3. Aristotle and Plotinus on the Intellect
Monism and Dualism Revisited
Mark J. Nyvlt
LEXINGTON BOOKS
Lanham • Boulder • New York • Toronto • Plymouth, UK
5. To my children, Hannah and Gabriel,
and
to the loving memory of my father, George
6.
7. vii
Foreword by Klaus Brinkmann ix
Acknowledgments xiii
Introduction 1
Part I
Chapter 1 Aristotle on the Platonic Two-Principles Doctrine:
The One and the Indefinite Dyad 11
Chapter 2 Aristotle and Speusippus 39
Chapter 3 Aristotelian Henology 57
Chapter 4 The Anatomy of Aristotle’s Metaphysics 73
Chapter 5 The Unmoved Mover and the Simplicity and
Priority of nou:V: Metaphysics L 7, De Anima
III.4–5, and Metaphysics L 9 97
Part II
Chapter 6 The =Epistrofhv of the One and the Derivation of nou:V 131
Chapter 7 Plotinus on Phantasia: Phantasia as the Home
of Self-Consciousness within the Soul 165
Chapter 8 Alcinous and Alexander on the Intelligibles within nou:V 187
Contents
8. viii Contents
Chapter 9 Plotinus on the Simplicity of nou:V: An Appropriation
and Critique of Aristotle’s Noetic Doctrine 215
Conclusion 233
Bibliography 241
Index 259
About the Author 263
9. ix
Mark Nyvlt’s book Aristotle and Plotinus on the Intellect: Monism and Dualism
Revisited is a remarkable study that doesn’t fall into the usual categories of schol-
arly publications. Hence, a foreword may offer some useful orientation to the
reader. As we might expect from a scholarly contribution, Nyvlt has submitted
a work of expert textual exegesis. But already the scope of the primary sources
discussed is unusual, ranging from key Platonic dialogues and their Pythagorean
motives to Aristotle’s doctrine of nous and his reports about (and criticism of)
Plato’s unwritten doctrine in the Metaphysics, to Speusippus’s theory of the One
(as presented by Iamblichus), the noetic doctrines of Alcinous and Alexander of
Aphrodisias, to Plotinus’s metaphysics in the Enneads. Nor does the argument
of the book unfold in a merely chronological progression. It is comparative in
nature, taking its bearings from two fundamental systematic problems to do with
the explanatory structure of these theories themselves and their foundational
principles. As the subtitle of the book indicates, the focus of Nyvlt’s study is the
problem of a satisfactory combination of a monistic principle or archē with the
derivation of a pluralistic ontology in one coherent metaphysical system. Plural-
ism seems to require a dualistic principle at the very least, whose derivation from
a strictly monistic principle seems, however, a hopeless undertaking. This is, of
course, the time-honored problem of the One and the Many that presents any
systematic thinker with serious difficulties. In this situation, perhaps the most
remarkable feature of Nyvlt’s study, and the aspect in which it differs mark-
edly from standard scholarly analyses, is its creative approach. Nyvlt not only
compares and contrasts the various formulations of the internal structure of the
Foreword
Klaus Brinkmann
10. highest principle and its connection with the Many from Plato to Plotinus, but
he also critiques, reinterprets, and recombines them so as to arrive at his own
original solution to this foundational problem.
The challenges of deriving all of being from a monistic archē are already ad-
umbrated in Plato’s Idea of the Good, itself a response to the Parmenidean One
that in negating all multiplicity is tautologically identical with itself and thus an
ultimate ground without a grounded. The Good is supposed to function both
as principle of intelligibility and as a real ontological ground giving rise to and
sustaining all beings and all life. As ground of all being, however, the principle
must be “beyond being” (epekeina tēs ousias) and thus beyond determinability,
a fact that seems to threaten its intelligibility. Moreover, in transcending be-
ing, the Good’s causal role with regard to finite reality becomes problematic.
Aristotle therefore tries to address both these concerns by making the very
paradigm of intelligibility itself (i.e., divine nous) the highest principle and by
attributing to it at least final causality. As Nyvlt argues, however, he also creates
a discontinuity between divine nous (which remains eternally self-enclosed in
self-contemplation) and the rest of the cosmos—nous hovers at the periphery of
the first heaven, as Aristotle tells us in the Physics. And there are other problems
with Aristotle’s thinking on thinking. If the object of this thinking is the pure act
of thinking itself, it seems to lose all content and to become a vacuous, perhaps
even a paradoxical, thinking about nothing. This problem seems initially to be
averted by Aristotle’s admission in Metaph. XII 9 that there is always a formal
difference between the act of thinking and its object, a difference that need not,
however, amount to a material difference as long as the object can exist self-
sufficiently without any matter. In the case of the divine nous, to maintain a
formal distinction within nous that is no “real” distinction seems to preserve both
the intelligibility and the immanence of this highest substance that is purely es-
sence. Let us assume that the object of this thinking could be called the concept of
self-contemplation, whereas the divine noēsis is the act of self-contemplation. Act
and object would then be different in form but the same in content, and a tau-
tological identity or a thinking about nothing would thereby have been avoided.
If, however, we accept Plotinus’s critique of Aristotle’s divine nous, the self-
reflective structure of noēsis noēseōs, in harboring at least a formal distinction,
thereby also includes potentiality, thus making this thinking less than divine
and unsuitable to function as an absolutely first principle. This is where Nyvlt
disagrees, and he may well be correct. The way I see it, since the concept of
divine noēsis consists in its being thought, and being thought eternally without
interruption, there is no transition into or out of potentiality here ever. The
concept never becomes either a mere abstraction or opposed to another concept
that would limit it. It is always and continuously enacted, realized through the
x Foreword
11. activity of self-contemplation. While there is a distinction within noēsis noēseōs,
there is no gap between act and concept, and so no potentiality. Nor is the divine
noēsis an empty thinking about nothing. We have thus successfully identified a
suitable first principle that does not contain dualism within itself, and yet we
have avoided the problem of the unintelligibility of this principle, a problem that
the Plotinian One cannot escape, since it is explicitly not only beyond being but
also beyond reason.
What is really remarkable about Nyvlt’s book is the fact that in his view the
matter concerning the highest principle cannot end here. Two more conditions
would have to be fulfilled by the first principle of everything, if it is to be fully
explanatory and a truly grounding principle rather than merely the summit
in the order of beings. To be the first substance (or the “primary essence,” as
Aristotle puts it once in Metaph. XII 8) is not enough, even if this substance
is a non-vacuous pure activity. We would also want the principle on which the
heaven and the earth depend to contain the intelligible forms of all beings. For
if the content of the divine noēsis consists of the concept of self-contemplation
alone, what do beings that are not self-contemplative, or only partially so, derive
their intelligibility from? And furthermore, if the divine noēsis remains forever
self-enclosed, how can it assume a genuine causal role vis-à-vis the cosmos? Must
not a first principle also be shown to be able to generate what depends on it? To
be sure, the general is not the same as his army, but is a general without an army
that he actively leads and commands truly a general?
It seems, then, that in addition to a minimalist concept of the divine noēsis
as self-contemplation, we need a richer content for this thinking on thinking,
a multiplicity of forms to function as paradeigmata of the finite beings. (As
an additional bonus of these considerations, we can now also appreciate the
real urgency of Aristotle’s question in Metaph. VII and VIII as to whether the
essence of materiate forms really does or does not contain a reference to their
matter: if it doesn’t, then all Aristotelian eidē may be no different from Platonic
ideai.) As objects of divine noēsis, these forms will still be without matter, thus
not introducing potentiality into the first principle. Here, Nyvlt takes his lead
from Alcinous and Alexander rather than the Plotinian intellect and follows
Alexander in attributing efficient causality to this highest principle in addition
to its final causality. Multiplicity of the content of noēsis does not prevent the
divine nous from remaining simple, he argues, because we are dealing with a
multiplicity-in-unity. Once again, the need for a Plotinian One beyond being
and reason falls away and the causal efficacy of the highest ground lets it be a
ground with a grounded.
Whether all these requirements for a highest explanatory principle that caps
a monistic account of being as a whole can be fulfilled in one coherent concep-
Foreword xi
12. tion the reader will have to decide for him- or herself. Nyvlt’s study shows us the
magnitude of the challenge we are up against in tackling these most fundamental
of fundamental issues, as it also contributes creatively toward their resolution.
Nyvlt’s book grew out of the dissertation he submitted as a PhD student in
philosophy at Boston University. To my deep regret, the co-mentor of the thesis,
John Cleary, professor of philosophy at Boston College and the National Uni-
versity of Ireland, Maynooth, is no longer among us to witness the publication
of a work that owes a lot to his care, insight, and support.
June 2011, Bonn, Germany
xii Foreword
13. xiii
The completion of this book is due to the involvement of many hands. My first
acknowledgment is to Jim Lowry and Francis K. Peddle, who opened my mind
to the ubiquitous activity of speculative philosophy. The result was a philosophi-
cal friendship (cf., Plato’s Theaetetus, 146A) that has since propelled me into
many new philosophical horizons.
I am deeply indebted to Klaus Brinkmann and John Cleary for their steady
guidance, intellectual honesty, and serious scholarship, all of which have inspired
me. John’s untimely death meant the loss of an excellent scholar, dear friend, and
colleague. As always, I am grateful to my colleagues at the Dominican Univer-
sity College for their speculative intellects, vivified philosophical conversations,
and unfailing intellectual support in this project; to Fr. Michel Gourgues, O.P.,
for awarding me with the Saint-Albert-Le-Grand fund, which financed part of
the production of this book; to Yves Bouchard and Gabor Csepregi, who never
ceased to encourage me in its publication; to Janina Muller, my research assistant
and a very promising researcher, who helped me considerably to develop my bib-
liography; to David Roochnik and Rémi Brague for their invaluable comments
on an earlier version of the book; to the anonymous reader for his or her very in-
sightful comments, which helped refine my argument; to my many friends, too
many to mention here, who have always provided me with support throughout
the writing process; to the editors of Ancient Philosophy (“Plotinus on Phanta-
sia: Phantasia as the Home of Self-Consciousness within the Soul,” in Ancient
Philosophy 29 [2009]: 139–56) and the Journal of Classical Studies Matica Srpska
(“Plotinus on the Generation of the Intellect: The Transformation of the Inher-
Acknowledgments
14. ited Platonic and Aristotelian Two Principles Doctrine,” Journal of Classical Stud-
ies Matica Srpska 12 [2010]: 101–19) for their permission to reprint my articles
in chapters 6 and 7 of this book; to Princeton University Press for the permission
to cite Aristotle from The Complete Works of Aristotle; and to Jana Hodges-Kluck,
associate editor of ancient philosophy and classics at Lexington, for her patience
and steady communication with me throughout the editing process.
