Aristotle and Plotinus on the Intellect: Monism and Dualism Revisited 0739167758, 9780739167755

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Aristotle and Plotinus on the Intellect

Aristotle and Plotinus on the Intellect Monism and Dualism Revisited

Mark J. Nyvlt

LEXINGTON BOOKS Lanham • Boulder • New York • Toronto • Plymouth, UK

Published by Lexington Books A wholly owned subsidiary of The Rowman & Littlefield Publishing Group, Inc. 4501 Forbes Boulevard, Suite 200, Lanham, Maryland 20706 www.lexingtonbooks.com Estover Road, Plymouth PL6 7PY, United Kingdom Copyright © 2012 by Lexington Books All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical means, including information storage and retrieval systems, without written permission from the publisher, except by a reviewer who may quote passages in a review. British Library Cataloguing in Publication Information Available Library of Congress Cataloging-in-Publication Data Nyvlt, Mark J., 1969– Aristotle and Plotinus on the intellect : monism and dualism revisited / Mark J. Nyvlt. p. cm. Includes bibliographical references (p. ) and index. ISBN 978-0-7391-6775-5 (cloth : alk. paper) — ISBN 978-0-7391-6776-2 (electronic) 1. Plotinus. 2. Aristotle. 3. Intellect. 4. Monism. 5. Dualism. I. Title. B693.Z7N98 2012 185—dc23 2011031013

™ The paper used in this publication meets the minimum requirements of American

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To my children, Hannah and Gabriel, and to the loving memory of my father, George

Contents



Foreword by Klaus Brinkmann Acknowledgments Introduction

ix xiii 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

vii

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

Foreword Klaus Brinkmann

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 scholarly 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. Pluralism 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 markedly from standard scholarly analyses, is its creative approach. Nyvlt not only compares and contrasts the various formulations of the internal structure of the ix

x      Foreword

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 adumbrated 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 being, 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 selfsufficiently 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 essence. 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 tautological identity or a thinking about nothing would thereby have been avoided. If, however, we accept Plotinus’s critique of Aristotle’s divine nous, the selfreflective 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

Foreword      xi

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-

xii      Foreword

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 University 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

Acknowledgments

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 philosophical 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 University 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 bibliography; 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 insightful 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 Phantasia: 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 Inherxiii

xiv      Acknowledgments

ited Platonic and Aristotelian Two Principles Doctrine,” Journal of Classical Studies 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.

Introduction

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 Neoplatonism 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: Aristotle 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 Neoplatonists 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). 1

2      Introduction

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 Metaphysics, Aristotle opposes the Neopythagorean and Platonic doctrine of the separability of Forms and Numbers from their material counterparts, a doctrine 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 confronting Plotinus. I wish to argue that Aristotle’s noetic doctrine provides an adequate 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 provide 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 cosmologies. 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-indiversity is preserved.

Introduction      3

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 twoprinciples 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 writings 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 contain 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 intuitionist 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 Speusippus, with the intention of determining the exact teaching, if possible, of Speusippus 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 examine 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

4      Introduction

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 Aristotle’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, subsequently, 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 Aristotle’s alternative solution to Plato’s two-principles doctrine, as we read in Metaphysics 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 employed by Aristotle in his account of nou:V. In chapter 5, I examine closely Aristotle’s doctrine of the absolute simplicity and priority of nou:V as presented in Metaphysics 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

Introduction      5

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 essentially 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 transforming the two-principles doctrine of Plato and Aristotle and affirming his strict monistic 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 separation or gap between the first principle and its effects. Therefore, Plotinus’s metaphysics 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 illustrated 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

6      Introduction

make a better comparison between it and inchoate nou:V, which is also ambiguous, 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 indicates 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 transformation 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 multiple 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 ultimate 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

Introduction      7

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 acceptance of Aristotle’s noetic doctrine in Met. L 7 and 9. The nature of this multiplicity 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 rendering 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 independence 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 because 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 emphasizes 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 astronomical 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

8      Introduction

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 Aphrodisias, 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 Proclus’s Elements of Theology and Commentary on the Parmenides.

Part I

c h a pte r one

Aristotle on the Platonic Two-Principles Doctrine The One and the Indefinite Dyad

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 twoprinciples doctrine. In order to proceed in this analysis, I will discuss the controversy 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 principles 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 Hellenic 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 perceived 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 question 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 11

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(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 Table 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 interpretation 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 differences 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 Pythagoreans, regarding the harmony of the cosmos, mathematics, musical ratios, and so forth. However, for the purposes of this chapter, I will concentrate solely

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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 composite 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,

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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 Goodness 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 Aëtius. 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 scientific 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 limiting 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

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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 philosophical 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 Aristotle were accepted by Plotinus and were instrumental in developing Plotinus’s original interpretation of Platonic and Aristotelian philosophy. In order to appreciate this very rich synthesis of Plato and Aristotle, it is crucial to discuss Aristotle’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, produced 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 influence over the entire cosmos.15 The Indefinite Dyad is essentially the limitless or

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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, function 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 numbers—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 derivation of these primal numbers by the Dyad producing the number two when it doubles the One, and then producing the subsequent numbers through the addition 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 Aristotle’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 solution 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 Indefinite 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

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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 interpretation contains three flaws, which discredits Aristotle’s testimony, according to Cherniss. First, Aristotle identifies space (in the Timaeus) with position (one of Aristotle’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 ejndecovmenon (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 Aristotle’s material principle. Space (cwvra), as matter, is immutable, and is a “preexisting 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 instantiated 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 Timaeus, 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, making 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).

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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, characterizing 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 Sophist 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

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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 attempts 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 testimony; 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 sensible 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 Numbers 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

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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 Aristotle’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 Vogel, is reinforced most recently by J. Findlay, K. Gaiser, H.-J. Krämer, T. Szlezák,

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and J. Dillon. In a lengthy but significant passage that generated an entire tradition 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 probably 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 immediate 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 unequivocally 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, Aristotle’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 really 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

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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 Aristotle’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 unlimited 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 identified 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 mixture 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.

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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 multiplicity, “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 Alexander 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

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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 controversial, 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 Theophrastus) 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 implications 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-

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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 originating 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 material 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 Greatand-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 doctrine of nonbeing, considered as Otherness (e{teron) and not absolute nonbeing, as seen in the Sophist.70 Consequently, continues Cherniss, Hermodorus’s testimony 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

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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 conclusion 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 postulated 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,

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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 Indefinite 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 omission 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 counterargues 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 Aphrodisias, 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 Alexander of Aphrodisias, in Metaph, 56 [13–21]:

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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 “apparently 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 principles, 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 concern 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-

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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,” Classical 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 precise 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 Parmenides (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 “revolutionary” transformation of Greek philosophy.   4.  Cornford, “Mysticism and Science in the Pythagorean Tradition,” 3. Here, Cornford adds a significant footnote: “Hence in the above passage from Aristotle (Met. A 5, 986a 19) I translate to; de; e}n eJx ajmfotevrwn ei\nai 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 ei\nai. 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 undifferentiated 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, generates 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.

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  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 Criticism 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 Happened 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 (Amsterdam: 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 mathématique 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 mathematical 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

Aristotle on the Platonic Two-Principles Doctrine      31

‘produces’ the ideas (themselves in some way designated as numbers), and, as the ideas are the causes of everything else, the two principles become universal causes.” See also P. Merlan, From Platonism to Neoplatonism, 2nd ed. (The Hague: Martinus Nijhoff, 1960). 13.  For an interesting discussion of Aristotle’s presentation and interpretation of Plato’s Great and the Small and the mathematical background to this doctrine, see K. Sayre, Plato’s Late Ontology (Princeton, NJ: Princeton University Press, c1983), 95–112. 14.  See Dillon, The Heirs of Plato, 18. 15.  See Dillon, The Heirs of Plato, 18. See also H.-J. Krämer, Arete bei Platon und Aristoteles. Zum Wesen und zur Geschichte der platonischen Ontologie (Amsterdam: P. Schippers, 1964). 16.  See J. Cleary, Aristotle and Mathematics: Aporetic Method in Cosmology and Metaphysics (Leiden; New York; Köln: E. J. Brill, 1995), 346–65. 17.  See parallel passages: Met. A 6, 988a7–15; L 10, 1075a35–36; N 4, 1091b32. 18.  See R. Turnbull, The Parmenides and Plato’s Late Philosophy (Toronto: Toronto University Press, 1988). 19.  See Dillon, The Heirs of Plato, 19, fn.37. 20.  See Dillon, The Heirs of Plato, 19. 21.  As Merlan says, “without the assumption of the Indefinite Dyad as one of the supreme principles, all being, they thought, would be frozen in the Parmenidean One” (Merlan, “Greek Philosophy from Plato to Plotinus,” 16). 22.  For further reading of Aristotle’s discussion of the first principles in Metaphysics M and N, see I. Mueller, “Aristotle’s Approach to the Problem of Principles in Metaphysics M and N,” in Mathematics and Metaphysics in Aristotele/Mathematik und Metaphysik bei Aristoteles: Akten des X. Symposium Aristotelicum, Sigriswil, 6.–12. September 1984 (Bern, Stuttgart: Berlag Paul Haupt, 1987), 241–59, especially 246–49. 23.  This will serve as the background of Plotinus’s theory of intelligible matter, the intelligible substrate for the plurality of Forms within nou:V. 24.  K. Sayre captures Cherniss’s central criticism against Aristotle very well: “The upshot of Cherniss’ argument is that Aristotle’s claims about Platonic doctrine are not based on oral teachings at all, but instead are based upon the written dialogues which Aristotle frequently misinterprets” (Sayre, Plato’s Late Ontology, 79). According to Cherniss, whom Sayre cites, the idea of an esoteric or unwritten doctrine is nothing but a “hypothesis set up to save the phenomena of Aristotle’s testimony,” which “has come to be treated as if it were itself part of the phenomena to be saved” (Cherniss, The Riddle of the Early Academy [New York: Russell & Russell, 1962], 29). Essentially, Cherniss concludes, as Sayre writes, that neither Aristotle nor any other member of the Academy “had resources for the interpretation of Plato’s thought beyond the dialogues themselves upon which we also rely” (See Cherniss, The Riddle of the Early Academy, 82). The single reference to “unwritten teachings” at Physics 209b15 is to be read instead as referring either to the lecture on the Good itself or just to opinions Plato may have expressed in conversation with his associates. (See Cherniss, The Riddle of the Early Academy, 15; and Sayre, Plato’s Late Ontology, 80.) Cherniss’s and Tarán’s reading of Plato and Aristotle will not, of course, go unchallenged. In fact, Dillon calls Cherniss’s and especially Tarán’s reading of Plato

