and explains the relationship between substantial non-quantitative number and monadic quantitative number as that between intelligible paradigm and its material copy.

This chapter examines the relationship of Substantial Number and all intelligible entities: Absolute Being as “unified number;” Intellect as “number moving in itself”; beings as “unfolded number;” and the Complete Living Being as “encompassing number.” A closer examination reveals that the four aspects of substantial number correspond to Plato’s primary kinds of rest, movement, otherness, and sameness respectively. The chapter concludes that the properties of substantial number enact the above four primary kinds, while the fifth primary kind, that of being, is the common denominator which represents them all. This conclusion also elucidates the relationship of substantial number with the One and Soul, as Plotinus does not identify them with a particular property of number. Since the properties of substantial number order Intellect on the inside and since both the One and Soul stand on the outside of Intellect, they do not inherit a particular property of number. Substantial number is an ontological expression of the One “beyond Being,” which does not possess any particular characteristic. Soul, however, as an image of Intellect, possesses all the properties of substantial number.

This chapter traces the historical and philosophical background of the concept of number from the Presocratics’ understanding of One and Many through Plato’s concepts of Limit and Unlimited, and Aristotle’s debate on the nature of number with Speusippus and Xenocrates, to the Neopythagoreans and Plotinus. Next, it examines the main difficulties with the concept of number in Plotinus: the unsystematic presentation of the concept in the Enneads, the lack of scholarly interest, and the brevity of Plotinus’ treatment of the subject. At the end, this examination focuses on the presentation of the concept in Ennead VI.6, the treatise On Numbers. From a bird’s-eye view, the subject of multiplicity begins and ends the thematic composition of the treatise. As multiplicity unfolds from the One and enfolds to the One, so does the composition of the treatise unfold and enfold in nesting circles, moving away from and yet turning toward their center. The concentric composition of VI.6 conveys non-discursively the higher ontological presence of number in the intelligible realm and iconically sketches the spherical figure of the universe.

This chapter investigates the Neopythagorean roots of Plotinus’ concept of number. Porphyry’s reports of Plotinus’ use of Neopythagorean sources in his teachings are quickly confirmed in the Enneads. In addition to Numenius’ influence on the definition of multiplicity as “separation,” this chapter reveals the programmatic significance of Moderatus’ distinction between the monad as the principle of numbers and the one as the principle of enumerated things on Plotinus’ two kinds of number. This discovery also shows Plotinus’ use of Moderatus’ definition of mathematical number in the formulation of the outward and inward directions of multiplicity. Next, the chapter examines the elements from Nicomachus of Gerasa’s Introduction to Arithmetic in Plotinus’ concept of multiplicity. The final conclusion of the chapter shows that Plotinus views multiplicity exclusively as number, which preserves it from dissipating into infinity and thus non-existence.

This chapter analyzes the relationship between number and substance in the intelligible realm. Plotinus formulates three hypotheses about the existence of number in the intelligible: 1) number is posterior to the Forms; 2) number is simultaneous with the Forms; and 3) number is anterior to the Forms. He proves that the last hypothesis is true. Based on the distinction between substance as ontological actualization of beings and quantity as the countability of individual units, he defines two kinds of number: Substantial Number, which is the activity of substance and a power of being; and Monadic Number, which enumerates individual things. As an activity of substance, the former enacts the limiting role of the Monad, while, as a power of substance, it enacts the role of the Indefinite Dyad as potentiality, limited into existence by the Monad. While substantial number actualizes the existence of that which has separated from the One in the intelligible, monadic number expresses quantitatively that which has been already defined by substantial number. Plotinus also pioneers the view of the substantial number as henad and, in turn, shapes the development of later Neoplatonic theory of number.

The concept of number is the troublemaker in the history of Platonism. It separated the followers of Plato and Aristotle into two camps for generations. For Plotinus, however, the concept becomes the peacemaker, which reconciles the camps. The importance of this reconciliation is central to Plotinus’ philosophical system because it not only uses Aristotle to defend Plato from Aristotle himself, but establishes Plotinus’ concept of number as the fundamental link between the number theories of the Neopythagoreans and the later Neoplatonists.This book demonstrates that the subject of number should be considered among the most important concepts for understanding Plotinus’ philosophy and therefore deserves greater scholarly attention than it has received. Plotinus adopts and adapts Platonic and Neopythagorean cosmology to place number in the foundation of the intelligible realm and the construction of the universe. Throughout the Enneads and especially in Ennead VI.6, he systematically peels off the layers of mathematical and quantitative perception from the concept of number to reveal that real intelligible number is the primary activity of substance, which orders the unfolding of the universe from its absolute source into a finite multiplicity.

The Routledge Handbook of Neoplatonism is an authoritative and comprehensive survey of the most important issues and developments in one of the fastest growing areas of research in ancient philosophy. An international team of scholars situates and re-evaluates Neoplatonism within the history of ancient philosophy and thought, and explores its influence on philosophical and religious schools worldwide. Over thirty chapters are divided into seven clear parts: sources, instruction and interaction Methods and Styles of Exegesis Metaphysics and Metaphysical Perspectives Language, Knowledge, Soul, and Self Nature: Physics, Medicine and Biology Ethics, Political Theory and Aesthetics The legacy of Neoplatonism. The Routledge Handbook of Neoplatonism is a major reference source for all students and scholars in Neoplatonism and ancient philosophy, as well as researchers in the philosophy of science, ethics, aesthetics and religion

Ancient Greek Philosophy routinely relied upon concepts of number to explain the tangible order of the universe. Plotinus' contribution to this tradition, however, has been often omitted, if not ignored. The main reason for this, at first glance, is the Plotinus does not treat the subject of number in the Enneads as pervasively as the Neopythagoreans or even his own successors Lamblichus, Syrianus, and Proclus. Nevertheless, a close examination of the Enneads reveals that Plotinus systematically discusses number in relation to each of his underlying principles of existence--the One, Intellect, and Soul. Plotinus on Number offers the first comprehensive analysis of Plotinus' concept of number, beginning with its origins in Plato and the Neopythagoreans and ending with its influence on Porphyry's arrangement of the Enneads. It's main argument is that Plotinus adapts Plato's and the Neopythagoreans' cosmology to place number in the foundation of the intelligible realm and in the construction of the universe. Through Plotinus' defense of Plato's Ideal Numbers from Aristotle's criticism, Svetla Slaveva-Griffin reveals the founder of Neoplatonism as the first post-Platonic philosopher who purposefully and systematically develops what we may call a theory of number, distinguishing between number in the intelligible realm and number in the quantitative, mathematical realm. Finally, the book draws attention to Plotinus' concept as a necesscary and fundamental linke between Platonic and late Neoplatonic schools of philosophy

This book is Yount's second installment in the Bloomsbury Studies in Ancient Philosophy. It comes on the heels of his debut in the series with Plotinus the Platonist: A Comparative Account of Plato and Plotinus' Metaphysics. The titles of both works clearly indicate what is close to Yount's heart; and he delivers, here as well as previously, the same passionate defense that there is an essentially inseparable connection between the philosophies of Plato and Plotinus. This stance may come as a surprise to the expert reader of late ancient philosophy. For no opinion to the contrary has been put forth in the Neoplatonic scholarship in the last 120 years if we take, with Yount, as our terminus post quem Shorey's...