Special gratitude is owed to my family in Ottawa, Montréal, and the Czech
Republic. To my mother, Josette; my brother, Carl; my sister, Monica, and her
husband, Ariel—thank you for your constant support. The death of my father,
George, prevented him from seeing the publication of this book, but he is to
be acknowledged as having provided me with the positive attitude and force
to complete this project. With equal gratitude, I would also like to thank my
children, Hannah and Gabriel. I dedicate this book to my children and to the
loving memory of my father.
xiv Acknowledgments
15. 1
If its intellectum were something extraneous to it, [this intellectum] would be
nobler and more excellent [than the Intellect]. For it would be the cause of
Intellect’s intellecting. . . . Everything that exists in consequence of [having]
something other than itself as its cause is inferior to the thing that is posited
as being its cause. Thus the intellect would be in potentia. . . . We shall say
that He intellects the things that are of the utmost excellence. If He were to
intellect inferior things, He would derive His nobility from inferior things.
This [conclusion] must be avoided.
Themistius, in CAG 5.4
The Problem
The attempt to harmonize Plato and Aristotle within the school of Neopla-
tonism has all too often resulted in the subordination of Aristotle’s metaphysics
and categories to Plato’s. The reason given for such subordination is clear: Aris-
totle concerns himself with the natural, physical world and its causes, while Plato
deals with the divine world. Consequently, there can be no overlapping of their
respective set of categories of each sphere. Plotinus has given Plato’s metaphysical
system precedence over Aristotle’s, and the subsequent generations of Neopla-
tonists have generally followed this positioning of Aristotle below Plato.1 This
reading of Aristotle and Plato is, naturally, manifest in all of Plotinus’s work, but
it is most noticeable in his account of the status and nature of the divine nou:V
(intellect).
Introduction
16. A corollary to this account of nou:V is a critique of Aristotle’s account of
the separate and autonomous nature of Forms and Numbers. In the Meta-
physics, Aristotle opposes the Neopythagorean and Platonic doctrine of the
separability of Forms and Numbers from their material counterparts, a doc-
trine allegedly expressed in Plato’s lecture, On the Good, and developed by
Speusippus. It is my conviction that within Aristotle’s criticism of Platonism,
one can see, in germ, what Aristotle’s response would be to Plotinus and the
subsequent Neoplatonists, should he have had the opportunity of confront-
ing Plotinus. I wish to argue that Aristotle’s noetic doctrine provides an ade-
quate response to Plotinus’s philosophical move of subordinating nou:V to the
One. I wish to take as my starting point Aristotle’s criticism of the Platonists
and then proceed to examine the doctrine of actuality and potentiality, to
demonstrate the Plotinian justification for such a subordination, and to pro-
vide an Aristotelian response to such a philosophical move. While I adhere
to the Aristotelian position of the supremacy of nou:V, I wish, however, to
emphasize the Neoplatonic originality of introducing into the first principle
not only final causality, as is the case with the Aristotelian presentation of
nou:V, but also efficient causality. Plotinus’s account of the inner “qualities”
of the One can enrich the Aristotelian concept of nou:V, regarded here as the
first principle. Moreover, I wish to acknowledge Plotinus’s astute recognition
of a formal duality within Aristotle’s divine nou:V, as object of itself and as
thinking subject.
In order to elucidate Plotinus’s originality, it will be imperative to illustrate
the difference between Plotinus, on the one hand, and Plato and Aristotle, on
the other: Plotinus’s project is, in part, to overcome the cwrismovV (separation)
between the first principle and the multiplicity of the cosmos; his monistic
system attempts to overcome the intrinsic duality in Plato’s and Aristotle’s cos-
mologies. According to Plato, the Forms remain absolutely separate from their
sensible counterparts, and according to Aristotle, the divine nou:V is separate
from the material world. Plotinus, however, attempts to unify the diversity into
a totality. The One, by exercising an efficient causal role, unifies by governing all
that is other than itself, by functioning as the ajrchv and the tevloV of a multiple
world. Whereas Plato and Aristotle maintain a strict duality between Forms and
matter and divine nou:V and the material world, respectively, Plotinus wishes to
harmonize the diversity into one system. The One is the efficient and final cause
of the cosmos, and is, therefore, the causal agent responsible for this harmony.
Whereas Plotinus preserves a duality and transcendence between the One and
the multiplicity, he asserts that the One “influences” the multiplicity via the
logos. Thus, in this way, the minimal chorismoi are overcome and the unity-in-
diversity is preserved.
2 Introduction
17. Structure
This book contains two parts and nine chapters, each of which highlights a
specific theme related to the Aristotelian and Plotinian doctrines of nou:V. Each
chapter may be summarized in the following way.
In part I, the first chapter attempts to demonstrate the Pythagorean and
Platonic two-principles doctrine and Aristotle’s presentation and philosophical
reaction to this tradition. Chapter 2 exposes part of this philosophical reaction,
which is perceived in his analysis of Speusippus’s doctrine of the One, of which
we know very little apart from Aristotle’s testimony, and of Iamblichus’s De
communi mathematica scientia, chap. 4. More specifically, in chapter 1, I first
examine the Pythagorean Table of Opposites, the Limited and Unlimited, and
the two-principles doctrine of the One and the Indefinite Dyad for the purposes
of providing the conceptual background against which Plato develops his two-
principles doctrine, the Great and the Small and the esoteric teachings of the
Ideal Numbers, which we read about in Aristotle’s writings and which is echoed
in other testimonies. The final section of this chapter consists of Aristotle’s
analysis and harsh criticism of Speusippus’s doctrine of the One. Throughout
this section, I have accepted Philip Merlan’s original thesis that Iamblichus’s
De communi mathematica scientia, chap. 4, is an excerpt of Speusippus’s writ-
ings and, as a result, should be read in light of Aristotle’s remarks. We soon see
certain discrepancies between Aristotle’s account and Speusippus’s doctrines.
Nonetheless, we equally see Aristotle’s response to a Neoplatonic metaphysics,
which specifically consists of subordinating the Aristotelian divine nou:V to the
One and, moreover, of asserting that because divine nou:V is plural, it must con-
tain potentiality and cannot be simple. I will argue that in Aristotle’s response to
Speusippus, whether he is accurate or not, we can detect a rationalist and intu-
itionist position that is aware of the possibilities of proposing a principle above
and prior to nou:V. Aristotle, as we see in chapter 3, did not accept this position
and argued vigorously against it.
Chapter 2 concludes with a discussion of Aristotle’s interpretation of Speusip-
pus, with the intention of determining the exact teaching, if possible, of Speusip-
pus and of demonstrating Aristotle’s recognition of theories that argue for the
subordination of divine nou:V to an ultimate principle. One reason why Aristotle
cannot accept either Speusippus’s model of the cosmos or a Plotinus-like model
is that neither of these models provides an adequate reason for the derivation of
multiple levels of being. As for the exact teaching of Speusippus, we must exam-
ine Iamblichus’s De communi mathematica scientia, chap. 4, in order to account
for what could possibly be the correct status of the Speusippean One. We know
from Aristotle that Speusippus’s first principle, the One, is not a being (i.e., is not
Introduction 3
18. an individual substance), but it is unclear whether this principle is above Being
or is inferior to Being. Clearly, Aristotle argues that it is comparable to a seed
and is inferior to its final product. As a result, it is not deemed worthy of being a
first principle; for, Aristotle asks, how can form and actuality derive from a first
principle that is no greater than a pure potentiality? This section explores Aristo-
tle’s analysis and critical judgment of the Speusippean One and draws out from
his response a conjecture about Plotinus’s doctrine of the One prior to nou:V.
In chapter 3, I emphasize Aristotle’s henology and noetic doctrine, with the
purpose of demonstrating that Aristotle accepts a multiplicity of intelligibles
within nou:V and that this multiplicity does not compromise in any way the
very integrity of the simplicity of nou:V. I first present Aristotle’s doctrine of the
“one,” considered first as a reaction to Plato’s account of the One. Aristotle, sub-
sequently, presents the “one” not as a transcendent and univocal substance, but
rather as a pros hen equivocal, which cannot be considered as a transcendent and
universal substance (see Met. D and I). The subsequent section highlights Aris-
totle’s alternative solution to Plato’s two-principles doctrine, as we read in Meta-
physics L 4–5. Aristotle, in lieu of Plato’s principles, proposes three analogous
principles of sensible substances: form, privation, and matter. Like the many
senses of the “one,” Aristotle asserts that these principles are not homogeneous,
but can be applied universally to all sensible substances. These principles are,
however, applied differently to separate substances, which are depicted as purely
simple and actual substances. Aristotle’s discussion of this realm of the cosmos
provides an effective transition into his account of the simplicity of divine nou:V
and its nature as a final cause.
Prior to the discussion of Aristotle’s doctrine of nou:V, however, I provide, in
chapter 4, a middle section that highlights the complexity of Aristotle’s usage of
duvnamiV, ejnevrgeia, and ejntelevceia in order to appreciate the concepts em-
ployed by Aristotle in his account of nou:V. In chapter 5, I examine closely Aristo-
tle’s doctrine of the absolute simplicity and priority of nou:V as presented in Meta-
physics L 7 and 9, and De Anima III. 4–5. The most salient theme that I wish
to emphasize in this section is that divine nou:V is not a composite substance, in
spite of its possession of multiple intelligible objects. To admit of a composition
within nou:V would be to admit of a degree of potentiality, thereby demoting
nou:V to a status subordinate to an ultimate and simpler principle. In my analysis,
I have accepted Jackson’s and Merlan’s positions, along with the general tenets of
the immanentist tradition, regarding the multiple intelligibles that function as
the content of divine nou:V. This doctrine influenced not only Alcinous but also
Alexander of Aphrodisias, from whom Plotinus received and refined his doctrine
of nou:V, according to his doctrine “That the Intelligibles are Not Outside the
Intellect” (see Enn. V.5). However, I have argued, contrary to the immanentist
4 Introduction
19. school, that divine nou:V exercises, according to Aristotle, only final causality
and not efficient causality. Nevertheless, I submit, divine nou:V knows the formal
structure of the world, but without it being infected with potentiality, for divine
nou:V is fundamentally separate and distinct from the world. Plotinus introduces
efficient causality into the first principle through the mediation of Alexander of
Aphrodisias, both of whose doctrines will be discussed in chapter 8. Plotinus,
however, does so at the cost of the ultimate position of divine nou:V; divine nou:V
becomes the second rank in this new monistic metaphysics.