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and of Speusippus “legalistic” (Dillon, “Speusippus in Iamblichus,” Phronesis 24 [1984]: 326). See E. Cattanei, Enti matematici e metafisica: Aristotele, Platone e l’Accademia antica a confronto, 130–41, esp. 130–31, for a counterargument to Cherniss’s thesis. 25.  See H. D. Saffrey, Le PERI FILOSOFIAS d’Aristote et la Théorie Platonicienne des Idées Nombres (Leiden: E. J. Brill, 1971); see also Cherniss’s compte rendu appended to Saffrey’s book, 71–89. 26.  See H. Cherniss, The Riddle of the Early Academy, 18. The parallel passage is Met. A 6, 988a11–14, where Aristotle indicates “an underlying matter of which the Forms are predicated in the case of sensible things, and Unity in the case of the Forms, [it is evident] that this is a dyad, the Great and the Small” (trans. Sayre). Prior to the Philebus, we do not perceive any reference to the identification of the Great and the Small and the underlying matter. K. Sayre is more moderate in his criticism of Aristotle than Cherniss. According to Sayre, “Aristotle’s conviction that this principle [sc. the Great and the Small] played the role of matter for Plato may be behind his remark at Physics 209b35–210a2 that the Great and (the) Small is the space of the Timaeus, which (he says) Plato there called u{lh. Among several anomalies associated with this remark is that the Timaeus does not contain the term u{lh in the sense of matter at all (compare 696a6). It is of course possible that Aristotle saw an earlier (or later) version of the Timaeus than the one we have which did employ the term in that sense” (Sayre, Plato’s Late Ontology, 285, fn.34). 27.  Related to this passage is Met. A.6, where Aristotle states that the Great-and-Small (the Indefinite Dyad) is identical to the material principle and that the One is identical to substance, or the formal principle. While Sayre sympathizes in part with Cherniss’s overall critique, he, nevertheless, prudently abstains from adhering to Cherniss’s exaggerated view of Aristotle’s testimony. (See Sayre, Plato’s Late Ontology, 81.) I, however, wish to argue that there is sufficient evidence to support the unwritten doctrine thesis. Sayre, in all fairness, admirably attempts to find a middle ground between Cherniss and his reconstructionist adversaries. “A middle ground is accessible by rejecting this common supposition, and in effect denying that there is any major discrepancy between written and alleged ‘unwritten teachings’ that requires explanation. For this middle course to be defensible, certainly, we must be able to find passages in the later dialogues that lend themselves to interpretation in terms of Aristotle’s description” (Sayre, Plato’s Late Ontology, 82). The later dialogue that Sayre has in mind is clearly the Philebus, which he proceeds to study on pp. 118–86. 28.  C. J. de Vogel, “Problems Concerning Later Platonism I,” Mnemosyne 4 (1949): 203, referring to the Timaeus 50b–d. 29.  de Vogel, “Problems I,” 204. 30.  See Findlay, Plato, 466 ff., on this particular topic, and for Findlay’s central criticism of Cherniss’s thesis. 31.  In Timaeus 48e ff., we are introduced to the receptacle. In this light, one cannot agree with Cherniss that Aristotle is an untrustworthy source. The conclusion we come to is this, as de Vogel articulates: “That it would be neither reasonable to reject this testimony nor to accept it without any critical reserve. As to the agrapha, finally, it has

Aristotle on the Platonic Two-Principles Doctrine      33

no other sense than that Plato in his unwritten teaching used to denote his decovmenon (Aristotle says, less correctly, his metalhptikovn) with another term (sc. the great-andsmall)” (de Vogel, “Problems I,” 205). 32.  See de Vogel, “Problems I,” 202. She moreover comments, “The mh; o[n is in the Sophist an Idea, which pervades all the Ideas, including that of being, by which it is pervaded in turn” (Soph. 258c, 259a–b). For a very interesting discussion of the nature of nonbeing in the Sophist, see S. Rosen, Plato’s Sophist (New Haven, CT: Yale University Press, 1983), 269–90, esp. 289–90. 33.  See Cherniss, Riddle, 19. 34.  The theme of Otherness will occupy our study of Plotinus’s doctrine of the One and the One’s relation with nou:V. 35.  Cherniss, Riddle, 19; see Sophist, 238c and 258e: “Stranger: You see the inference then. One cannot legitimately utter the words or speak or think of that which just simply is not; it is unthinkable, not to be spoken of or uttered or expressed”; 258e: “Stranger: Then let no one say that it is contrary of the existent what we mean by ‘what is not,’ when we make bold to say that ‘what is not’ exists. So far as any contrary of the existent is concerned, we have long ago said good-by to the question whether there is such a thing or not and whether any account can be given of it or none whatsoever.” 36.  “Moreover it is utterly impossible that Plato admitted of a ‘material principle’ with regard to the Ideas, for this would destroy the very character of Idea itself ” (de Vogel, “Problems I,” 203). The theme of material principle in Aristotle is important, as is its rapport with space and with the One and Indefinite Dyad. It will be seen in the subsequent chapters how Aristotle’s doctrine of intelligible matter profoundly influenced Plotinus’s conception of the intelligible substrate within nou:V. (See also Sayre, Plato’s Late Ontology, 92–93, and 285, fns. 34–37; and Z. Bechler, Aristotle’s Theory of Actuality [Albany, NY: SUNY Press, 1995], 177–79). 37.  See de Vogel, “Problems I,” 203. 38.  Cherniss, Riddle, 20. See Aristotle, Metaphysics A 6, 988a11–14. 39.  In Aristotelis Physica Commentaria (H. Diels, ed., Commentaria in Aristotelem Graeca, Vols. IX–X, Berlin, 1882–1895), 151, 12–19. 40.  K. Sayre also moves in this direction of saving Aristotle’s testimony of Plato’s doctrines. See Sayre, Plato’s Late Ontology, 76–77. 41.  J. Stenzel, Zahl und Gestalt bei Platon und Aristoteles, 2nd ed. (Darmstadt: Wissenschaftlich Buchgesellschaft, 1959), 45–46. 42.  See Stenzel, Zahl und Gestalt bei Platon und Aristoteles, 86–89. 43.  Stenzel, Zahl und Gestalt bei Platon und Aristoteles, 70. 44.  Plotinus, as will be discussed below, is fully aware of the perennial problem of the derivation of plurality or multiplicity and will propose an ingenious solution, using the central tenets of Pythagorean, Platonic, Aristotelian, and Neopythagorean metaphysics, which will allow Plotinus to transform the dualistic doctrine into a radically monistic one (see Enn. VI 3 [44] 3). 45.  See Met. A 8, 990a19–32; M 6, 1080b22; M 7, 1081a18–21; M 8, 1083a30–31; M 8, 1083b3; N 2, 1088b34; N 3, 1090b33–1091a5; N 3, 1099b33; N 4: All of chapter.

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46.  Merlan, “Greek Philosophy from Plato to Plotinus,” 16. 47.  F. A. Trendelenburg, Platonis De Ideis et Numeris Doctrina ex Aristotele Illustrata (Lipsiae: Vogelli, 1826). 48.  Aristoxenus—a member of the Lyceum—reports, in the second book of his Harmonics, Aristotle’s account of Plato’s presentation on the Good. Many commoners attended, but they were disappointed by the esoteric content of the lecture, dealing with topics of mathematics, numbers, geometry and magnitude, astronomy, and, finally, with an account of the Good as the One. See Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 72–73; Cherniss, Riddle, 1–2. With respect to the nature of the Ideal Numbers— as best as it can be represented—see G. Reale, Toward a New Interpretation of Plato, trans. from tenth edition by J. R. Catan and R. Davies (Washington, DC: Catholic University of America Press), chapter 8, “The Ideal Numbers and the Ideas, Mathematical Numbers as Intermediates, and the Hierarchical Structure of Reality.” For an opposing view, see Cherniss, Riddle, 1–30, and also L. Tarán, Speusippus of Athens: A Critical Study with a Collection of the Related Texts and Commentary (Leiden: E. J. Brill, 1981), 12ff. 49.  Plato, Plato: Collected Dialogues, ed. E. Hamilton and H. Cairns (New York: Pantheon Books), 1963, 1588–89, Letters VII, trans. L. A. Post, 341c–d. On the topic of the authenticity of Plato’s Letter VII, see L. Edelstein, Plato’s Seventh Letter (Leiden: E. J. Brill, 1966), who doubts that Plato was the author; A. E. Taylor, Plato, 6th edition (London: Methuen, 1955), p. 295, who argues that Plato was the authentic author of this Epistle; B. Stenzel, “Is Plato’s Seventh Epistle Spurious?,” A.J.P. 74 (1953), 394; and J. Harward. “The Seventh and Eighth Platonic Epistles,” Classical Quarterly 22 (1928), 143–54, where it is reaffirmed that Plato is the genuine author of these Epistles. 50.  Plato, Letters II, trans. L. A. Post, 314c. 51.  There are, of course, other ways of interpreting Plato’s attitude to the written works. See Platonic Writings, Platonic Readings, ed. C. L. Griswold (New York: Routledge, 1988). It is beyond the scope of this project, however, to discuss this alternative reading of Plato’s works. 52.  J. Burnet, Greek Philosophy: Thales to Plato (New York: St. Martin’s Press, 1968), 312, 313–14. 53.  See Cherniss, Riddle, 29–30. 54.  See also Cherniss, in his foreword to Aristotle’s Criticism of Plato and the Academy, I (New York: Russell and Russell, 1962), xxi. 55.  Cherniss, Riddle, 17. 56.  “To this, consequently, appeal all those critics who desire to find in the dialogues some corroboration of Aristotle’s report that the ideas were identified with numbers and derived from ‘the One’ and ‘the great and small’ as ultimate principles,” says Cherniss. Cherniss, Riddle, 18, referring to Stenzel, Zahl und Gestalt bei Platon und Aristoteles, iii–iv, 8–69; M. Gentile, La dottrina platonica delle idee numeri e Aristotele (Pisa: Pacini-Mariotti 1930), 39–41; J. Chevalier, La notion du nécessaire chez Aristote et chez ses prédécesseurs, particulièrement chez Platon (Paris: F. alcan, 1915), 88–90; and L. Robin, La Théorie Platonicienne des Idées et des Nombres d’Après Aristote: Étude Historique et Critique (Paris: Presses Universitaires de France), 154–56.

