[Table of contents is provided at the end of the review.]
Svetla Slaveva-Griffin’s book, Plotinus on Number, is an investigation into the complicated world of Ennead VI.6. This short but dense book is remarkably enjoyable; Slaveva-Griffin works through the major issues in the treatise systematically and yet the book is not a commentary on the work. Instead, using Enn. VI.6 as a reference point, the book explains Plotinus’ contribution to the Platonic conception of number, particularly with respect to how Plotinus differs from Aristotle’s interpretation of Plato’s concept of number. The approach of the book allows the author to place Plotinus in the history of late antique mathematics, the scholarship for which has been heavy on Proclus and the Neopythagoreans to the neglect of Plotinus. In addition, this book provides insight into issues in Plotinian metaphysics, but one word of caution: Slaveva-Griffin does lay out some basic principles of Neoplatonism in her introduction, but the book assumes a certain level of understanding, especially of terms like “indefinite dyad” or “monad”. With this in mind, it would be best for the novice Platonist or historian of mathematics to start with a more general book on Neoplatonism or Plotinus first. Still, the book is certainly not overly-technical and it uses minimal Greek quotations, so it could be of use in an upper-level undergraduate seminar on Neoplatonism, but only after basic tenets of Platonic metaphysics had been thoroughly established. With that said, the book is truly interesting and very well-written; without doubt, it is a notable contribution to the field.
In the introduction, Slaveva-Griffin establishes that Plotinus, unlike Aristotle, distinguishes between intelligible number and arithmetical number. Slaveva-Griffin argues that Plotinus was “the first Post-Platonic philosopher who develops a theory of numbers”(p.12), which is interesting in light of Neopythagorean figures such as Nichomachus of Gerasa likening the monad to God or Middle Platonists such as Moderatus, who Slaveva-Griffin includes in her discussion of the topic (p.13). The main point which Slaveva-Griffin sets out in the introduction is that Plotinus views multiplicity as number, an argument which is supported by her systematic look at Enn. VI.6.
In Chapter One, “Platonic Cosmology on Plotinian Terms”, Slaveva-Griffin argues that Enn. VI.6 converts the systasis of the Timaeus into apostasis so that the Plotinian cosmology describes emanation from the One rather than a composition of the world by the demiurge. The author links this apostasis with creation of multiplicity from the One, which proceeds mathematically from the One. In Chapter Two, “Multiplicity as Number”, Slaveva-Griffin shows how the mathematical hierarchy of multiplicity from the One stems from a Neoplythagorean tradition of multiplicity and number. Here, she argues, I think most rightly, that Plotinus relies upon Moderatus’ definition of the One, or three Ones, in this case. While for Moderatus the first One is absolute stability, the second One acts as the principle of creation, and the third One is the principle of material reality and the principle which enumerates individual things. In these first two chapters, Slaveva-Griffin does a fine job of showing how Plotinus manipulates a Neopythagorean tradition to explain how the multiplicity comes from the One at the time of the creation of the universe. By probing into the historical sources of Plotinus’ understanding of number, this book offers a nice historical-philosophical approach to the question of number.
Next, the issue of infinity is taken up, starting with Plotinus’ critique of Aristotle’s Ph. 208a15 in Enn. VI.6.2. In Chapter Three, “The Number of Infinity”, Slaveva-Griffin first discusses the Platonic view of the generation of numbers and the distinction between Ideal numbers and arithmetical numbers, the former of which is left out in Aristotle’s understanding of number. Here, Slaveva-Griffin addresses the question of whether number is incidental to the Forms by looking at the discussion of time and movement in Enn. III.7.12.
Chapter Five, “Number and the Universe” is a joy to read. The discussion here centers on the difference between monadic number, which gives quantity, and substantial number, which, like the One, does not participate in quantity; rather, it acts as a holding place for being. In terms of a diagram of the universe, the One stands at the head of the universe, with substantial number between it and monadic number. Substantial number, thus, is ontologically important; as an intermediary figure, it shortens the distance between the One and number which enumerates physical reality. The remainder of this chapter outlines the various functions of substantial number. Slaveva-Griffin discusses how Being cannot function without substantial number because Being is unified substantial number. Substantial number is also an expression of Intellect insofar as Intellect is number moving in itself. This chapter describes how substantial number generates Being, Intellect, beings and complete Living Being because they are pure intelligible entities. The whole universe, thus, is a single living being which encompasses all living beings within it.
Chapter Six, “Unity of Thought and Writing” is more of an appendix, as the bulk of the argument is completed at the end of Chapter Five. Here, Slaveva-Griffin describes how Porphyry arranged Plotinus’ work in relation to Plotinus’ concepts of multiplicity and number, as well as late Neopythagean thought. Thus, just as the cosmos is a multiplicity ordered by number, so is the Enneads an outfolding into multiplicity. Most of the ideas in this chapter were covered in previous chapters; still, this is a fine chapter and the topic is of interest to many who read the Enneads.
Slaveva-Griffin’s Plotinus on Number is scholarly and challenging.
Table of Contents
Introduction: One by Number
1. Platonic Cosmology on Plotinian Terms
Ennead VI.6 and the Timaeus
Origin of Multiplicity in Plotinus
Plotinus’ Apostasis and Numenius’ Stasis
The Universe as Degrees of Separation from the One
2. Multiplicity as Number
Surfacing from the ‘Neopythagorean Underground’
Outward and Inward Direction of Multiplicity in Ennead VI.6
Multiplicity as Effluence and Unity
3. The Number of Infinity
Aristotle’s Criticism of Plato and the Platonists
4. Number and Substance
Plotinus’ Three Hypotheses about Number in the Intelligible Realm
Is Substantial Number Discrete and Incidental?
The Whole Number of Beings
Substantial and Monadic Number
5. Number and the Universe
Substantial Number and the One
Substantial Number and Absolute Being
Substantial Number and Intellect
Substantial Number and Beings
Substantial Number and the Complete
Soul and Number
The Unfigured Figure of Soul’s Dance
6. Unity of Thought and Writing
Porphyry and the Enneads
“Six Along with the Nines”
Conclusion: In Defense of Plato