In part II, chapter 6, I discuss the Plotinian derivation of nou:V from the One,
considered as a monistic system. Whereas Plato and Aristotle have asserted a
dualistic principle as their starting point, Plotinus proposes a monistic starting
point, thereby asserting the One above Being, Life, and nou:V. This chapter es-
sentially discusses the reasons why Plotinus is compelled to assert a single causal
principle in lieu of the Platonic two-principles doctrine, and how these lower
levels of being are derived from the One.
More specifically, I discuss one of the most controversial passages in Plotinus’s
account of the derivation of nou:V, as seen in Enneads V.4[7].2, V.1[10].6–7.
Multiplicity entails the radical Otherness between the One and the multiplicity
of the cosmic hierarchical system. The Dyad is characteristic of an infinite desire,
and this desire or longing is rooted in nou:V. These passages reveal that nou:V is
derived from the One through a conversion of the One toward itself. The result
is the derivation of the Indefinite Dyad and of inchoate nou:V, thereby transform-
ing the two-principles doctrine of Plato and Aristotle and affirming his strict mo-
nistic framework of the cosmos, which, according to Plotinus, is an attempt to
overcome the “gap” between the Aristotelian first principle, divine nou:V, and the
world. However, although Plotinus makes a fundamental distinction between
the One and the first effluence from the One, he also depicts the One as a final
and efficient causality—a causal role that can successfully overcome the separa-
tion or gap between the first principle and its effects. Therefore, Plotinus’s meta-
physics can confidently be called minimally dualistic, unlike Aristotle’s strict and
firm duality. The emanation of the first effluence of the One establishes a causal
continuity of the first principle and its effects.
This fluid continuity of causality from the One to its first effluence is illus-
trated in the derivation and generation of the Indefinite Dyad, which Plotinus
has interpreted as intelligible matter—the intelligible substrate that cooperates
in the production and generation of inchoate nou:V and the multiple intelligibles
within nou:V. I demonstrate in chapter 7, moreover, that intelligible matter shares
many similar characteristics with Imagination and, more specifically, with the
higher Imagination. Both intelligible matter and Imagination are ambiguous and
lack definition. As a result, the ambiguity of Imagination further allows us to
Introduction 5
20. make a better comparison between it and inchoate nou:V, which is also ambigu-
ous, for it is not yet formed, and its indefinite and potential nature keeps “it”
out of the reach of scientific inquiry.
Moreover, the separation of nou:V from the One is a result of the tovlma,
which allows for the first effluence to assert itself and its unique activity, thereby
daring to assert itself and to affirm its identity-in-difference (i.e., the unity of
the multiple intelligibles within nou:V). The doctrine of the tovlma clearly indi-
cates a tension within the nature of nou:V. One sees the Plotinian-Aristotelian
tension here: on the one hand, nou:V wishes to remain self-sufficient, but, on the
other, it is dependent upon the One for its activity and even for its impetus to
affirm itself. The Indefinite Dyad is essential for Plotinus, if this transition from
simplicity to multiplicity, from the One to nou:V, is to occur successfully. This
tension within the nou:V is symptomatic of its self-assertion over and against the
One. This procession of nou:V from the One is for Plotinus a spurious activity
of self-assertion, radically rupturing itself from the One, with the intent of fully
actualizing itself independently of the One. The Plotinian doctrine of the tovlma,
moreover, appears to be a transformation of the Neopythagorean doctrine of
the Indefinite Dyad, emerging and separating itself from the monad. It will be
stressed, however, that the dyad is not multiplicity itself, but the very condition
of multiplicity (see Enn. V.4.2).
Chapters 8 and 9, finally, discuss Plotinus’s transformation of the Aristotelian
and Alexandrian noetic doctrines. Plotinus will propose his own noetic doctrine,
which consists of a duality (formal and material) and multiplicity within nou:V. I
also discuss Plotinus’s philosophical justification for asserting such a composition
within nou:V. Prior to this discussion, which is located in chapter 9, however, I
first consider the two philosophers who had a great impact on Plotinus’s transfor-
mation of the nature of nou:V: namely, Alcinous and Alexander of Aphrodisias, a
topic covered in chapter 8. In the first section, I concentrate on Alcinous’s theory
of nou:V, which attempts to synthesize Plato’s and Aristotle’s metaphysics into a
unified noetic doctrine. In the course of this presentation, I also highlight for
the reader the conundrum around Alcinous’s statement of an Intellect superior to
the cosmic nou:V. For Alcinous’s proposal of a superior Intellect clearly influenced
Plotinus to propose a principle—namely, the One—above and prior to nou:V.
According to Alcinous, the Aristotelian doctrine of the intelligibles or the mul-
tiple content within divine nou:V plays a fundamental role in the development of
first principles of the cosmos, as seen in the second section, in our discussion of
Alexander of Aphrodisias.
Alexander of Aphrodisias, like Aristotle, proposes the doctrine that the ulti-
mate principle of the cosmos is the productive nou:V in its absolute simplicity. By
introducing efficient causality into the first principle, Alexander seems to have
6 Introduction
21. developed the Aristotelian doctrine of the intelligibles within the productive
nou:V, which orders and participates within the cosmos, in which, moreover, we
find the material nou:V, which is raised to the level of nou:V in habitu through the
participation and causal influence of the productive nou:V.
Following this discussion, I discuss the nature of the productive nou:V as it is
compared to the metaphor of light, according to Alexander. I concentrate on this
analogy for the purpose of demonstrating a common trait between Alcinous and
Alexander—namely, that nou:V is superior to all other principles and is purely
actual and simple, even if the content within nou:V is multiple—a general accep-
tance of Aristotle’s noetic doctrine in Met. L 7 and 9. The nature of this mul-
tiplicity with nou:V, however, is challenged by Plotinus, as I show in chapter 9.
In chapter 9, I wish to show that Plotinus transforms the nature of nou:V.
The One generates nou:V, due to its dual (formal and material) and multiple
nature. We explore the dynamic within nou:V. I show that, on the one hand,
Plotinus agrees with Alexander that the intelligibles are within nou:V, but, on the
other, Plotinus disagrees with Alexander about the absolute simplicity of nou:V.
According to Plotinus, nou:V is derived from the One—that is, it is subordinate
to the One, because its content is really distinct and multiple, thereby render-
ing it potential. Thus, nou:V must contain a degree of potentiality within it, for,
once again, the intelligibles are really distinct from one another, and, moreover,
the intelligibles define and actualize nou:V. Prior to the definition of nou:V, nou:V
remains purely potential with respect to its intelligibility. Therefore, although
the intelligibles operate within nou:V, they are independent of nou:V, and this in-
dependence introduces “otherness” within nou:V. As a result, Plotinus can reject
the Aristotelian and Alexandrian claims for the simplicity of nou:V and of the
identity of the intelligible content of nou:V and of nou:V proper. Therefore, nou:V
is subordinate to a superior principle—namely, the One—because the novhsiV of
nou:V is ajovristoV and is determined by the intelligible objects which it receives.
Moreover, it is argued that Plotinus subordinates nou:V to the One not only be-
cause of the multiplicity of content found in nou:V, but also because of its formal
duality, as object of itself and as a thinking subject.
My conclusion recapitulates much of the content of the book but also em-
phasizes the central theme that Aristotle was aware of the philosophical attempt
to subordinate divine nou:V to a prior and absolute principle. I have argued that
Aristotle transforms the Platonic doctrine of Ideal Numbers into an astronomi-
cal account of the unmoved movers, which function as the multiple intelligible
content of divine nou:V. Thus, within Aristotle’s philosophy, we have in germ the
Plotinian doctrine that the intelligibles are within nou:V. While the content of
divine nou:V is multiple, it does not imply that divine nou:V possesses a degree of
potentiality, given that potentiality entails otherness and contraries. Rather, the
Introduction 7
22. very content of divine nou:V is itself; it is novhsiV nohvsewV novhsiV. The pure
activity of divine nou:V, moreover, allows for divine nou:V to know the world, and
the acquisition of this knowledge does not infect divine nou:V with potentiality.
The status of the intelligible object(s) within divine nou:V is pure activity that is
identical with divine nou:V itself, as Th. De Koninck and H. Seidl have argued.
Therefore, the intelligible objects within divine nou:V are not separate entities
that determine divine nou:V, as is the case in Plotinus. Based on his argument in
Met. L 9, I wish to argue that Aristotle succeeds in demonstrating that divine
nou:V is a unity-and-plurality within the cosmos, but that this does not admit
of any potentiality within its being, thereby stamping divine nou:V with the title
of the ultimate principle of the cosmos. The ultimate principle, then, must be
purely active and simple and, given Aristotle’s argument, must be nou:V. As I wish
to show, this conclusion is best developed and expressed by Alexander of Aphro-
disias, who has identified the productive nou:V of Aristotle’s De Anima with the
unmoved Mover of Met. L 7–9. We see in Alexander the limitation of Aristotle’s
own noetic doctrine, that it lacks efficient causality, which Alexander provides in
order to complete the Aristotelian project of preserving the unity-and-diversity
within the cosmos.
Note
1. This can be seen in Syrianus’s commentary on Aristotle’s Metaphysics and in Pro-
clus’s Elements of Theology and Commentary on the Parmenides.
8 Introduction
25. 11
Introduction
The question of the One and the Indefinite Dyad is intimately related to the
twin theme of monism and dualism. In this chapter, I will essentially concentrate
on Aristotle’s interpretation of the (allegedly) Platonic teaching of this two-
principles doctrine. In order to proceed in this analysis, I will discuss the con-
troversy surrounding Aristotle’s credibility as a witness and authentic source of
Plato’s philosophy. This discussion will inevitably lead us in the direction of the
debate found within the Academy between Aristotle and the Platonists (notably
Speusippus, whom we shall study in chapter 2). I wish to defend the view that
the philosophical motivation behind this debate about the status of first prin-
ciples revolves around Aristotle’s attempt at explaining the derivation of plurality
from the first principle, whether the first principle be singular or dual in nature.
The dualistic framework of the cosmos, represented by philosophies of the Hel-
lenic age and also the Hellenistic age, especially Neoplatonism, allows for Greek
philosophers to entertain the possibility of a monistic conception of the cosmos,
since these philosophers attempt to preserve unity amid the multiplicity per-
ceived within the cosmos. Each philosopher must answer the question, “What
is the nature of this principle (or these principles) that allows for the multiple
degrees of being to exist within a unified cosmos?” Depending on how this ques-
tion is answered, the philosopher may be inclined toward dualism or monism.