Aristotle on the Platonic Two-Principles Doctrine      35

57.  de Vogel aptly summarizes this issue: Thus, in Aristotle’s time, there is “a doctrine which makes the One and excess and defect the principles of being; namely, in this way that the One is the active (or formal) principle, the other passive or material principle. Recognize here two ultimate principles of Plato’s later doctrine: the One or péras on the one hand, and on the other the Infinite which is called the Great and Small or also the Infinite Dyad. Aristotle finds this latter principle foreshadowed in the mano;n kai; puknovn of the older physicists. This thought is also expressed in Meta A. 9, 992b1–7. This confirms that Aristotle is greatly influenced by this two-principles doctrine of the One and the Indefinite Dyad. One can also see this in his interpretation of Anaxagoras in Meta I 8, 989a30–b21. . . . From this it follows, then, that he must say that the principles are the One (for this is simple and unmixed) and the Other, which is of such a nature as we [oi|on tivqemen we in the school of Plato] suppose the indefinite to be before it is defined and partakes of the same form. Therefore, while expressing himself neither rightly nor clearly, he means something like what (the later thinkers say) and what is now more clearly seen to be the case. . . . Therefore, one must infer that Sextus with his uJperoch; kai; e[lleiyiV, like Hermodorus with his ma:llon kai; h{tton, did speak indeed Platonic language, and that the term qavteron as well as that of a[peiron could be used to indicate the ‘other’ principle which, according to Plato’s later doctrine, stands opposite to the One” (de Vogel, “Problems I,” 216). See also Robin, La Théorie Platonicienne des Idées et des Nombres d’Après Aristote, 645 ff. This, furthermore, attests to the fact that he finally accepted the two-principles doctrine, all other things being mixed with one another and nou:V only being unmixed and pure. 58.  See Sayre, Plato’s Late Ontology; Turnbull, The Parmenides and Plato’s Late Philosophy; and Dillon, The Heirs of Plato. 59.  de Vogel, “Problems I,” 202. See also an exceptional article by de Vogel. “La théorie de l’apeiron chez Platon et dans la tradition platonicienne,” Revue Philosophique de la France et l’Étranger 149 (1959), 21–39. 60.  Cherniss, Riddle, 18. 61.  See Dillon, The Heirs of Plato, 16–21; P. Natorp, Platos Ideenlehre. Eine Einführung in den Idealismus, 2nd ed. (Leipzig: Dürr, 1921), p. 434; J. Chevalier. La Notion du nécessaire chez Aristote et chez ses prédécesseurs, particulièrement chez Platon, p. 94. 62.  Cherniss, Riddle, p. 18. 63.  See Dillon, The Heirs of Plato, p. 21, who corroborates this view. See also M. van Raalte, Theophrastus Metaphysics (Leiden: Brill, 1993), 271–75. 64.  See G. Reale, A History of Ancient Philosophy, vol. II, ed. and trans. J. R. Catan (Albany: State University of New York Press, 1987), 74; see also M. Isnardi Parente, “Théophraste, Metaphysica 6a23 ss.,” Phronesis 16 (1971b): 49–64. 65.  See C. J. de Vogel, “On the Neoplatonic Character of Platonism and the Platonic Character of Neoplatonism,” Mind 62 (1953): 52–54. 66.  See L. Robin, La Théorie Platonicienne, 645: “En outre d’Ar. de Théoph., d’Alex. et de Simplic., que nous avons cités plus haut, Zeller mentionnne un intéressant témoignage de Hermodore, disciple immédiat de Platon, dans lequel nous retrouvons, plus explicitement exposée, la division qu’Hermod. attribue à Platon. Mais elle y est rapportée

36      Chapter 1

aux Pythagor., du moins à des Pythagor. qui faisaient de la dua;V ajovristoV un genre comprenant comme espèce subordonnées l’Excès et le Défaut, puis l’Inégal.” We shall discuss the rapport between Sextus Empiricus ad Hermodorus below (Robin, La Théorie Platonicienne, 645–47; see fn.15 for a discussion on Sextus Empiricus, Adv. Math. X, 263 sqq, and Adv. Phys. II, 529, 11 sqq Bekk). 67.  de Vogel rightly refutes Cherniss’s thesis. See de Vogel, “Problems I,” 208, fn.28. See also Cherniss, Criticism, 169 ff and fn.96. 68.  See Dillon, The Heirs of Plato, 202. 69.  Moreover, while Hermodorus identifies the a[peiron with the Great-and-Small or with matter, he also states that matter is not a principle equal to the One, due to the fact that matter is not active or creative. This claim lends itself to a monistic reading of Plato’s metaphysics, which would appear to be at odds with Speusippus’s account of the derivation of the various levels of being through the One’s accession of the Indefinite Dyad. (See Dillon, The Heirs of Plato, 202–3.) 70.  See Sophist, 258b. 71.  Cherniss, Riddle, p. 13, to which de Vogel rightly responds: “Therefore,” continues de Vogel with her summary of Cherniss’s argument, “if Hermodorus says in this passage that it is not fitting to such like things (tw:/ toiouvtw/) to participate of being, he is in flat contradiction with Plato’s own words, and cannot be taken as evidence for Plato’s doctrine of the ‘material substrate’” (de Vogel, “Problems I,” 209). See Cherniss’s response: Cherniss, Criticism, 171; see also 284 ff., fn.192. 72.  See Ross’s illuminating commentary, p. 434, Met., II, 1081a14. Moreover, Ross, p. 434, Met., II, comments on line 1081a1. Pp. 434–45, on passage 14, makes it clear that Indefinite Dyad (and even if distinguished from Great-and-Small) means the same thing—the material principle. See also Findlay, Plato, 445–47: “Aristotle is saying that, on Plato’s theory of Principles, the Eide must be Numbers of some sort, and that, as being Mathematical Numbers would violate their uniqueness, they must be Eidetic Numbers” (p. 446); see also Dillon, The Heirs of Plato, 198–204. 73.  Sextus Empiricus, Adv. Math, trans. R. G. Bury, Vol. III (Cambridge, Mass.: Loeb Classical Library, 1983–1990), 331–61. See Dillon, The Heirs of Plato, 203–4, for a brief but helpful account of these passages by Sextus; M. Isnardi Parente, “Speusippo in Sesto Empirico, Adv. Math, VII 45–146,” La Parola del Passato 24 (1969), 203–14; Krämer, Arete bei Platon und Aristoteles, 284–87; and see A. Metry, Speusippos: Zahl—Erkenntnis—Sein, 59–60, and fns.63–66. 74.  Rist provides merely one solution to this conundrum: “He is talking here of an upward path of investigation leading toward first principles (cf. Phaedo 109D, Phaedrus 249C and Ennead 6.7.9.45 for ajnevkuyani), and, once he had reached the stage of the two ajrcaiv, he may have thought that he was now back to the position he had described in 261 and that there was therefore no need for further elaboration on the theme of the ultimate derivation of the Dyad from Unity. (Cf. Syrianus, in Met. 925B27ff, where an ultimate unity is attributed to Archaenetus and Philolaus)” (J. Rist, “Monism: Plotinus and Some Predecessors,” Harvard Studies in Classical Philology 69 [1965]: 336, including fn.24). The discussion about the Hellenistic interpretation of Platonic first principle(s)

Aristotle on the Platonic Two-Principles Doctrine      37

will be critical in our study of the transition from a dualistic to a monistic doctrine in the Neopythagoreans, notably in the writings of Alexander Polyhistor, with his emphasis on the doctrine of the tovlma, and, ultimately, on Plotinus—a transition that will have great implications for the reform of the Aristotelian doctrine of the simplicity of nou:V. 75.  See de Vogel, “Problems I,” 211. 76.  See also Sayre, Plato’s Late Ontology, 89–91. 77.  Cherniss, Criticism, 171, end of fn.96. 78.  de Vogel, “Problems I,” 212. See also Alexander of Aphrodisias, who likewise attributes this doctrine to Plato, Metaph, 56 H, 1.18–20; Simplic Phys. 151.6D; and P. Merlan in Philologus 89 (1934), who argues that Sextus in Adv. Math X echoes an Academic doctrine, rather than a Pythagorean one, and this is confirmed in the writings of Hermodorus (P. Merlan, “Beiträge zur Geschichte des antiken Platonismus, I., Zur Erklärung der dem Aristoteles zugeschriebene Kategorienschrift,” Philologus 84 [1934]: 35–53); see also Dillon, The Heirs of Plato. 79.  Alexander of Aphrodisias, in Metaph. (Hayduck) 56[13–21]; esp. 1.16–17. 80.  Wilpert also refers to Divisiones Aristoteleae. See especially Florilegium of Stobaeus (preserved by Diogenes Laertius). 81.  On Xenocrates’ rich development of the One and the Indefinite Dyad, see the excellent section of Dillon, The Heirs of Plato, 89–155, esp. 98–136; see also M. Baltes, “Zur Theologie des Xenokrates,” in Knowledge of God in the Graeco-Roman World, eds. R. van den Broek, T. Baarda, and J. Mansfeld (Leiden: Brill, 1988); Baltes, “Plato’s School, the Academy,” 5–26; H. J. Krämer, Der Ursprung der Geistmetaphysik. Untersuchungen zur Geschichte des Platonismus zwischen Platon und Plotin (Amsterdam: P. Schippers, 1964) (see chapter 1, “Die Nus-Monas als Weltmodel”); and J. Dillon, “‘Xenocrates’ Metaphysics: Fr. 15 (Heinze) Re-examined,” Ancient Philosophy 5 (1986): 47–52.

c h a pte r t w o

Aristotle and Speusippus

Introduction The two-principles doctrine was transformed significantly by Speusippus, Plato’s pupil and nephew. A full exposé of Speusippus’s philosophical doctrine is, undoubtedly, difficult, if not impossible.1 Yet the fragments remaining from his work are largely contained in Aristotle’s Metaphysics, and (possibly) in Iamblichus’s De communi mathematica scientia (Universal Math.), chapter IV. The purpose of this chapter is not to provide an exhaustive and systematic account of Speusippus’s doctrines, but rather to explore and focus on Aristotle’s interpretation and critique (legitimate or illegitimate) of Speusippus’s philosophical position. This critique will furnish us with the conceptual framework in which to understand Aristotle’s conception of the One and his contribution to the twoprinciples or dualistic doctrine. This chapter will be divided into two sections: 1) Metaphysics Z 2, and 2) Metaphysics N 4–5 and L 7. Each section will, inevitably, cross-reference other passages throughout the Aristotelian corpus.

Metaphysics Z 2: Degrees of Speusippus’s Cosmos In Metaphysics Z 2, 1028b8–14, Aristotle articulates several candidates that may be called substance (oujsiva). Aristotle favors perceptible entities, such as “animals, plants, their parts” (1028b8–13), and so on, but he arrives at this conclusion through the (Aristotelian kind of ) dialectic, by listing the various reputable opinions and then (satisfactorily) classifying these positions accordingly. Aristotle challenges the Pythagoreans, who claim that the “limits of a body, e.g., surface, 39

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line, point, and unit, are thought by some to be substances, and more so than the body and the solid” (b15–18). This is a claim Speusippus would have, undoubtedly, reaffirmed (see Met. Z 2, 1028b15–20). In Met. Z 2, 1028b18–27, Aristotle continues to challenge Plato and then Speusippus. Aristotle levels several criticisms at what he takes to be Speusippus’s metaphysical doctrine. In Met. Z 2, 1028b18–27, Aristotle makes reference to the degrees of substance in Speusippus’s cosmology. There is controversy surrounding the specific number of levels in his cosmology.2 A central passage in this text, which will be discussed in detail below, is at line b22, where Aristotle states, “and Speusippus, who, starting from the one . . .” ajpo; tou: eJno;V ajrxamenoV.3 The question related to this passage is, “What is the status of the One?” As mentioned and confirmed in this passage, Aristotle claims that Plato advances three levels of reality or substance, whereas Speusippus advanced many more. Aristotle has reported that Speusippus rejected Plato’s theories of Forms and Ideal Numbers. Limiting the Platonic intelligible world to Plato’s lowest common denominator—namely, mathematicals—Speusippus approximates to the Pythagorean standpoint of the ajrchv of the cosmos (see Met. M 8, 1083a20ff; Frags. 42d Lang). Aristotle, furthermore, argues that Speusippus arrived at this position because he was unable to overcome the Platonic aporia inherent in the theory of Forms (see Met. M 9, 1086a2ff ). The mathematical and geometrical entities, which in the Platonic schema are considered to be the intermediaries between the Forms and the sensibles, are the sole intelligibles, now that the Forms and the Ideal Numbers have been rejected. Moreover, these entities remain separate from their sensible counterparts (see Met. L 1, 1069a30ff ). This separation is the lasting Platonic element retained in Speusippus, and it is enough to distinguish Speusippus from the Pythagoreans, who did not uphold any such separation.4 Speusippus’s grades of reality also reveal an alteration to Plato’s general philosophy, an alteration that Aristotle criticizes again. According to Speusippus, there are two principles governing each level of substance (see Met. Z 2, 1028b21–27). The problem Aristotle sees with this is quite clear: the episodic character of this cosmos reflects a poorly governed cosmos. It is imperative, therefore, according to Aristotle, to retain the Platonic position that the cosmos circulates or pivots around a dual principle—namely, the One and the principle of multiplicity or plurality (plh:qoV)5 (see Met. L 10, 1075b36ff ). Domenico Pesce has argued that Speusippus does retain the Platonic metaphysical foundation and, contrary to what Aristotle says about Speusippus, appears to have maintained a unified cosmos. The One and multiplicity . . . though identical in themselves, by acting on every level of reality on different materials give rise to successive levels of reality. With greater

Aristotle and Speusippus      41

precision, it could be said that multiplicity and matter are the same thing, and so only the One remains exactly identical, because the other principle is multiplicity at the first level, extension at the second, movement at the third, and corporeity at the fourth.6

According to Reale, however, Pesce’s derivation of such a conclusion is unwarranted, for no text provides such evidence. Moreover, Aristotle explicitly claims that Speusippus makes a fundamental distinction between the material principle of the various levels of the cosmos and their respective formal principles, which differ from these levels of reality7 (see Met. N 3, 1090b13ff ). The question at hand, however, is twofold: Is the One counted as a substance, and how are the subordinate substances derived from the One? Little is known about the nature of the One—that is, its attributes—and, as a result, such scant information may entail the priority of the One over the levels of substances— namely, number, magnitudes, soul, and finally perceptible objects. Merlan and Krämer disagree on the levels of Speusippus’s cosmology. Whereas Krämer argues that there are four kinds, although admitting of a five-stage classification, Merlan acknowledges five kinds or levels, which excludes the One as a level. Table 2.1 compares both accounts, as Tarrant illustrates.8 Each level, according to Aristotle, contains a different principle: one for Numbers, one for magnitudes, one for soul, and finally, one for perceptible bodies. For the purposes of this thesis topic, however, the puzzle of the various stages of substances or being in either Plato or Speusippus can be forgone, for our current concern is with respect to the status of the One in Speusippus and, ultimately, Aristotle’s response to the doctrine of the One and of first principles in general, as will be seen in our study of Metaphysics I in chapter 3.

Metaphysics N 4–5 and L 7: One is neither a Being nor the Good and the Beautiful More critically, Aristotle takes issue with the two-opposites-principle doctrine, the One and plh:qoV (Plurality). This can be seen in Met. N 4 and 5 (1091a29– Table 2.1. Merlan

Krämer Attributes

Level Class

Attributes

Level

Class

1 2 3 4 5

Being, Beauty Being, Beauty Goodness Baseness, evil Baseness, evil

1 2 3 4 5

The One Numbers Geometricals Soul Body

Numbers Geometricals Soul Body Inferior bodily entities

None Being, Beauty Being, Beauty Goodness, evil Goodness, evil

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1092a21).9 The problem is twofold: Speusippus claims that the two-opposites principle is (a) concurrently a principle of the Good and Evil and (b) that the two-opposites principle generates numbers. Moreover, in Metaphysics N 4–5, Aristotle reports that Speusippus’s doctrine of the One implies that the One is not a being (oujde; o[n), which can either mean that the One is inferior to Being or that the One is beyond Being (see Metaphysics N 4, 1091a29–1091b3). In this text, Aristotle states that the Good and the Beautiful are posterior to the first principle—namely, the One—for they are introduced simultaneously in the generation of Being.10 This confirms the Speusippean doctrine that the One is not a being. According to Aristotle, Speusippus discusses the One as that first principle that precedes Being, likening it to a seed out of which emerges more completion and perfection (Fr. 34A, E, F Lang).11 The particular “thinker” to whom Aristotle refers in Metaphysics N 5, 1092a11–17 is most likely Speusippus. The doctrine illustrated here, assuming it is Speusippus’s, entails the exclusion of Being from the One. However, with such a status of the One, we are not given much information on the status of the plh:qoV, as Speusippus expresses it.12 What happens to what is traditionally known as the opposite supreme principle? Does it also precede Being? Is Speusippus advocating a monistic system?13 These are questions which will be discussed in the course of our study. In Metaphysics L, Aristotle introduces the derivation of the degrees of substance by way of a seed analogy, which also attests to the Speusippean claim that the One is not the Good nor the Beautiful.14 In the seed analogy, Aristotle asserts that the seed is not the plant itself, but rather that it is the principle of the plant, and that the principle of a thing is not the thing itself (see Met. L 7, 1072b30–1073a3). Aristotle, therefore, claims that Speusippus’s One is identical neither with the Good nor the Beautiful.15 In light of line 1072b32, that the Pythagoreans and Speusippus assume that the Beautiful and the best are not in the principle, Aristotle, referring to his first principle, the unmoved mover, claims that the Pythagoreans and Speusippus are incorrect in this assumption. Aristotle’s first principle—which will be discussed in the next chapter—is the best and most beautiful. Reference to a first principle does not entail a temporal beginning. The question of the derivation of the substances, especially the substance or level of Numbers, must not be seen as a temporal process, for given the account of Speusippus’s cosmology in Z 2, Numbers, along with the Forms of Plato, are considered to be eternal substances.16 Speusippus, however, introduces a serious fissure between Plato’s philosophy and his own. In the Republic and the Timaeus, and also in the unwritten teachings, it is said that the Good is the first principle, whereas Speusippus argues that the Good and the Beautiful are derivatives of the first principle. Speusippus

Aristotle and Speusippus      43

likens the first principle to a seed, which, as Reale says, “is not good or beautiful, neither is the source which would correspond to the principle, but only the developed organism, that is the completed being.”17 Speusippus upheld this position in order to obviate the problem of identifying the principle of plh:qoV with evil18 (see Met. N 4, 1091b30 ff ). Speusippus also distinguishes between the first principle, the One, and nou:V. Aëtius testifies that “Speusippus said that God is Intelligence, which is neither identical with the One nor with the Good, but it has an individual nature of its own.”19 Intelligence, furthermore, is explained as being a dynamic and “vital force which rules things.20 The Intelligence must be identical, therefore, with the world-soul, a position which distinctly prefigures one of the most famous doctrines of the Stoics.”21 The theme of the relation between the One and nou:V was entertained by the Middle Platonists, especially Alcinous, the Stoics, and primarily Plotinus. I must, however, reserve the discussion of this rich theme for chapters 8 and 9. The process of derivation or generation in Speusippus is only with regard to the proofs of eternal, notably mathematical, objects. Derivation has less to do with the coming into being of sensible objects than it does with eternal objects that we come to know. In his commentary on Euclid, Proclus writes: Again, the propositions that follow from the principles he divides into problems and theorems, the former including the construction of figures, the division of them into sections, subtractions from and additions to them, and in general the characters that result from such procedures, and the latter concerned with demonstrating inherent properties belonging to each figure. Just as the productive sciences have some theory in them, so the theoretical ones take on problems in a way analogous to production. Some of the ancients, however, such as the followers of Speusippus and Amphinomus, insisted on calling all propositions “theorems,” considering “theorems” to be a more appropriate designation than “problems” for the objects of the theoretical sciences, especially since these sciences deal with eternal things. There is no coming to be among eternals, and hence a problem has no place here, proposing as it does to bring into being or to make something not previously existing—such as to construct an equilateral triangle, or to describe a square when a straight line is given, or to place a straight line through a given point. Thus it is better, according to them, to say that all these objects exist and that we look on our construction of them not as making, but as understanding them, taking eternal things as if they were in the process of coming to be.22

A mathematical construction, therefore, illuminates the eternal mathematical objects and their dependence on other objects, such as lines for the equilateral triangle. In light of the Timaeus’s “creation” account, if Proclus is correct, generation or derivation is to be interpreted pedagogically, with the intention of