The trajectory from dualism to monism will be the overarching theme and will,
as I hope to show, characterize much of our discussion of the simplicity of nou:V
c h a pte r one
Aristotle on the Platonic
Two-Principles Doctrine
The One and the Indefinite Dyad
26. (intellect) in both Aristotle’s and Plotinus’s philosophical systems. We shall, as
a result, read and interpret Aristotle’s philosophical concepts and doctrines in
light of the backdrop of the debate about the two-principles doctrine within the
Academy in order to equip ourselves with the conceptual tools to study Plotinus’s
reading and critique of Aristotle’s doctrine of the simplicity of nou:V.
In this chapter, I will discuss Aristotle’s interpretation of the Pythagorean Ta-
ble of Opposites, for this interpretation provides the lens through which Aristotle
discusses Plato’s two-principles doctrine of the One and the Indefinite Dyad.
This doctrine was significantly reformed by Aristotle, as we shall see in chapter 3.
Given that Aristotle highlights salient doctrines that both the Pythagoreans and
Plato share, I will explore Aristotle’s interpretation of the Pythagoreans in order
to configure the medium through which we can perceive Aristotle’s interpreta-
tion of Plato. This will also help in Aristotle’s own metaphysics, which is in part
generated as a reaction to Platonism.
Aristotle and the Pythagoreans
In Metaphysics A 6, 987b14–35, Aristotle highlights the similarities and differ-
ences between the Pythagoreans and Plato with respect to their doctrines of first
principles. The preeminent philosophical problem plaguing the Pythagoreans
and Plato—and Aristotle and Plotinus—is the derivation of multiplicity in the
cosmos. Very little is known about the Pythagorean society, apart from the few
fragments remaining from Philolaus. Most of our knowledge is derived from
Aristotle’s account and his critique of their central doctrines. I wish primarily
to concentrate on the theme of the dual principle doctrine, the Limited and
Unlimited, or the One and the Indefinite Dyad, as it was later called. I am
not concerned with the exact teachings of the Pythagoreans, nor, incidentally,
with Plato, but I wish to concentrate on Aristotle’s presentation of both the
Pythagoreans and Plato. For it will be Aristotle’s interpretation (accurate or not)
that will influence subsequent peripatetics, such as Theophrastus and especially
Alexander of Aphrodisias, and ultimately Plotinus (who can also be called, with
qualification, a Neoaristotelian) in his formulation—or reformulation—of the
key philosophical problems of the nature or status of nou:V.1 What needs to be
discussed first or established is the first-principles doctrine of the Pythagoreans,
for Plato’s general metaphysics of first principles is widely influenced by the
Pythagoreans, with several differences, as Aristotle notes. To begin with, the
analysis of the Pythagoreans is and, with some exception, must be mediated by
Aristotle’s presentation of this society. Plato is in many ways indebted to the Py-
thagoreans, regarding the harmony of the cosmos, mathematics, musical ratios,
and so forth. However, for the purposes of this chapter, I will concentrate solely
12 Chapter 1
27. on the rapport between the Pythagoreans and Plato regarding the first principles,
a relation of which Aristotle spoke on many occasions.
The Pythagoreans and Plato on the Two-Principles Doctrine:
The Aristotelian Interpretation
According to Aristotle, the Pythagoreans attempted to understand the cosmos
numerically (i.e., that the nature of reality consists in numbers). Aristotle says,
“[T]hey supposed the elements of numbers to be the elements of all things,
and the whole heaven to be musical scale [harmonia] and a number” (Met. A
5, 986a2). Numbers play a central role in the cosmos for the Pythagoreans, as
Aristotle reminds us in Met. A 5, 986a16–21. This rich text captures one of the
most salient themes of the Pythagorean philosophy: that the One is both even
and odd and that number is derived from the One, which is a composite of the
even and odd, or, using other terminology, the Limited and the Unlimited.
Aristotle, furthermore, illustrates the Pythagorean Table of Ten Opposites,
which characterizes the One as consisting of two principles2 (see Met. A 5,
986a21–26). The table begins with the limited/unlimited as a representation
of the basic dual nature of the One and the Indefinite Dyad, out of which is
derived number and the whole cosmos. Elsewhere, Aristotle reaffirms the link
between the One and the limited (see Met. N 3, 1091a16–17). The One is
equated with the limited here and imposes itself on the unlimited, such that the
One represents the active principle influencing the opposite principle—namely,
the undifferentiated Dyad—the combination of which results in the production
of number and multiplicity or plurality. Given that the two principles are the
first principles, one can also legitimately assert that the unlimited is limited by
the limited. The result of such cooperation is a harmonious cosmos, in which all
elements and principles are proportionately balanced. Only in this regard can the
Pythagoreans admit of endorsing a monistic doctrine; however, the foundation
of such a cosmos is dualistic, for the two coequal principles produce number
from the One’s influence on the Indefinite Dyad, a production which is a com-
posite of the limited and unlimited.3 “For the universe is composed of limited
[pevraV] and unlimited [a[peiron]” (Fr. 6, Philolaus). From this dual principle,
therefore, results the plurality of beings in the cosmos.
Cornford, however, suggests something different. According to Cornford, the
Table of Opposites entails the priority of the One, regarded as the Monad or
as a principle of Unity, from which plurality is derived. Cornford states that in
“this interpretation of the Monad in the tetractys I have taken the view that the
Monad is prior to, and not a resultant or product of, the two opposite principles,
Odd or Limit, and Even or Unlimited.”4 This view, however, is not the view that
will be upheld in this chapter. Rather, I wish to maintain, along with Aristotle,
Aristotle on the Platonic Two-Principles Doctrine 13
28. that the Pythagoreans, notably Philolaus, advanced a two-principles doctrine,
the Limited and the Unlimited, or the One and the Indefinite Dyad, in order to
explain the harmony of the cosmos.
Aristotle considers the Pythagorean principles of Limited, Unity, and Good-
ness and Unlimited, Plurality, and Badness to be strange principles (see Met. A
8, 989b29). Is it the case that the left-hand column is ontologically prior to the
elements of the right-hand column? The scientific aspect of the Pythagorean
doctrine, I argue, maintains an equal priority of both opposite principles. The
dual first principles—the One and the Dyad—are, moreover, attested by Aë-
tius. There appears to be more evidence to assert, contra Cornford’s claim of a
monistic system, that the original Pythagorean philosophy is dualistic, that it is
expressed best by a two-principles doctrine of the Limited and the Unlimited.
These “strange” principles, as Aristotle calls them, are extended throughout the
cosmos, creating order and intelligibility. Aristotle’s reading of the Pythagoreans,
and the Table of Opposites, represents essentially the scientific strand of the
society, as opposed to the religious one.
I begin my discussion of Plato, therefore, with the assumption that this scien-
tific strand of the Pythagorean society influenced Plato and his advancement of
a two-principles doctrine, which is confirmed by Aristotle’s testimony. Even in
the Academy there was great discussion and disagreement about the derivation
of Forms and Ideal Numbers out of the One and the Indefinite Dyad. Unity
remained the primary principle out of which were derived the Ideal Numbers,
whereas the second principle, the Indefinite Dyad, as Aristotle describes it, or
the Great-and-Small (or the Great and the Small), is the boundless material
upon which the One or the Unity impresses itself in order to create order and
finitude. Unity appears to be identified with the Good, within the Table of
Contraries in the Pythagorean society5 (see Phil. 25e–26b). Plato, to be certain,
does not articulate this in his writings, but according to Aristotle, he held it in
his private teachings within the Academy (see Met. A 6, 988a13–15). However,
in the Philebus, as Cleary points out, Unity is associated with the Pythagorean
principle of Limited (pevraV).6
The second Pythagorean principle of the Unlimited or the Indefinite is what
Plato calls the Great-and-Small in order to discuss the two extremes of indefinite
increase and decrease (see Phys. V 12, 220b27–28). The principle is characterized
differently according to the multiple aspects of Being. The Many and the Few
represent the plastic material that generates the integral numbers, by the limit-
ing activity of Unity (see Met. N 1, 1087b16, 987b34–5); as Long and Short,
referring to lines; as Broad and Narrow, referring to planes; and as Deep and
Shallow, referring to solids7 (see Met. A 9, 992a10–15). According to Findlay,8
each of these pairs, representing the Great and the Small, are not reducible to the
14 Chapter 1
29. sensible realm; rather, they belong to the ideal configurations of arithmetic and
geometry. There is one exception, however: the Great-and-Small, according to
Aristotle, operates within the instantial or sensible realm as cwvra or space (see
Phys. IV 2, 209b11–17), as will be discussed below.
Aristotle’s Reading of Plato: The Controversy Surrounding the Esoteric
Teaching of Plato
The question related to the teachings of Plato on critical matters such as the
two-principles doctrine and the proper status of the Ideas and Numbers is this:
How credible is Aristotle’s testimony about Plato’s teaching when certain philo-
sophical accounts of Plato’s teaching found in Aristotle are not found in Plato’s
dialogues? Depending on how this question is answered, either one can discard
Aristotle’s account as that of an untrustworthy witness and align oneself with
“conventional” Platonists, who claim that all of Plato’s teachings are found in his
dialogues, or one can accept Aristotle’s testimony as credible, leaving little doubt
that Plato had an oral teaching, which is not reflected in his writings—a teaching
to which only Plato’s students and close colleagues were privy.9
It should be noted at the outset that the Platonic elements presented by Ar-
istotle were accepted by Plotinus and were instrumental in developing Plotinus’s
original interpretation of Platonic and Aristotelian philosophy. In order to appre-
ciate this very rich synthesis of Plato and Aristotle, it is crucial to discuss Aristo-
tle’s presentation of Plato’s philosophy, giving special importance to the doctrine
of the One and the Indefinite Dyad, the One being the active principle that
imposes a limit or defines the opposite and dual principle, the Indefinite Dyad.10
According to Aristotle, Plato, being influenced by the Pythagoreans, pro-
duced a system that includes the pair of opposite principles—namely, the
One and the Indefinite Dyad—and a triple division of being (the intelligible,
mathematicals,11 and physicals or sensibles).12 This reading can be seen in
two passages of Aristotle’s Metaphysics: firstly, in A 6, 987b14–29, which also
highlights the similarities and differences between Plato and the Pythagoreans,
as Aristotle understands them; and secondly, in Z 2, 1028b18–32 (a passage
to be studied later).
It is clear from Met. A 6, 987b14–35 that, according to Aristotle, Plato
developed the doctrine of the Pythagoreans about the One and the Indefinite
Dyad (or the Great-and-Small, as Plato calls it).13 Once again, the One is the
active principle that imposes a limit (pevraV) on the indefiniteness (a[peiron)
of the Dyad or the opposite principle. The Indefinite Dyad is a dual principle,
given that it can be indefinitely large or small—that is, infinitely extensible or
divisible.14 As a result of such a duality, the Indefinite Dyad exercises an influ-
ence over the entire cosmos.15 The Indefinite Dyad is essentially the limitless or
Aristotle on the Platonic Two-Principles Doctrine 15
30. otherness on which the One acts, and it is also the irrational dimension of the
soul and the “material” substrate, as Aristotle labels it, of the physical cosmos,
likening it to the receptacle of the Timaeus.
Deriving from the interaction of the One and Indefinite Dyad are the Ideal
Numbers,16 out of which are then produced the Forms, which, in turn, func-
tion as the cause of all other beings. Aristotle identifies these two principles as
formal and material causes.17 To be more specific, only by limiting and acting
on the Indefinite Dyad can the One generate the order of natural numbers, as
can be see in a rudimentary form in the Parmenides (143a–144a),18 and of Ideal
Numbers.19 There is clearly a Pythagorean influence on Plato’s account of the
generation of Ideal Numbers, which resemble the tetraktys or the primal num-
bers—one, two, three, and four, all amounting to the number ten, the Decad.
The primal numbers appear to be inherent in the One and are actualized on
the occasion of the One’s limiting of the Indefinite Dyad. In Metaphysics N 7,
1081b10 ff., Aristotle accounts (rather obscurely) for the generation and deriva-
tion of these primal numbers by the Dyad producing the number two when it
doubles the One, and then producing the subsequent numbers through the ad-
dition of two to each number or doubling either the One or itself.20 From this
production of the Ideal Numbers through the Indefinite Dyad, Aristotle tells us
that Plato’s unwritten teachings entail the identification of the Ideal Numbers
with the Forms. (Whether this is an accurate or tendentious account of Aristo-
tle’s presentation of Plato’s unwritten teachings is difficult to assess.)
These two principles, the One and the Indefinite Dyad, account, therefore,
for the plurality and provide a feasible (Platonic) solution and a feasible solu-
tion to the Parmenidean conundrum that plurality or multiplicity cannot exist
or be derived from the One (i.e., Being). The Indefinite Dyad, to be specific,
accounts for plurality. For it is the very condition for the existence of plurality in
the cosmos.21 Aristotle makes this point in Met. N 1088b29–1089a6 but refers
to the Indefinite Dyad here as nonbeing (mh; o[n).22 According to Aristotle, the In-
definite Dyad, or the Great-and-Small, is identified with the material principle,
thereby identifying the One with the formal principle.23 This identification is
clearly contested by Cherniss,24 who is followed by Tarán, whose thought will be
examined below. Several passages either allude to or make explicit reference to
Plato’s unwritten teaching or private lectures.
The first text is De Anima 404b8–30,25 and the second, and undoubtedly the
most controversial, passage fueling this debate is found in Phys. IV 209b11–20:
This is why Plato in the Timaeus says that matter (u{lh) and space (cwvra) are
the same; for the “participant” and space are identical. (It is true, indeed, that
the account he gives there of the “participant” is different from what he says in
16 Chapter 1
31. his so-called unwritten teaching. Nevertheless, he did identify place and space.)
I mention Plato because, while all hold place to be something, he alone tried to
say what it is. In view of the facts we should naturally expect to find difficulty in
determining what place is, if indeed it is one of these two things, matter or form.
They demand a very close scrutiny, especially as it is not easy to recognize them
apart. (Phys. IV, 209b11–20, trans. R. P. Hardie and R. K. Gaye)
Cherniss claims with confidence that Aristotle’s interpretation can be controlled
by juxtaposing Aristotle’s account here with that of the Timaeus itself. This inter-
pretation contains three flaws, which discredits Aristotle’s testimony, according to
Cherniss. First, Aristotle identifies space (in the Timaeus) with position (one of Ar-
istotle’s categories); second, the “participant” in question is said to be identical with
Aristotle’s own “material principle”; and third, he confidently asserts that Plato
has said that matter and space are identical.26 These are sufficient grounds, argues
Cherniss, to reject Aristotle’s testimony as unreliable, for nowhere in the Timaeus
does Plato write any of these three claims. As a result, Aristotle’s reference to the
unwritten teachings of Plato must also be considered to be fallacious.27
C. J. de Vogel, however, rightly refutes Cherniss. She acknowledges that Plato
does not say exactly in the dialogues that matter and space are identical. The ejn-
decovmenon (Tim. 48e–49a) or cwvra is described as “the space in which all things
are formed.”28 Nevertheless, there are similarities between the cwvra and Aris-
totle’s material principle. Space (cwvra), as matter, is immutable, and is a “pre-
existing something, which has, by the very fact of its perfect indetermination, a
vague and shadowy existence.”29 This point of view is corroborated by Findlay.30
Thus, it is clear that in the Timaeus dialogue, Plato does not write that the
cwvra is identical with matter, in the way that Aristotle interprets the cwvra in
light of his own conception of u{lh. The resemblances are clear, however: both
have a permanent character to them. Cherniss’s claim is that the Forms are in-
stantiated in and through space, but space itself is not matter; it shares rather the
indefinite characteristic of matter.
It is reasonable to sympathize with Aristotle’s interpretation, for in the Ti-
maeus, the cwvra is presented with a vague and evanescent existence, which is
only “apprehensible by a kind of bastard reasoning (logismw:/ tini novqw/) by
the aid of non-sensation” (Tim. 52b), and which is said to be identical with mh;
o[n, or rather the Great and the Small, is identified with nonbeing (see Phys. I.9,
192a6–8, which will be discussed below). The cwvra resembles mh; o[n, but not,
of course, in the sense given in the Sophist. In this dialogue, mh; o[n is e{teron
(otherness), which, in turn, is an Idea. However, e{teron in the Timaeus, mak-
ing up one of the aspects of the world-soul (see Timaeus 35a–b), is later in the
dialogue—in the “creation” account of the material or physical world—not to
be regarded as a Form31 (see Tim. 48e).
Aristotle on the Platonic Two-Principles Doctrine 17
32. A second attempt to control Aristotle’s account draws our attention to the
passage found in Phys. I, 192a6–8: “They, on the other hand, identify their Great
and Small alike with what is not being (mh; o[n), and that whether they are taken
together as one or separately.” The mh; o[n is not to be interpreted as absolute
nonbeing. Aristotle states here that Plato identifies the Great-and-Small with
mh; o[n. This interpretation is contested by some. Plato did not intend mh; o[n to
mean absolute nonbeing; rather, he attributes to it a positive significance, char-
acterizing it as e{teron32 (see Soph. 257b–259b). In Physics I, 192a6–8, therefore,
Aristotle identifies the Great and the Small with nonbeing, and, moreover, he
states, in response to Parmenides, that the material principle “was conceived and
explains the absolute genesis of things from nonbeing” (Phys. I, 191b35–192a1).
The reference to Parmenides in this passage attests to Aristotle’s claim that Plato
identifies the Great-and-Small with mh; o[n, an identification said to be made in
the Metaphysics (1088b35–1089a6), where Aristotle argues that the Platonists
were led astray in their pursuit for the ultimate principles of the cosmos by the
mistaken manner in which they framed the problem.33 The reference here is to
the Sophist 237a:
Stranger: The audacity of the statement lies in its implication that “what is not”
has being, for in no other way could a falsehood come to have being. But, my
young friend, when we were of your age the great Parmenides from beginning
to end testified against this, constantly telling us what he also says in his poem,
“Never shall this be proved—that things that are not are, but do thou, in their
inquiry, hold back thy thought from this way.” (Soph. 237a)
Yet, to ensure that there is no misunderstanding, Plato emphatically asserts
that nonbeing does not stand in opposition to Being. Rather, nonbeing is to
be regarded as e{teron34 (see Soph. 257b–259b). Thus, according to Cherniss,
Aristotle has (perhaps intentionally) misunderstood this passage in the Soph-
ist by defining nonbeing as absolute nonbeing, “a notion which Plato expressly
dismisses as meaningless.”35 Again, the controversy surrounds Aristotle’s claim
that the Great-and-Small is identified with the nonbeing (see Soph. 258c and
259a–b). Space, then, and its (alleged) identification with the Great-and-Small
does not make contact with the sensible objects that emerge into being alongside
it. Space is not a Form, nor does it approximate the Forms.36
According to Cherniss, however, this Aristotelian account of Plato is simply
(and grossly) inaccurate, since Aristotle’s account admits of contradictions in
his interpretation of the key points in the dialogues—namely, on the doctrines
of mh; o[n (Sophist), the participant (Timaeus), and the infinite (Philebus).37 If it
were possible to control Aristotle’s account on these key points, then this would
allow for the possibility of controlling his interpretation of the so-called Ideal
18 Chapter 1
33. Numbers and would show that here his claims are inconsistent with one another
and do not reflect any teaching of Plato found in the dialogues. Thus, according
to Cherniss, Aristotle’s (mis)interpretation is motivated by his polemical method.
It is evident, according to Cherniss, that the participant of the Timaeus and the
nonbeing of the Sophist are not identical, and because Aristotle “identifies them
both with ‘the great and small,’ we are in duty bound to suspect the truth of his
general statement in the Metaphysics that this same principle was at once the
substrate of phenomena and of the Ideas.”38 Even Simplicius39 recognizes the
impossibility of Aristotle’s statement that the Great and the Small is identical
with the so-called material principle of the Timaeus.
J. Stenzel, fully aware of Simplicius’s work, however, attempts to save Aristotle
from the accusation of misunderstanding Plato’s teachings.40 Stenzel rightly at-
tempts to systematize Aristotle’s comments about Plato’s oral teachings and the
date we have from the dialogues.41 Stenzel argues that the Indefinite Dyad of the
Great-and-Small is not to be understood as being identified with the cwvra in
the Timaeus, but rather, it is to be regarded as the universal extension, through
which the participant of the Timaeus and “otherness” of the Sophist operate.42
Stenzel, therefore, is suspicious of Simplicius’s report regarding Aristotle’s testi-
mony; Simplicius, it would appear, did not fully grasp the wider implications of
Aristotle’s testimony.43
Returning to Metaphysics N, 1088b29–1089a6, the Platonic emphasis is on
the intermediary status of mathematicals, with the Forms influencing the sen-
sible counterparts. While, on the one hand, mathematicals share the common
feature of the Forms in being immutable, they are, on the other hand, also
akin to the sensibles in that they are plural or multiple.44 If, then, the Forms
were identical with Numbers, they would have to be different in nature from
the mathematical numbers. The concept of the Ideal Number may insinuate
this difference, as is seen in Aristotle’s Metaphysics M 9, 1086a4–5: “For those
who make the objects of mathematics alone exist apart from sensible things,
seeing the difficulty about the Forms and their fictitiousness, abandoned ideal
number and posited mathematical.”45 One unique feature of the Ideal Num-
bers is that each one is individual and unique and is not constituted of unities.