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elucidating the eternal structures of the intelligible realm. Speusippus subscribes to the Platonic doctrine that mathematicals are eternal and unchanging, and, therefore, that coming-to-be and passing-away (i.e., generation or derivation) are to be understood analogously, for these terms, which refer to the mathematical propositions, contain theorems—that is, the objects of contemplation (qewrhvmata). Derivation, then, is closely related to causality, what one appeals to when explaining the why of something, which excludes a temporal dimension. Thus, Speusippus, when discussing derivation, refers to causality in a construction.23 Metaphysics L emphasizes the Seed analogy. In his criticism of Speusippus, Aristotle states that, according to Speusippus, the causes of animate objects, plants and seeds, are not Beautiful or Good in themselves, for Beauty and Goodness are products of these causes; they are posterior to the principles and are derived from their principles. According to Aristotle, however, the cause must itself be a complete and self-sufficient­ reality, and therefore, it must contain Beauty and Goodness. In other words, Aristotle disagrees with Speusippus that the first principle does not contain Goodness and Beauty, for the principle is prior to the result, and if Beauty and Goodness are in the principle, then they assume the priority of the cause of the objects in question. The seeds, according to Aristotle, are derived from an agent that precedes them, that is actually prior to them. This echoes his metaphysical doctrine that actuality precedes potentiality. Given that the One is likened to the seed, the One, according to Aristotle, must, if it is to be a principle, contain Goodness and Beauty, for the products necessarily inherit these attributes from the principle. So, Goodness and Beauty must be located in the principles. The true cause of anything is the actual agent, not the product in germ. A. C. Lloyd calls this the Transmission Theory of causality.24 It implies that every cause transmits its power to another object. Dancy spells it out in the following way: “(T) c causes x to be F inasmuch as c is itself F.”25 In this light, Speusippus does not adhere to the Transmission Theory, for the One, while it causes objects to be Beautiful and Good, itself does not contain these attributes. (This point will be essential to retain for our examination of Plotinus’s discussion of the One and its relation to nou:V.) As a result, Speusippus concludes that the One is not a being. This appears to be Aristotle’s conclusion or inference.26 His argument is clearly in line with the Transmission Theory and has little to do with an ontological argument about the status of the One, as articulated in Metaphysics L.27 As was brilliantly argued by Philip Merlan, the doctrine of the One above Being is also confirmed in Iamblichus’s book On Universal Mathematical Science (Universal Math.).28 Universal Math. IV contains many Speusippean leitmotifs: that the generation of Numbers is due to a dual principle—namely, the One and plh:qoV, the latter of which is responsible for division (diaivre-

Aristotle and Speusippus      45

siV)29 and is also compared to pliable matter, which, furthermore, assures the generation of the level of magnitude. In fact, it is the combination of the One and u{lh, the source of Plurality, that is the generative cause of Numbers. The co-principle of Plurality or the hyletic principle is not equivalent to the evil, for this principle is the receptacle of the One’s causality, and a receptacle in and of itself does not possess qualitative value, such as good or evil. Moreover, in Universal Math. IV, the content states clearly that the first principles are not equivalent to the good or evil, nor to the Good or the Beautiful, which emerge later in the emanationist system. The exact source of Iamblichus remains questionable, whether it is an interpolation of Aristotle’s account of Speusippus or whether it recapitulates Plotinian themes. There is evidence to demonstrate, however, that this chapter is an extract of Speusippus’s work On Pythagorean Numbers, which has been lost. The first and foremost distinction between Aristotle’s presentation and Universal Math. IV pertains to the problem of the status of the One. According to Aristotle, as we have seen, the One is given an inferior status, it is nonbeing in the sense of “something” that is only potentially a being; it is not a being yet. Universal Math. IV, however, echoes the similar formulation that the One is oujde; o[n, but interprets it as being above being.30 The significance of these words should be interpreted in the same manner in which it is said that the One is not the Beautiful or the Good. The two questions which must be asked, then, are 1) did Aristotle understand the Speusippean doctrine correctly? and, if so, 2) did Aristotle “depict” Speusippus’s doctrine accurately? With regard to the first question, Aristotle asserts that the One is inferior to Being, and out of the One emerge increasing levels of perfection. Thus, Merlan makes it very clear that this question must be answered in the negative. Aristotle, according to Merlan, neglected to take into account the second superior principle—namely, the principle of Plurality or the material principle—and accentuated his critique of the One at the expense of the dual nature of the first principles. We are given the fleeting impression that Aristotle views Speusippus as a monist. It would appear, however, that Speusippus is operating within a dualistic framework, in which the One and plh:qoV cooperate to produce the subsequent levels of Being, and that plh:qoV is not reducible to the One. Given this dualistic starting point, Aristotle’s reference to the evolution of the One, as a seed in development, must entail also the evolution of the material principle. The Aristotelian reference to the first principle as a seed, therefore, must be taken only as a metaphor. Aristotle’s statement mhde; o[n ti ei\nai to; e|n aujtov must be translated as either “so that the One itself is not any being either” or “so that we should not even say of the One itself that it is some being.”31 Following Dodds’s interpretation of Aristotle’s presentation of Speusippus,32 Merlan declares that Aristotle’s intention was to as-

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sert that the Speusippean One is not to be considered as a being, but rather that the One is uJperouvsion, or, rather, ajnouvsion.33 However, if the traditional interpretation of Aristotle’s view of Speusippus’s One, being inferior to Being, were correct, the second question would still have to be answered in the negative. It would seem, in light of Universal Math. IV, that Speusippus would not have agreed with Aristotle’s evaluation of the One in light of Aristotle’s duvnamiV-ejnevrgeia metaphysical principles, a dual concept that positions the One as a potential Being.34 Merlan writes, “It seems that Speusippus would not have admitted that the seed is inferior to the plant; it seems he would have compared their relation with the relation between the four and the ten. Full perfection appears only in the ten; but is the four inferior to the ten? Or else Speusippus would have protested against pressing his simile too far; the One may be like the seed—does it have to be so in every respect?”35 (See W. Jaeger, Aristoteles [1955] 233.) Merlan, therefore, argues, in light of Universal Math. IV, that Aristotle overextended his duvnamiV-ejnevrgeia principles in evaluating the status of the Speusippean One.36 In this light, it is apparent that Univ. Math. IV could not have drawn its source solely from Aristotle, for there remain fundamental differences between both presentations on the status of the One. Moreover, Merlan adds a very compelling piece of evidence by noting that Theophrastus, after having articulated the Aristotelian theory that Nature does not act in vain, reaffirms that this is particularly to be seen in what is first and most important—a seed being what is the first and most important (De causis plant. I 1, v.II 1 Wimmer). By “first and most important” Theophrastus designates the ultimate principles—here and also in his Metaphysics I 3, p. 4 Ross and Fobes, where he says that some consider number to be that which is the first and most important. Clearly, Theophrastus makes a distinction between what is undeveloped and what is inferior (or imperfect in the ordinary sense of the word). While the seed is in his opinion the former, it is not the latter. Indeed, the idea that what is undifferentiated and undispersed is higher than the differentiated and spread out, so that the seed is higher than the organism, seems like a rather natural one.37

According to Merlan, because Speusippus argues that mathematical principles are derived from the supreme principles, he has in mind a descending movement from the One to multiplicity, rather than the ascending movement that Aristotle describes. It would appear, therefore, that Aristotle “expressed himself ambiguously and that the One in Speusippus was meant to be non-being in the sense of better (higher) than being.”38 Speusippus would appear, in fact, to inherit the allegedly Platonic doctrine of a principle beyond Being—as it was interpreted by Plotinus and the subsequent Neoplatonists—and to transform this doctrine into

Aristotle and Speusippus      47

his two-opposites-principle doctrine.39 According to Proclus, Speusippus elevates the One above Being, governing the subordinate levels of reality. Proclus writes in his commentary on the Parmenides, giving the impression that Speusippus reflected the general sentiments of the ancients: For thinking the one better than being and that from which the being [derives], they even deliver it from the status that accords with a principle. But, judging that if one posits the one itself conceived as separate and alone, without [the?] others, in its own right, adding no other element to it, nothing of the others would be made, they introduced the indefinite duality as principle of the beings.40

Aristotle, of course, is claiming that the One is not a principle, and that the One is not the Good, in a Platonic sense. If the One were the Good, then Plurality, the counterpart of the One, would be the Ugly or the Bad, which, according to Aristotle and to Iamblichus, would be absurd (see Met. N 1091b30–35). Proclus’s assertion is confirmed in Iamblichus’s Universal Math., chapter IV, in which the doctrine of the One transcends Being. According to Merlan, we should read Speusippus’s doctrine of the One in this light, contrary to Aristotle’s interpretation. If Merlan is correct, then we can perceive a doctrinal continuity from Speusippus to Plotinus. Plotinus’s doctrine of the One is, according to Plotinus, to be found in Plato’s Parmenides, along with the doctrine that the intelligibles are within the Intellect,41 and we can assume that Plotinus interpreted Aristotle’s presentation of Speusippus’s One in this way. Speusippus’s One is irreducible to the Good (see Fr. 35 A, B, D, E Lang) and to Intelligence or nou:V (see Fr. 35D Lang). The theme of the subordination of nou:V to the One is clearly echoed in the philosophy of Plotinus and has raised the possibility of reading Speusippus’s philosophy as monistic, which would be a radical rupture from the Platonic legacy, which, according to Aristotle, he apparently tacitly accepted. Plotinus also accepts the Speusippean line that the One is not equivalent to the Good. Although Plotinus generally accepts Plato’s teaching that the ultimate metaphysical principle is the Good, he is reticent to accept this isomorphism. Plotinus is much more inclined to uphold the position that the Good is the condition or source of all goodness in the cosmos. Moreover, Speusippus did not claim that the One is co-principled with evil (Fr. 35D, Lang), which allows for an interpretation of a monistic two-opposites-principle doctrine.42 Regarding Plotinus’s conception of the One, which will be further discussed below, and the conception of the One in Universal Math. IV, the most fundamental difference is that, according to Plotinus, the One is equivalent to the Good, whereas for Universal Math. IV, the One is neither the Good nor the Ugly nor Evil, for it remains above these latter stages of being. Merlan concludes,

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“Thus, we repeat: according to both Isc and what Aristotle either reported or should have reported Speusippus said of his One that it is not even being in precisely the same sense in which Plotinus said of his One that it is oujde; o[n (Enn VI 9, 3, 38 Bréhier).”43 In Universal Math. IV, the One is clearly presented as superior to the Beautiful and the Good, and as the highest principle of the cosmos (duvo ta;V prwvtistaV kai; ajnwtavtw . . . ajrcavV, tou: ajgaqou: uJperavnw ei\nai, 16.11).44 Tarán disagrees strongly with Merlan’s thesis. According to Tarán, Iamblichus’s text disproves the hypothesis that Speusippus is the source for Universal Math. IV. Tarán writes, “The preceding arguments conclusively prove, I trust, that DCMS IV cannot go back to Speusippus and also that this text cannot be used as a source for the reconstruction of its thought.”45 Tarán has argued against the claim in Met. N 5, 1092a11–17 that the One is not a being, for Aristotle does not include the verb phrase he says.46 Tarán is of the opinion that Aristotle interpolates Speusippus’s doctrine and misconstrues it in order to confirm his (Aristotle’s) own theory of causality and of first principles.47 Thus, according to Tarán, Aristotle’s claim that Speusippus upheld the doctrine that the One is not a being is merely an inference on the part of Aristotle. As a result, Tarán asserts that Speusippus did not argue this point. In the Universal Math. IV, however, the author explicitly states that the One is not a being. Tarán concludes, therefore, that Universal Math. IV is not a text by Speusippus, nor does it express a doctrine that Speusippus himself advanced. However, Tarán has not disproven the possibility that Speusippus did infer the doctrine that the One is not a being. Tarán claims to have concluded that because Aristotle did not include the proper grammatical signals to indicate the thought of Speusippus, Speusippus could not have affirmed the very claim that Aristotle makes regarding Speusippus’s doctrine. While Aristotle may be tendentious and sarcastic about Speusippus’s conclusion, the essential structure of Aristotle’s representation may be correct, as J. Dillon has argued.48 In fact, in Universal Math. IV, we read the following claim, which, in fact, echoes what would almost conclusively be Speusippus’s doctrine: But it is fit to call the one neither beautiful nor good, because of the fact that it is above the beautiful and the good; for it was when nature proceeds farther away from the things in the principle that, first, the beautiful appeared, and, second, when the elements had an even longer distance, the good.49 (Universal Math. IV, 16.10–14)

This contains all the elements of Aristotle’s presentation of Speusippus in Metaphysics N 4, 1091a33–36, although in the Universal Math., the Beautiful and the Good do not emerge simultaneously, for the Beautiful precedes the Good.

Aristotle and Speusippus      49

But the elements out of which the numbers [are produced] do not yet obtain there as either beautiful or good; but out of the combination of the one and the matter that is [the] cause of plurality number subsists, and first in these being and beauty appear, while next out of the elements of lines geometrical substance appears, in which in the same way there is being and the beautiful, but in which there is nothing ugly or bad; but at the extreme, among the fourths and fifths, which are combined from the last elements, [it is possible] for badness to come-to-be, not directly, but from something’s falling away from the failing to retain possession of that which accords with nature.50 (Iamblichus, Universal Math. IV, 18.1–2)

In this light, Beauty and Being emerge at the level of Number, whereas Goodness emerges posterior to this stage. Moreover, we can confidently assert that the One is not a being, in light of this passage, which carries Speusippean overtones or which may be an excerpt of Speusippus’s writings.

Conclusion In this chapter, I discussed Aristotle’s scathing criticism of Speusippus’s doctrine of the One, as Aristotle presents it, and I viewed this doctrine in light of Iamblichus’s De communi mathematica scientia, chapter 4, which P. Merlan convincingly identifies as a fragment of Speusippus’s writings. The purpose of this section was to 1) determine Speusippus’s exact doctrine of the One, and 2) demonstrate Aristotle’s overt awareness of theories proposing to subordinate nou:V to an ultimate principle. According to Aristotle, Speusippus’s alternative solution to the aporia of Plato’s first principles is no better than Plato’s in that it is unable to demonstrate how the principles causally influence and derive the various levels of being. We know through Aristotle’s account and from chapter 4 of Iamblichus’s De communi mathematica scientia that Speusippus’s first principle, the One, is not a being. What remains ambiguous, however, is the exact status of Speusippus’s One: Is the One not a Being because it is so much more complete and self-sufficient that it is superior and prior to Being and nou:V; or, is it, by contrast, not a Being in the sense that it is not even worthy of being considered a Being, for it is analogous to a “seed,” a pure potentiality with no causal influence on any being or substance whatsoever? The first claim of the disjunct reflects Iamblichus’s (i.e., the Neoplatonists’) position, whose presentation elevates the One to a superior principle, over and above nou:V and Being. The latter part of the disjunct is Aristotle’s scathing rebuke of Speusippus and of any philosopher whose reflex it is to elevate a principle above nou:V, for, according to Aristotle, nou:V is self-sufficient and an independent substance or being. What is clear, in light of chapters 1 and 2, is this: Aristotle refuses to accept the Pythagorean, Platonic, and, especially, Speusippean doctrine of first princi-

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ples, for the two-principles doctrine fails to account for a causal continuity in the derivation of levels of Being subsequent to the first principle. Aristotle attempts to provide this account of derivation from a first principle by transforming the two-principles doctrine into a brilliant account of the superiority of nou:V, considered as the ultimate principle of the cosmos. Up to this point, I have not discussed Aristotle’s official position on the One and the Indefinite Dyad and his response to this doctrine. Essentially, Aristotle does not reject duality within the first principles—for he is not a monist—but he does preserve multiplicity and plurality within divine nou:V, or the unmoved Mover, as we shall see in our examination of Metaphysics L 7–9. In chapters 3, 4, and 5, I will discuss Aristotle’s solution to the two-principles doctrine by examining his conception of the One and his philosophical reasons for upholding the unity-in-diversity doctrine. I will argue that Aristotle preserves the plurality of the cosmos, despite his assertion of a singular substance— namely, divine nou:V—which orders the entire cosmos and is responsible for its movement. Aristotle’s henology and noetic doctrines are philosophical reactions to a central problem in the Pythagorean, Platonic, and Speusippean doctrines of the One and the Indefinite Dyad, the problem being that these doctrines fail to provide the final causality of the ultimate principles. Only by asserting final causality in the ultimate principles can Aristotle preserve unity-in-plurality, by taking into account the purpose of the parts within the whole, which Aristotle succeeds in demonstrating in Metaphysics L 8. Moreover, Aristotle’s preservation of plurality within unity, and his admission of final causality within the ultimate principles, provides a fuller and more satisfying account of the (causal) derivation of individual substances that we find within the cosmos. While not fully succeeding in eliminating the “gap” between divine nou:V and the world, Aristotle manages to identify a continuity of substances through the causal influences of the principles prior in simplicity to the lower orders of the cosmos. Chapters 3, 4, and 5 are, therefore, not only a response to the Pythagoreans, Plato, and Speusippus, but also an effective transition into Aristotle’s doctrine of the simplicity of divine nou:V—a doctrine that profoundly influenced subsequent Aristotelian commentators, notably, Plotinus.

Notes   1.  For a recent commentary of Speusippus’s fragments, see M. Isnardi Parente, Speusippo: Frammenti; Edizione, traduzione e commento (Naples: Bibliopolis, 1980); Tarán, Speusippus of Athens. Prior to these commentaries, scholars consulted P. Lang, De Speusippi Academici scriptis (Bonn, 1911), reprinted (Hildesheim: Georg Olms, 1965); and F. Čáda, “Platonuv nástupce v Akademii,” Listy filologické XLIV (1917): 1–15, 81–95, and 161–75.

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  2.  See H. A. Tarrant’s excellent article, “Speusippus’ Ontological Classification,” Phronesis 19 (1974): 130–45.   3.  See R. M. Dancy’s translation: “taking off from the one as principle,” R. M. Dancy, Two Studies in the Early Academy (Albany: State University of New York Press, c1991), 78.   4.  See Aristotle, Met. M 6, 1080b16ff; and G. Reale, History of Ancient Philosophy, vol. 3, 68.   5.  See A. Metry, Speusippos: Zahl—Erkenntnis—Sein (Bern; Stuttgart; Wien: Verlag Paul Haupt, 2002), 125–29.   6.  D. Pesce, Idea, Numero e Anima (Padua: Libraria Gregoriana Editrice, 1953), 57, trans. by Reale, A History of Ancient Philosophy, Vol. III, 69.   7.  See Reale, A History of Ancient Philosophy, 70. See L. Tarán, Speusippus of Athens: A Critical Study with a Collection of the Related Texts and Commentary (Leiden: E.J. Brill, 1981), 49ff., for a discussion against Aristotle. J. Dillon, however, disagrees with Tarán here. See Dillon, The Heirs of Plato, vii and 41–42. In this light, Dillon wishes to defend Speusippus against Aristotle’s charge of incoherency in Speusippus’s philosophy. If it is the case that Speusippus’s writings are retained and reproduced in Iamblichus’s De communi mathematica scientia, ch. 4, which, contrary to Cherniss and Tarán’s claims, there is sufficient evidence, as Merlan, From Platonism to Neoplatonism, 98–140, has proven, then it stands to reason that Aristotle clearly exaggerates and perhaps misrepresents Speusippus in his criticism. Nevertheless, Aristotle still recognizes the philosophical reflex to subordinate nou:V to a superior principle, which, in this case, is the One, and attempts to demonstrate (in Metaphysics L 7–9) that this “gap” is unwarranted, for the most simple principle of the cosmos, according to Aristotle, is the intelligible object of nou:V—namely, nou:V itself. (This theme will be discussed in detail in chapter 5.) See also J. Dillon, “Speusippus in Iamblichus,” Phronesis 29 (1984), 325–32. M. Wilson argues that it is Aristotle who, in fact, should be charged with the same charge of an episodic tragedy, given that Aristotle does not explain sufficiently the passage from genus to species. “Aristotle once accused Speusippus of representing nature like an episodic tragedy, on the grounds that he had made each hypostasis independent and isolated from every other (Met. N.3, 1090b19–20). His own theory of the subject-genus, however, was perhaps even more vulnerable to this charge” (M. Wilson, Aristotle’s Theory of the Unity of Science [Toronto: University of Toronto Press, 2000], 239).   8.  See Tarrant, “Speusippus’ Ontological Classification,” 134. See Metry, Speusippos: Zahl—Erkenntnis—Sein, 112–24.   9.  See also Met. L 7, 1072b30–34 and 10, 1075a36–37. This will be discussed below. 10.  See Dancy, Two Studies, 161, fn.143. Without reference to Universal Math. IV, however, it is difficult to perceive the Neoplatonic character in Speusippus. This, however, will be discussed below. 11.  See Dillon, The Heirs of Plato, 43. Dillon claims that Aristotle is being tendentious here, for the seed analogy can only be related to the One insofar as the seed is apparently simple, unlike the One, which is actually simple—“there could be no implication of incompleteness or imperfection in the case of the One.” For a contrasting view, see