As a result, the Ideal Numbers are “qualitative rather than quantitative and
therefore inaddible.”46
Trendelenburg’s work on the Ideal Numbers of Plato47 initiated the guiding
question of nineteenth- and twentieth-century Platonic scholarship: Are all of
Plato’s teachings contained in his dialogues? At several passages in his corpus,
Aristotle makes reference to the doctrine of the Ideal Numbers and attributes this
doctrine to Plato. There is not a word written in the Platonic dialogues about
this doctrine. This “inconsistency” has caused Trendelenburg and other classical
Aristotle on the Platonic Two-Principles Doctrine 19
34. scholars to infer a Platonic oral teaching, to which Aristotle, as a member of the
Academy, had access and was privy.48
In addition to this discrepancy between the written word of Plato and Aris-
totle’s presentation about Platonism, we are informed by the author of Ep. VII
(allegedly Plato) that Plato expresses a certain disdain—specifically in the case of
these subjects—for the writing of books. Moreover, Plato discredits all reports
by others on this doctrine.
One statement at any rate I can make in regard to all who have written or
who may write with a claim to knowledge of the subjects to which I devote
myself—no matter how they pretend to have acquired it, whether from my
instruction or from others or by their own discovery. Such writers can in my
opinion have no real acquaintance with the subject. I certainly have composed
no work in regard to it, nor shall I ever do so in future, for there is no way of
putting it in words like other studies. Acquaintance with it must come rather
after a long period of attendance on instruction in the subject itself and of
close companionship, when, suddenly, like a blaze kindled by a leaping spark,
it is generated in the soul and at once becomes self-sustaining.49 (Epistle VII,
341c–d, trans. B. Jowett)
Epistle II, 314c, is a parallel passage to this: “I have never written anything about
these things (peri; w|n ejgw; spoudavxw), and why there is not and will not be
any written work of Plato’s own. What are now called his are the work of a
Socrates embellished and modernized”50 (Epistle II, 314c). Finally, we read in
the Phaedrus 274e–275b an echo of Plato’s suspicion of the effectiveness of the
written word, as King Thamous responds to the Egyptian Theuth regarding the
art of writing:
This discovery of yours will create forgetfulness in the learner’s souls, because they
will not use their memories; they will trust to external written characters and not
remember of themselves. The specifics which you have discovered is an aid not
to memory, but to reminiscence, and you give your disciples not truth, but only
the semblance of truth; they will be hearers of many things and will have learned
nothing; they will be tiresome company, having the show of wisdom without the
reality. (Phaedrus 274e–275b, trans. B. Jowett)
If this is an accurate portrayal of Plato’s views about the general function of the
activity of writing, then the authority of the dialogues, as an expression of Plato’s
teachings, is clearly undermined and the credibility of Aristotle’s testimony of
Plato’s teachings is fortified.51
This position, taken by J. Burnet, J. Stenzel, L. Robin, E. Frank, and de Vo-
gel, is reinforced most recently by J. Findlay, K. Gaiser, H.-J. Krämer, T. Szlezák,
20 Chapter 1
35. and J. Dillon. In a lengthy but significant passage that generated an entire tradi-
tion of Platonists of the unwritten doctrines, J. Burnet asserts that Plato
did not choose to commit it [sc. Plato’s central doctrine] to writing, and we are
almost entirely dependent on what Aristotle tells us. . . . One thing, at any rate,
seems clear: Aristotle knows of but one Platonic philosophy, that which identified
the forms with numbers. He never indicates that this system had taken the place of
an earlier Platonism in which the forms were not identified with numbers, or that
he knew of any change or modification introduced into his philosophy by Plato
in his old age. That is only a modern speculation. Aristotle had been a member of
the Academy for the last twenty years of Plato’s life, and nothing of the kind could
have taken place without his knowledge. We may be sure too that, if he had known
of any such change, he would have told us. It is not his way to cover up what he
regards as inconsistencies in his master’s teaching. If the “theory of Numbers” had
been no more than a senile aberration (which appears to be the current view), that
is just the sort of thing Aristotle would have delighted to point out. As it is, his
evidence shows that Plato held this theory from his sixtieth year at least, and prob-
ably earlier. It is certain, then, that Plato identified forms and numbers; but, when
we ask what he meant by this, we get into difficulties at once.52
These difficulties were to produce a radical schism between interpreters of
ancient philosophy, as was seen in the twentieth century. Burnet had few im-
mediate followers, but Stenzel and Robin can be counted as the few who did
find Burnet’s thesis compelling. They wished to attach a greater importance to
Aristotle’s testimonial account of Plato’s teaching, rather than portraying the
Plato of the dialogues alone. Aristotle’s testimony was to complement what was
presented in writing by Plato, in spite of some discrepancies.
This thesis, as can be expected, faced serious opposition by Teichmüller, and
later by P. Shorey, C. Ritter, and H. Cherniss, and most recently by Tarán, as seen
below with regard to the Aristotelian presentation of the identification of the
cwvra with his conception of the material principle. This school asserts unequiv-
ocally that Plato’s true and only teaching is found in his writing, repudiating any
account by Aristotle that Plato had a secret or oral teaching. As a result, Aristo-
tle’s testimony about Plato’s teaching of Ideal Numbers is to be considered utterly
worthless and merely a symptom or expression of his polemical methodology.53
P. Shorey is an even more severe critic of Aristotle. Not only does he discard
Aristotle’s testimony, but he also asserts that Aristotle’s Metaphysics is confusing
and, thus, hardly contains a coherent account of Aristotle’s own philosophy. In his
review of Stenzel’s Zahl und Gestalt, Shorey writes the following: “We do not re-
ally know what Aristotle’s testimony is. The Metaphysics, as it stands, is a hopeless
muddle.”54 H. Cherniss, though aligning himself with Shorey and this tradition,
is a little more sympathetic to Aristotle’s Metaphysics than Shorey; however, he still
Aristotle on the Platonic Two-Principles Doctrine 21
36. regards it as containing grave misinterpretations of Plato’s teachings. Cherniss’s
central claim is that Aristotle, by his polemical method, misinterprets Plato and
criticizes him for a doctrine that Plato never expressed in his writings. As an
advocate of “true Platonism,” Cherniss assumes the responsibility of controlling
Aristotle’s interpretation of Plato; Cherniss hopes to demonstrate the misguided
direction of the various Greek scholars who place their great confidence in Aristo-
tle’s testimony about an unwritten teaching of Plato within the Academy regarding
the prior status of Ideal Numbers before the Forms. Cherniss’s book The Riddle of
the Early Academy is a fierce attack on and “rejection” of Aristotle’s testimony and
of scholars sympathetic with Aristotle’s interpretation.
The thesis that there is an oral teaching of the theory of Ideal Numbers is
said to be found in the Philebus, a thesis which Cherniss firmly denies.55 In the
Philebus, Plato affirms four classes: the limited, the unlimited or infinite, the
mixture of the two, and the cause of the mixture56 (see Phil. 23c–27c). Aristotle
says in Met. A 6, 987b25–27 that the Great-and-Small is equivalent to the un-
limited or infinite. A parallel passage is also found in Phys. I 6, 189b8–16:
All, however, agree in this, that they differentiate their One by means of the
contraries, such as density and rarity and more and less, which may of course be
generalized, as has already been said, into excess and defect. Indeed this doctrine
too (that the One and excess and defect are the principles of things) would appear
to be of old standing, though in different forms; for the early thinkers made the
two the active and the one the passive principle, whereas some of the more recent
maintain the reverse. (Phys. I 6, 189b8–16, trans. R. P. Hardie and R. K. Gaye)
This passage is not primarily about Plato. However, its reference to the physicists
who argued that the ajrchv is to be reduced to one element echoes in part the
Platonic line of thought, according to Aristotle.57
Modern scholars,58 who wish to give credibility to Aristotle’s testimony, claim
to have identified this Aristotelian account in the Philebus, where pevraV is iden-
tified with the One (the formal principle, according to Met. A 6) and a[peiron
with the material principle, the Great and the Small. Once again, Cherniss
dismisses this account, for a[peiron in the Philebus does not signify the material
principle, but rather the multiplicity of phenomena, and the One (pevraV) “is
any given Idea, the Ideas being called monads, and being described as eternally
immutable and unmixed.”59 The third class in this dialogue—namely, the mix-
ture of the two—signifies that pevraV and a[peiron are identified with the Ideas,
which is an utterly misconstrued interpretation, according to Cherniss. Finally,
Cherniss states that there is not one mention of the identification of Ideas and
Numbers in the Philebus, and as a result, Aristotle’s account must be rejected and
branded as a false and inaccurate (and gross) misinterpretation.
22 Chapter 1
37. Cherniss comments about the alleged isomorphism between the limited with
the pevraV:
If this classification in the Philebus corresponds to the theory of principles as
Aristotle reports it, however, the class of the limit must be identifiable with “the
One” and the class of the mixture with the ideas; unfortunately for all attempts to
maintain the correspondence, the class of the mixture in the dialogue is distinctly
and unequivocally equated with the objects and events of the phenomenal world,
the things that are in process of becoming and never really are (Phil. 27a11–12
(also 59a), while the ideas are called “monads” (Phil. 15a–b) and are described as
“eternally immutable and unmixed” (Phil. 59c). Here, then, the classes of the limit
and the unlimited are not ultimate principles from which the ideas are derived,
and no identification of ideas and numbers is involved in this classification, just
as no such theory is implied by Plato’s admonition to observe the exact number
between the unlimited and the One.60 (see Phil. 16d–e)
With this last claim regarding the Philebus, scholars cite this passage as a
reference to the doctrine of the Ideal Numbers.61 However, Cherniss replies that
here, too, “the unlimited” is not a principle of the ideas but the phenomenal mul-
tiplicity, “the One” is any given idea, and the number referred to is not an idea but
just the number of specific ideas which there may be between any more general
idea and the unlimited multiplicity of particulars which reflect or imitate any one
idea in the sensible world.62
This is but one attempt to control Aristotle—to obviate the problem by asserting
that Aristotle fabricated such a doctrine of Ideal Numbers in order to later reject
and discard the Plato of the dialogues.