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Tarán, Speusippus of Athens, 33–34. Tarán clearly discredits Aristotle’s testimony. Also see A. H. Armstrong, The Architecture of the Intelligible Universe in the Philosophy of Plotinus (Cambridge: Cambridge University Press, 1940), 22, for a comparison between Speusippus and the Neopythagoreans. The Neopythagorean introduction of a monistic system must be studied separately in chapters 5 and 6. 12.  See Dillon, The Heirs of Plato, 42; see also M. Isnardi Parente, “Proodos in Speusippo?,” Athenaeum 53 (1975) 88–110; and Robin, La théorie Platonicienne, 654 ff. 13.  Speusippus attempts to explain what Aristotle calls his episodic cosmos (Met. Z 1028b21–4) by postulating some “mechanism. . . . The best he [sc. Speusippus] could come up with,” says Dillon, “is the theory that the (logically) first product of the union of the two ultimate principles should then become a principle in its turn, mating, so to speak, in an incestuous union, with its mother (which Speusippus has been careful to characterize . . . as ‘a totally fluid and pliable matter’), and producing the next level of being.” Dillon, The Heirs of Plato, 46. Speusippus, it would seem, was concerned with the derivation of a multi-leveled cosmos from a “pair of totally simple first principles.” Dillon, The Heirs of Plato, 47. See also Metaphysics M 9, 1085a34–b4. In light of this passage, one witnesses an explanation, albeit weak, for the derivation and production of the varying levels of being within the cosmos and the derivation of principles governing each level of the cosmos. (See Dillon, The Heirs of Plato, 46–47.) Dillon, moreover, states, when discussing Aristotle’s unjust critique of Speusippus’s alleged abandonment of the Ideal Numbers that Speusippus held a monistic metaphysical system (i.e., two-principles doctrine, the One and the Indefinite Dyad). (See Dillon, The Heirs of Plato, 51.) Clearly, Aristotle was not satisfied with Speusippus’s explanation of the transition to plurality from unity, for this transition does not seem to preserve a fluid continuity between the causal influence of the ultimate principles and the subsequent diverse levels of being. Once again, we shall see that the two-principles doctrine was radically transformed by Plotinus and the subsequent Neoplatonists. However, it should be stated that Aristotle’s criticism, strictly speaking, of the episodic stages of principles does not directly attack Speusippus’s dualistic starting point, of the One and plh:qoV. While Aristotle does have reservations about the transition from unity to plurality, he does not directly associate his criticism of the One and the Plethos with the episodic stages of principles. 14.  See Metry, Speusippos: Zahl—Erkenntnis—Sein, 129–32. 15.  See Ross’s Commentary, vol. II, 381, with respect to the derivation of perfect from imperfect in the Pythagoreans. 16.  E. Cattanei, Enti matematici e metafisica: Aristotele, Platone e l’Accademia antica a confronto (Milano: Vita e pensiero, 1996), 148–55. 17.  Reale, A History of Ancient Philosophy, Vol. 3, 70. 18.  See Reale, A History of Ancient Philosophy, Vol. 3, 70. See also L. Elders, Aristotle’s Theory of the One: A Commentary on Book X of the Metaphysics (Assen, Netherlands: Koninklijke Van Gorcum & Comp., 1960), 10. See Met. M 9, 1085b4–34, where Aristotle employs terms such as “one,” “number,” and “multiplicity,” when criticizing Speusippus. Dillon is correct, however, to state that Aristotle is being tendentious and polemical here. Aristotle interprets (it would seem intentionally) these terms in light of his own

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philosophical system and, consequently, reduces Speusippus’s philosophical claim into an incoherent absurdity. “What he [sc. Aristotle] does not allow for is that Speusippus is postulating first principles of unity, multiplicity, and number which are not subject to Aristotelian definitions” (Dillon, The Heirs of Plato, 47). See also A. Falcon, “Aristotle, Speusippus, and the Method of Division,” Classical Quarterly 50 (2000), 402–14; J. Barnes, “Homonymy in Aristotle and Speusippus,” Classical Quarterly 21 (1971), 65–80; L. Tarán, “Speusippus and Aristotle on Homonymy and Synonymy,” Hermes 106 (1978), 73–99; and Metry, Speusippos: Zahl—Erkenntnis—Sein, 102–10. 19.  Aëtius, quoted in Stobaeus Anth. 1.1; Diels DG 303b; frag. 38 Lang; frag. 89 Isnardi Parente; frag. 58 Táran. (Found in Reale, A History of Ancient Philosophy, 392, fn.19.) 20.  See Reale, A History of Ancient Philosophy, Vol. 3, 70, and see Cicero De natura deorum 1.13.32; LCL 35; Minucius Felix Octav. 19.7; frags. 39a–b; frags. 90–91 Isnardi Parente; frags. 56a–b Táran. 21.  Reale, 70, and fn.21: “With regard to the human soul, it would seem that Speusippus maintained the immortality of all its parts, as Olympiodorus says in his commentary on the Phaedo (frag. 55 Lang; frag. 99 Isnardi Parente; frag. 55 Táran).” 22.  Proclus, A Commentary on the First Book of Euclid’s Elements, trans G. R. Morrow. (Princeton, NJ: Princeton University Press, 1970), 63–64, corresponding to Friedlein (1873), 77.7–78.6. 23.  See Dancy, Two Studies, 85. 24.  A. C. Lloyd. “The Principle that the Cause is Greater than its Effect,” Phronesis 21 (1976), 146–56. See also Dancy, Two Studies, 86. 25.  Dancy, Two Studies, 85. 26.  Tarán, Speusippus of Athens, 338, fn.141: “Some scholars, e.g., Krische, Forschungen, 253, fn.1 and Ross in his note on 1092 A 13–15, say that this sentence is probably an inference of Aristotle, but they say nothing about the fact that its syntax shows it is merely an inference. It is at the very least ambiguous and misleading to translate this clause of intended result as ‘so that the One itself is not even an existing thing’ (Ross; similarly Annas).” 27.  Dancy is correct to remind us of Aristotle’s treatment of Leucippus and Democritus, both of whom discussed being that did not “exist,” and Aristotle did not conclude that their theories were absurd, contrary to Aristotle’s assessment of Speusippus’s philosophy. Dancy writes, “Recall his [Aristotle’s] treatment of Leucippus and Democritus: theirs was a theory to be reckoned with despite its Meinongianism, and Aristotle did not profess to find anything absurd in it because of that Meinongianism. Aristotle is, no doubt, an Actualist at heart, but his Actualism is not so well-entrenched that he can see in Meinongian consequences an obvious refutation of their antecedents” (Dancy, Two Studies, 88). It must be assumed, in light of the given evidence, that Speusippus did uphold the doctrine that the One is not a being. 28.  Merlan, From Platonism to Neoplatonism. See also J. Dillon, The Heirs of Plato, 41 ff., and 41, fn.28; and see Metry, Speusippos: Zahl—Erkenntnis—Sein, 26–46. 29.  See Metry, Speusippos: Zahl—Erkenntnis—Sein, 73–110.

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30.  See J. Dillon’s very interesting remark in The Heirs of Plato, 42 and fn.30. See also J. Halfwassen, “Speusipp und die metaphysische Deutung von Platons ‘Parmenides,’” 365–72; and G. Bechtle, The Anonymous Commentary of Plato’s Parmenides (Bern: P. Haupt, 1999), 111–17. 31.  Merlan, From Platonism to Neoplatonism, 105. 32.  E. R. Dodds, “The Parmenides of Plato and the Origin of the Neo-Platonic One,” Classical Quarterly 22 (1928): 129–42, esp. 140, fn.5. For a counter-claim, see J. Rist, “The Neoplatonic One and Plato’s Parmenides,” Transactions of the American Philological Association 93 (1962), 389–401. See also J. Halfwassen, “Speusipp und die metaphysische Deutung von Platons ‘Parmenides,’” in EN KAI PLHQOS: Einheit und Vielheit. Festschrift für Karl Bormann, eds. L. Hagemann and R. Glei (Würzburg: Oros Verlag, 1993), 339–73, especially 343–57. 33.  See also C. Sandulescu-Godeni, Das Verhaeltnis von Raionalitaet und Irrationalitaet in der Philosophie Platons (1938) 25; G. Nebel, Plotins Kategorien der intelligiblen Welt (Tübingen: Mohr, 1929), 32 f. For the opposite point of view, see, for example, A. H. Armstrong, The Architecture of the Intelligible Universe in the Philosophy of Plotinus, 18 and 22; see also his Introduction to Ancient Philosophy (Lanham, MD: A Littlefield, Adams Quality Paperback, 1981), 67. See also H. R. Schwyzer, art. Plotinus, RE XXI/1 (1951): 559 ff. 34.  This Aristotelian response to Speusippus will be crucial to our discussion of Plotinus’s critique of Aristotle’s first principle of nou:V. More striking, and strongly related to the topic of the simplicity of nou:V in both Aristotle and Plotinus, is the following passage in Universal Math. IV, which attributes simplicity to the One, confirming the status of nonbeing of the One and of the principle of plurality, both of which are responsible for the generation of mathematical numbers. For the mathematical numbers one must posit two [things], the first and highest principles, the one (which indeed one ought not yet even call a being, because of the fact that it is simple and because of the fact that it is a principle for the things that are, while the principle is not yet such as are the things of which it is a principle), and again another principle, that of plurality, which can by virtue of itself provide division as well. (Iamblichus, Universal Math. IV, 15.6–12, trans. Dancy, Two Studies, 90–91)

With regard to Speusippus’s reform of the Platonic singular principle of the One and the Indefinite Dyad, Speusippus retains the doctrine of the One but replaces the Indefinite Dyad with the principle of Plurality, for the reason that once the Ideal Numbers and the Forms have been eliminated in his cosmology, and, consequently, explaining the diversity of the cosmos through the derivation of mathematical entities, multiplicity rather than the Indefinite Dyad appears to have better explained the plurality of the cosmos. (See Reale, A History of Ancient Philosophy, 69.) Two passages from the Metaphysics best articulate this insight: Metaphysics N 1, 1087b4ff and N 5, 1092a33ff. The simplicity of the One can be identified in Plato’s Parmenides (137c–142a). It has even been suggested by two prominent scholars that Plato, who is allegedly aware of Speusippus’s metaphysical doctrine, is responding to Speusippus in the Parmenides. See A. Graeser, “Platon gegen Speusipp: Bemerkungen zur ersten Hypothese des Platonischen Parmenides,” Museum