However, the subsequent testimonies to Aristotle’s presentation of the doctrine
of Ideal Numbers by Hermodorus, Sextus Empiricus, Theophrastus, and Alexan-
der of Aphrodisias confirm that Aristotle’s testimony is legitimate and is to be taken
as a credible source of Plato’s philosophy. In the Republic, 509d–511e, Plato, as
reported by Aristotle in the Metaphysics A 6, 987b14–18, locates the mathematical
objects as alleged intermediates between the Forms and the sensibles, but in this
same passage Aristotle furthermore highlights Plato’s theory of first principles, the
One and the Indefinite Dyad, which are contextualized within the doctrine of
Ideal Numbers. This is confirmed in Hermodorus, the alleged Pythagorean source
of Sextus, Math. X, 363 ff. and in Theophrastus’s Metaphysics 6 B 11–14:
Now Plato in reducing things to the ruling principles might seem to be treating of
the other things in linking them up with the Ideas, and these with the numbers,
and in proceeding from the numbers to the ruling principles, and then, following
Aristotle on the Platonic Two-Principles Doctrine 23
38. the order of generation, down as far as the things we have named; but the others
treat of the ruling principles only.
In this passage, Theophrastus reiterates the Aristotelian testimony of Plato’s
teaching of the priority of Ideal Numbers over the Forms.63 At the summit of
this hierarchical order, Plato positioned the One and the Indefinite Dyad, the
two polar extremes of this hierarchical cosmos, in which are situated the Forms,
the mathematicals, and the sensibles, in descending order. What is most contro-
versial, however, is the status of Ideal Numbers vis-à-vis the Forms. The Ideal
Numbers are not identified with Mathematical objects; they are prior to them.
And while there is a link between the Ideal Numbers and the Forms, they are not
identical, either, nor can each Form be reduced to a particular Ideal Number.64
Aristotle’s passage and other testimonies (i.e., those of Hermodorus and Theo-
phrastus) confirm that the Ideal Numbers may precede the Forms within the
cosmological structure of polar principles, the One and the Indefinite Dyad.65
These themes, as we will see, dominate Neoplatonism and will have direct im-
plications for our continued remarks of Plotinus’s reading and transformation of
Aristotle’s doctrine of nou:V.
Other Sources Supporting Aristotle’s Presentation: Hermodorus,
Sextus, and Alexander of Aphrodisias
Hermodorus of Syracuse (who was a student of Plato) testifies in his book about
Plato (a testimony that is independent of Aristotle’s) to the unwritten teachings
of Plato. A fragment of this book in question was passed down to Simplicius
(Phys. 247[30]–24[15]) from Porphyry, and to Porphyry from Dercyllides (a
middle Platonist). Simplicius prefaces this fragment in which Hermodorus’s
writings are cited:
As Aristotle often mentions that Plato called matter the great-and-small, the
people must know that Porphyry communicates that Dercyllides in the eleventh
book of his “Philosophy of Plato,” where he speaks about matter, cites a passage
of Hermodorus, the disciple of Plato’s, from which it appears that Plato admitted
matter in the sense of the infinite and indeterminate, and that he showed with this
that it belongs to things which admit of a more and less, to which belongs also the
great and small. (Trans. de Vogel)
The fragment of Hermodorus runs as follows:
Plato states that of the things that are (ta onta), some are said to be absolute (kath’
hauta), such as “man” or “horse,” others alio-relative (kath’ hetera), and of these,
some have relation to opposites (enantia), as for instance “good” and “bad,” others
to correlatives (pros ti); and of these, some to definite correlatives, others to indefi-
24 Chapter 1
39. nite ones . . . and those things which are described as being “great” as opposed to
“small” are all characterized by more and less; for it is possible to be greater and
smaller to infinity; and in like manner what is broader and narrower, and heavier
and lighter, and all that can be described in similar terms, will extend to infinity.
Those things, on the other hand, which are described as “equal” and “stable” and
“harmonious” are not characterized by more and less, whereas the opposites to
these have this character. For it is possible for something to be more unequal than
something else unequal, and more mobile than something else mobile, and more
unharmonious than something else unharmonious, so that, in the case of each of
these pairs, all except the unitary element (in the middle) possess moreness and
lessness. So (hoste) such an entity [sc. any given pair of such opposites] may be
described as unstable and shapeless and unbounded and non-existent, by virtue
of negation of existence. Such a thing should not be credited with any originat-
ing principle (arkhē) or essence (ousia), but should be left suspended in a kind of
indistinctness (akristia); for he shows that even as the creative principle (to poioun)
is the cause (aition) in the strict and distinctive sense, so it is also a first principle
(arkhē). Matter (hylē), on the other hand, is not a principle. And this is why it is
said by Plato and his followers (hoi peri Platōna) that there is only a single first
principle.66 (Trans. J. Dillon)
With this text, we are referred to Phil. 24c, where a[peiron is defined as “that
which has a more and less in itself.” Hermodorus, therefore, appears to identify
a[peiron with the Great-and-Small, which Aristotle identifies with the mate-
rial principle. The Great and the Small did, in fact, fall under the subclass of
a[peiron—that is, it remains one characteristic or aspect of a[peiron, as it is
predominantly called by Plato.67 If Plato did identify a[peiron with the Great-
and-Small, then he intended to apply the term to the entirety of the infinite and
indefinite aspect of the cosmos.68 Hermodorus’s testimony is, therefore, a clear
and independent (of Aristotle’s) account of the unwritten doctrines of Plato and
of the identification of a[peiron with the Great-and-Small or matter.69
Cherniss, however, argues that Hermodorus’s testimony about Plato’s doctrine
is only an inference. In the last sentence, beginning with w{ste, the inference is
drawn that, apart from the first principle, “which is equal and unchangeable,”
everything else is unequal, unstable, formless, infinite, and nonbeing, “because
being is denied of it.” According to Cherniss, this claim contradicts Plato’s doc-
trine of nonbeing, considered as Otherness (e{teron) and not absolute nonbeing,
as seen in the Sophist.70 Consequently, continues Cherniss, Hermodorus’s testi-
mony is suspect and cannot be accepted as proof of Plato’s doctrine of a material
substrate.71
The passage in question is Metaphysics M 7, 1081a14: “But if the Ideas are
not numbers, neither can they exist at all. For from what principles will the
Ideas come? It is number that comes from the One and the indefinite dyad, and
Aristotle on the Platonic Two-Principles Doctrine 25
40. the principles or elements are said to be principles and elements of numbers,
and the Ideas cannot be ranked as either prior or posterior to the numbers.”72
It is possible, as Cherniss argues, that Hermodorus is not the author of the
passage cited by Simplicius, but does this disapproval warrant Cherniss’s con-
clusion that the One and the Indefinite Dyad is not a Platonic teaching? The
passage indicates that the two ultimate principles, the One and the Indefinite
Dyad, are derived from the initial triple classification of being, and that this
derivation is a Platonic teaching, whether the passage quoted was written by
Hermodorus or not.
Nevertheless, this testimony of the triple classification of being is confirmed
to be that of Hermodorus by Sextus Empiricus, Adv. Math. X, 4, ¶¶248–82.73
In this text by Sextus, one perceives the same triple division of being as seen in
Hermodorus. The first group entails things that are conceived absolutely and
that are given enough independence such that they can subsist by themselves,
such as man, horse, plant, and so on; for each of these is regarded absolutely and
not in respect of its relation to something else. The second group entails “those
[things] which are regarded in respect of their contrariety one to another, such
as good and evil, just and unjust, advantageous and disadvantageous, holy and
unholy, pious and impious, in motion and at rest, and all other things similar to
these” (¶264). Finally, the third group entails the things conceived as standing
in relation to something else, such as right and left, above and below, double
and half, such as correlatives (see ¶265). Sextus continues to explain that each
class contains a genus. “Above the first class ‘the sons of the Pythagoreans pos-
tulated the one (see ¶270), above the second the equal and unequal . . . (¶271),
above the third they put excess and defect” (¶273). The last one reminds one of
ma:llon kai; h|tton of the Philebus and in the fragment of Hermodorus. All this
finally reduces to two principles in Hermodorus, and now also in Sextus, who
answers in the affirmative the question of whether these genera can be reduced
to others. For, “equality (ijsovthV) is brought under the One (for the One first
of all is equal to itself), and inequality (ajnisovthV) is seen in excess and defect
(uJperoch; kai; e[lleiyisV), things of which the one exceeds and the other is
exceeded being unequal.” Sextus continues, “But both excess and defect are
ranked under the head of the Infinite Dyad, since in fact the primary excess and
defect is in two things, that which exceeds and that which is exceeded. Thus as
the highest principles of all things there have emerged the primary One and the
Indefinite Dyad” (¶275).
With these passages by Sextus Empiricus, we once again revisit one of the
leitmotifs of this book, that of monism and dualism. The discussion in question
here is whether Sextus is presenting a monistic or dualistic paradigm in 248–84.
At 261–62, Sextus tells us that the Indefinite Dyad is generated by the One,
26 Chapter 1
41. leaving aside the One itself to be the sole ajrchv. This is clearly a presentation of
a monistic doctrine. At 276, however, no mention of the derivation of the Indefi-
nite Dyad from the One is made. The ambiguity in 248–84 leads us to consider
two conclusions: that we are to assume either that Sextus is drawing on a single
source when representing the Pythagoreans or Plato and that at 276, the omis-
sion of the Indefinite Dyad as an offspring of the One is due to his assumption
that this theme, from 261–62, need not be reiterated (for the whole reflection
consists of one unit); or that in 263–76, Sextus is presenting a dualistic doctrine
but failed to recognize the discrepancy between the dualistic doctrine in 261–62
and the monistic doctrine in 276.74
Sextus gathers this information and relates it to the Pythagorean doctrine. Yet,
when compared with Aristotle’s testimony in Met. A 6, 987b18–27, in addition
to Hermodorus’s account of what is said in the Philebus, it becomes clear that
this is not a Pythagorean teaching, but rather a Platonic one.75 As mentioned
above, Aristotle emphasizes the similarities and dissimilarities between Plato and
the Pythagoreans.76 They are similar in that both the Pythagoreans and Plato
accepted the One as the ultimate principle, and not as an accident or a property
of another principle, and also that Numbers were the causes of the beings. As
for the dissimilarities, Aristotle highlights three. First, whereas the Pythagoreans
advance a single a[peiron, Plato accepts the dyad of the Great-and-Small. In this
light, if a[peiron, in the sense of the Philebus (i.e., as something admitting of
more or less, etc.), is characterized as an Indefinite Dyad, then we can perceive a
Platonic, and not a Pythagorean, teaching.
In response to Ross’s comment (in Metaphysics II, p. 434), Cherniss counter-
argues by asserting that “there is no mention of this phrase [sc. “the evidence of
Hermodorus” for ascribing to Plato “the indefinite dyad”] in the fragment,”77
which, when literally taken, is confirmed by the lack of such wording in the
dialogues. In general, however, Cherniss’s claim is proven to be questionable.
De Vogel writes, very compellingly, that if Hermodorus finally puts the $En as
the one principle opposite to all that admits of the more and the less, and if in
this last qualification we find back Plato’s own description of what he calls (in
the Philebus) the apeiron, which contains, according to Robin’s right expression,
“all that oscillates between two extremes,” then, without any doubt, we must
acknowledge that by these words a description is given of that principle which,
according to the testimony of Aristotle and his commentator Alexander of Aph-
rodisias, was called by Plato also the ajovristoV duavV.78
This passage by Sextus and the fragment of Hermodorus are treated again by
Wilpert. Wilpert compares the text of Sextus, where the three groups are reduced
to the two highest principles, with the short compendium that is given by Alex-
ander of Aphrodisias, in Metaph, 56 [13–21]:
Aristotle on the Platonic Two-Principles Doctrine 27
42. Again, thinking he was proving that the equal and the unequal are the principles
of all things, both of those that exist independently and their opposites (for he
tried to reduce all things to these as their simplest elements), Plato assigned the
equal to the unit and the unequal to excess and defect; for inequality involves two
things, a great and a small, which are respectively excessive and defective. For this
reason, he also called it the “indefinite dyad,” because neither of the two, neither
that which exceeds nor that which is exceeded, is, of itself, limited, but indefinite
and unlimited. But he said that when the indefinite dyad has been limited by the
One, it becomes the numerical dyad; for this kind of dyad is one in form.79
Wilpert, moreover, concludes that the account of Sextus and Alexander “ap-
parently must be traced back to the same source: Aristotle’s account of Plato’s
lecture peri; tajgaqou:.” Sextus, however, used a source in which this doctrine
was qualified as Pythagorean.80
Conclusion
In this chapter, I discussed the Pythagorean Table of Opposites, the Limited and
Unlimited—that is, the two-principles doctrine of the One and the Indefinite
Dyad. This is the background to Aristotle’s presentation of Plato’s ultimate prin-
ciples, the One and the Great and the Small, which we have generically called
the Indefinite Dyad for the sake of continuity. Aristotle’s presentation of Plato is
most enigmatic in passages such as Met. A 6, 987b14–29 and Phys. IV 209b11–
20, where Aristotle makes explicit reference to an unwritten Platonic doctrine,
relating to Ideal Numbers. The doctrine in and of itself does not centrally con-
cern me in this book. Rather, it is Aristotle’s transformation of this doctrine, in
his noetic theory in Met. L 7–9, that has sustained my interest and discussion.
The two-principles doctrine of the Pythagoreans, Plato (and Speusippus,
as we shall see in the next chapter) provoked a strong response from Aristotle.
The ultimate question behind this doctrine is, “How can plurality be derived
from unity?” This question, however, can make sense only within a dualistic
conception of the cosmos, as Aristotle repeatedly confirms in his exegesis and
presentation of each philosopher’s interpretation of the two-principles doctrine.
The purpose of this chapter, therefore, is to elucidate Aristotle’s philosophical
response to this dualistic doctrine, with the ultimate intention of drawing out
Aristotle’s own philosophical principles.
The doctrine of the One and the Indefinite Dyad was altered by subsequent
generations of Platonists, notably by Speusippus and Xenocrates.81 However,
the dualistic paradigm of the cosmos was always maintained and assumed as an
unquestionable starting point for any Platonic reform. It is Speusippus to whom
I now turn in order to perceive the transformation of the two-principles doc-
28 Chapter 1
43. trine, now classified as the One and plh:qoV. In the next chapter, I shall discuss
how Speusippus’s doctrine fundamentally challenged Aristotle to respond with
his conception of the One and his conception of first principles of the cosmos.
Notes
1. For the Pythagoreans, as Proclus claims, and especially the Neopythagoreans, such
as Alexander Polyhistor, the roles and natures of nou:V and the Indefinite Dyad are closely
related to the doctrine of the tovlma (tolma). Cornford writes that “later mysticism [i.e., the
Neopythagorean philosophers] regards the emergences of the dyad as an act of rebellious
audacity” (F. M. Cornford, “Mysticism and Science in the Pythagorean Tradition,” Clas-
sical Quarterly 17 [1923]: 6, fn.3). See Plotinus, Enn. V.1.1., and Proclus, on Plato, Alib
I. 104E, who explicitly recognizes this use of the tovlma to come from the Pythagoreans
(see Cornford, “Mysticism and Science in the Pythagorean Tradition,” 6, fn.3). The pre-
cise impact that the Neopythagoreans had on Plotinus will be discussed in greater detail
below. Suffice it to say that the doctrine of the tovlma does not seem to be apparent in the
early Pythagorean school, simply because, as I argue, the two-principles doctrine does not
provide enough room for an audacious act of nou:V to repel itself from a single principle,
for the tolmic action presupposes a repulsion from a single principle—namely, the One.
2. F. M. Cornford, Plato and Parmenides: Parmenides’ Way of Truth and Plato’s Par-
menides (London: K. Paul, Trench, Trübner, 1939), 7, says that this table represents “ten
different manifestations of the two primary opposites in various spheres; in each pair
there is a good and an answering evil.”
3. It will be shown later, however, that to interpret the Pythagoreans as monistic
philosophers will have significant ramifications for the development of Plotinus’s “revo-
lutionary” transformation of Greek philosophy.
4. Cornford, “Mysticism and Science in the Pythagorean Tradition,” 3. Here, Corn-
ford adds a significant footnote: “Hence in the above passage from Aristotle (Met. A 5,
986a 19) I translate to; de; e}n eJx ajmfotevrwn einai touvtwn ‘the One consists of both of
these’ (odd and even), not (with Ross, e.g.) ‘the 1 proceeds from both of these.’ . . . It is
true that ‘proceeds’ is appropriate to the following words, to;n d’ajriqmo;n ejk tou: eJnoV,
but in any case the relation here expressed by ejk cannot be the same as in ejx ajmfotevrwn
einai. It may, however, be doubted whether Aristotle himself clearly understood.” He
continues, “In favour of this view the position of the Monad at the head of the tetractys
seems to be decisive. . . . The Pythagorean Monad similarly symbolizes the primal undif-
ferentiated unity, from which the two opposite principles of Limit (physically, light or
fire) and the Unlimited (space, air, ‘void’) must, in some unexplained and inexplicable
way, be derived. The union of the two opposite, as Plato explains in the Philebus, gen-
erates to; miktovn, when ‘the equal and the double and whatsoever puts an end to the
mutual disagreement of the opposite, by introducing symmetry and concord, produce
number’ (25D)” (Cornford, “Mysticism and Science in the Pythagorean Tradition,”
3–4). This interpretation, ultimately, will justify his view that the tovlma was an earlier
Pythagorean doctrine, as Proclus proclaims.
Aristotle on the Platonic Two-Principles Doctrine 29
44. 5. “In short, the principle of Unity seems to have been linked with the principle of
the Good, which appears briefly in the Phaedo and Republic” (J. Cleary, “Aristotle’s Criti-
cism of Plato’s First Principles,” in Pensée de l’‘ Un’ dans l’histoire de la philosophie: Études
en hommage au professeur Werner Beierwaltes, eds. J.-M. Narbonne et A. Reckermann.
(Laval, Canada: Les Presses de l’Université Laval, 2004), 73.
6. See Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 74. See also J. Cleary,
“Aristotle’s Criticism of Plato’s Theory of Form Numbers,” in Platon und Aristoteles—sub
ratione veritatis. Festschrift für Wolfgang Wieland, zum 70. Geburststag. Herausgegeben
von Gregor Damschen, Rainer Enskat und Alejandro G. Vigo (Göttingen: Vandenhoeck
Ruprecht, 2004), 3–30, esp. 12–16.
7. Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 74.
8. J. N. Findlay, Plato: The Written and Unwritten Doctrines (London, New York:
Humanities Press, 1974), 43.
9. For an excellent survey of the research done in the area of Plato’s Unwritten
Teachings, see C. J. de Vogel, Rethinking Plato and Platonism (Leiden: E. J. Brill, 1986),
chapter one, “Plato: The Written and Unwritten Doctrines, Fifty Years of Plato Studies,
1930–1980,” 3–56; see also T. A. Szlezák, Reading Plato, trans. G. Zanker (London and
New York: Routledge, 1999); and especially J. Dillon, The Heirs of Plato, 16–29, and J.
Dillon, The Middle Platonists, 2nd ed. (London and Cornell: Cornell University Press,
1996), 2–11. For a discussion of Plato’s school or Academy, see J. Dillon, “What Hap-
pened to Plato’s Garden?” Hermathena 133 (1983): 51–59; Dillon, The Heirs of Plato,
2–16; and M. Baltes, “Plato’s School, the Academy,” Hermathena 155 (1993): 5–26.
10. See K. Gaiser, Platons ungeschriebene Lehre (Stuttgart: Ernst Klett Verlag, 1963) for
key passages of Aristotle’s presentation of Plato’s philosophy. Gaiser is primarily interested
in Aristotle’s account of Plato. See also H. J. Krämer, Arete bei Platon und Aristoteles (Am-
sterdam: P. Schippers, 1967); see also R. Heinze, Xenokrates. Darstellung der Lehre und
Sammlung der Fragmente (Leipzig; repr. Hildescheim: G. Olms, 1965), 10–47.
11. For an excellent discussion of the Pythagorean influence on Plato’s mathematical
paradigm of the cosmos, see D. H. Fowler, The Mathematics of Plato’s Academy: A New
Reconstruction (Oxford: Clarendon Press, 1987); C. Mugler, Platon et la recherche mathé-
matique de son époque (Strasbourg and Zurich: P. H. Heitz, 1948); and E. Cattanei, Enti
matematici e metafisica: Aristotele, Platone e l’Accademia antica a confronto (Milano: Vita
e pensiero, 1996).
12. See Dillon, The Heirs of Plato, 17–18: “To begin with first principles, it seems
clear that Plato, at least in his later years, had become more and more attracted by the
philosophical possibilities of Pythagoreanism, that is to say, the postulation of a math-
ematical model for the universe. . . . He arrived at a system which involved a pair of
opposed first principles, and a triple division of levels of being. . . . Reflections of these
basic doctrines can be glimpsed in such dialogues of the middle and later periods as the
Republic, Timaeus, Philebus, and Laws, but could not be deduced from the dialogues
alone.” See P. Merlan, “Greek Philosophy from Plato to Plotinus,” in The Cambridge
History of Later Greek and Early Medieval Philosophy (Cambridge: Cambridge University
Press, 1967), 14–132. Merlan also writes on p. 15 that the “interaction of these principles
30 Chapter 1