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Helveticum 54 (1997), 45–47; A. Graeser, “Anhang: Probleme der Speusipp-Interpretation,” in Prolegomena zu einer Interpretation des zweiten Teils des Platonischen Parmenides [Berner Reihe philosophischer Studien 25] (Bern: Verlag Paul Haupt, 1999), 41–53; J. Halfwassen, “Speusipp und die metaphysische Deutung von Platons ‘Parmenides,’” 357–73; and J. Halfwassen, Jens, “Speusipp und die Unendlichkeit des Einen: Ein neues Speusipp-Testimonium bei Proklos und seine Bedeutung,” Archiv für Geschichte der Philosophie 74 (1992), 43–73. In the first hypothesis of the Parmenides (137c–142a), Parmenides (137c) states that the One cannot be identified with the Many and is without parts (137c–d). As a result, the One cannot in any way be predicated, for to predicate anything of the One would be to introduce into the One multiplicity (141e). Nor can we predicate Being of the One (141e). For this reason, Plato (followed by Speusippus) asserts that the One is not. (See also R. S. Brumbaugh, Plato on the One: The Hypotheses in the Parmenides [New Haven, CT: Yale University Press, 1961]; and B. Mates, “Identity and Predication in Plato,” Phronesis 24 [1979]: 211–29.) 35.  Merlan, From Platonism to Neoplatonism, 105. 36.  See also Metry, Speusippos: Zahl—Erkenntnis—Sein, 139–57 and 162–67. 37.  Merlan, From Platonism to Neoplatonism, 105–6. 38.  Merlan, “Greek Philosophy from Plato to Plotinus,” 31. 39.  See Proclus’s commentary on Plato’s Parmenides, in R. Klibansky, C. Labowsky, Procli Commentarium in Platonis Parmenidem (1953), 38, 33–41, 10. See also Dillon, The Heirs of Plato, 42, fn.30. 40.  See Proclus’s commentary on Plato’s Parmenides, in R. Klibansky, C. Labowsky, Procli Commentarium in Platonis Parmenidem (1953), 40.1–5. 41.  Frag. 5, Diels; Enn. V 1 [10] 8; V 9 [5]; see also A. H. Armstrong, “The Background of the Doctrine ‘That the Intelligibles are not outside the Intellect,’” in Les Sources de Plotin, Tome V (Vadoeuvres-Genève: Fondation Hardt, 1960), 391–413, which will be discussed in greater detail in chapter 9. 42.  Merlan, “Greek Philosophy from Plato to Plotinus,” 32 including fn.2. However, see also Tarán, Speusippus of Athens, 356–58, where it is held that Speusippus’s One is not exactly a precursor to the Plotinian doctrine of the One. 43.  Merlan, From Platonism to Neoplatonism, 106. 44.  According to Dancy, there is no discrepency between Aristotle’s and the Universal Math’s account of the One. In the latter, the One is above (uJperavnw) the Good, the Beautiful, and Being, but with Aristotle, what is meant is that the One is first and responsible for every other Being, it is the cause of beings. See Dancy, Two Studies, 94. This debate is anchored in the interpretation of Republic VI 509b2–10, whether the Good is beyond Being or substance. The Neopythagoreans and later Platonists accepted the claim that the Good is beyond Being. Moderatus of Gades “shows that the first one is above being and all substances” (Simplicius, In Physica 230.36–37; see Dancy, Two Studies, 165, fn.174). Plotinus accepted this doctrine (see Enn. VI.9.3.36–38 and also VI.9.3.52). In this light, the Good is not Being, but rather beyond Being. According to Dancy and others, this latter claim is not what Plato meant (see also N. P. White, A Companion to Plato’s Republic [Indianapolis: Hackett Publishing Company, 1979], 180–81), and I

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do not think that Aristotle understood it this way either. Plato’s phrase “beyond being” (ejpevkeina th:V oujsivaV) does not mean the transcendence of Being, for the Good is apparently still an object of knowledge. ejpevkeina th:V oujsivaV can mean “on the far side of it” (Dancy, Two Studies, 96)—that the Good is on the far side of Being. (Although, admittedly, this expression does not amount to any further clarification of the status of the One to Being.) Moreover, the Good here is mentioned as one type of Form, which is within the realm of Being (see Rep V 474a4 and also VI 484c6 and d4, where is it indicated that Being is parallel with things that are Good). “There is no room in the Republic for Meinongianism about the Good,” says Dancy (Two Studies, 96). There do not seem to be any Platonic overtones in this respect in Speusippus, for Speusippus clearly, according to the testimony of Aristotle and of Universal Math., did not equate the first principle with the Good. Dancy makes reference to a very significant passage found in Simplicius, which relates directly to our topic, whether or not there is a principle that precedes nou:V. (See also Dancy, Two Studies, 165, fn.182.) This will be discussed in greater depth in the subsequent chapters. 45.  Tarán, Speusippus of Athens, 107. 46.  Not just Tarán, but also Ross (1924), vol 2, 489 ad 1092a13–15: “Speusippus’ argument is represented as follows: (1) The One is the beginning of all things. (2) All beginnings are imperfect. Therefore the One is imperfect. From this Aristotle draws a consequence of his own probably not drawn by Speusippus: (3) What is imperfect cannot be said really to be. The One is imperfect. Therefore the One is not. Aristotle denies the premise numbered (2) above.” (See Dancy, Two Studies, 162, fn.146.) 47.  See Tarán, Speusippus of Athens, 338–39. 48.  See J. Dillon, “Speusippus in Iamblichus,” Phronesis 24 (1984), 326. Aligning himself with P. Merlan’s thesis of the inclusion of Speusippus in Iamblichus’s Universal Math. ch. IV, Dillon, on p. 332, states clearly his disagreement with Tarán. 49.  Dancy, Two Studies, 115. 50.  Dancy, Two Studies, 90.

c h a pte r t h r ee

Aristotelian Henology

Introduction Aristotle’s criticism of Plato’s conception of the One raises the question, what is Aristotle’s solution to this aporia? This chapter will attempt to provide an answer to this question—an answer and analysis that will lead us to Aristotle’s doctrine of the simplicity and priority of nou:V. Chapter 3 will essentially discuss Aristotle’s transformation and renewed conception of Plato’s doctrine of the One. As with his doctrine of Being, Aristotle asserts that the “one” is a pros hen equivocal; the “one” is not to be considered a universal substance, as it is considered in Plato’s metaphysics. I will concentrate on books D and I of Aristotle’s Metaphysics and will give more emphasis to Aristotle’s account of the “one” from Metaphysics I.

Aristotelian Henology: Aristotle’s Many Senses of the One How does Aristotle understand the principle of the “one”? It is clear, as with his interpretation of Being, that the “one” is a pros hen equivocal, rather than a univocal substance. The One, then, cannot assume the same operation as it does in Plato’s metaphysics. Metaphysics I recapitulates Aristotle’s discussion of the many senses of the “one,” as expressed in Metaphysics D 6, and also makes reference to the aporetic question as to whether the “one” (and Being) are substances of entities, as was discussed in Metaphysics B. It is clear that Aristotle is taking issue here with Plato, the Pythagoreans, and especially the Platonists, like Speusippus. 57

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Briefly, Aristotle recapitulates his conception of the “one” per se in Metaphysics I 1: Things are one when 1) they are continuous in general or by nature; 2) they are whole; 3) the things in question are one by definition; and 4) they are individuals. Moreover, these things are one due to their indivisibility regarding their movement, conception, and definition. In order for something to be one, it must be considered as the first measure of a kind, and this measure is of quantity. In addition to this, measure has an epistemological dimension, for it is depicted as that by which something is known. Knowledge presupposes an adequate standard or measure of objects, and this assertion will further advance and determine the course of our study on the topic of the simplicity of nou:V. And nou:V has itself for its sole object; nou:V is indivisible and identical or homogeneous with the object that it measures—namely, itself. In the case of the “one,” the “one” is indivisible just because the first of each class of things is indivisible. Unity, then, is a measure, “more properly of quantity, and secondly of quality” (Met. I 1, 1053b4–9). It has been argued that within the Academy discussions were held not only about the nature of the “one” as a principle, but also about the theories of predication of unity, thereby interconnecting the ontological with the logical orders. Initially, Aristotle limits his study to the theme of the predication of the “one,” but subsequent to this, he discusses the multiple ways in which the one can be predicated by appealing to the theory of measure. This method is clearly of the logical order, as we also see in Met. D 6, 1016b8 ff. The language used to itemize the many senses of the “one” differs slightly in Met. D 6 and I 1. Aristotle continues to itemize four senses of the “one” per se, but there are subtle differences. In Met. I 1, 1052a33, Aristotle includes a new sense of the “one,” that the object is indivisible in kind or in number. This sense is omitted in Met. D; whereas, the “one,” by considering the genus as a unity in D 6, 1016a25ff, is no longer retained in Met. I: w|n to; gevnoV e{n. Metaphysics I appears to be a later work, for it abandons the genus-concept theory and adopts rather the more refined theory of individual unity, which was omitted in Met. D 6.1 The omission is indicative of a possible progression in Aristotle’s conception of the “one.” In Met. I, Aristotle appears to have abandoned the doctrine of the natural unity of the genus, while placing a greater emphasis on his conception of the individual. Because Met. I appears to be a progression in Aristotle’s thought of the doctrine of the “one,” it is a more natural starting point for our discussion of his conception of the “one.” In Met. I, Aristotle essentially defines the one or unity as a measure, first and foremost a measure of quantity and, subsequently, of one quality (see Met. I 1, 1053b4–9). Clearly, Aristotle here wishes to overthrow any Platonic claim that the “one” is a transcendent principle of the cosmos. In Met. I 1, Aristotle recapitulates the four fundamental ways in which the “one” is said per se (essentially).

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I begin with the first of the four fundamental ways in which the “one” is said per se (i.e., the continuous). That which is continuous is so generally and absolutely or by nature, because its self-motion is indivisible, simple, and one: “and of these, that has more unity and is prior, whose movement is more indivisible and simpler” (Met. I 1, 1052a20). Aristotle states that the “one” is continuous “either in general, or especially that which is continuous by nature and not by contact nor by being tied together” (h[ aJplw:V h] mavlista ge to; fuvsei kai; mh; aJfh:/ mhde; desmw:/). Elders claims that 1056a19 specifically does not have a “full disjunctive value.”2 He opts to translate this passage in the following way: “‘The continuous in general, and especially the continuous by nature.’”3 This characterization of the “one” as continuous was stated in Met. D 6, 1016a1–17, where Aristotle distinguishes between the continuous in a general way, by either external contact or by internal unity (see Met. D 6, 1016a5–6). This double aspect of the continuous is not, however, articulated in De Caelo 306b23–25. Here, Aristotle does not articulate the continuous by composition, for he is discussing organic unity (see Phys. III, 227a7–17). It would appear here that Aristotle is accentuating the unity of a natural sort over and against the atomistic viewpoint of Democritus (see De Caelo I 7, 275b29 and De Gen. et Cor. I 8, 325a6). The second participant in his list of four entails the “one” that is seen as a whole4—a whole with respect to its movement as being one and indivisible in place and time. That which is whole and contains a determinate form is also considered to be one in a more superior way (see Met. I 1, 1052a23–32). By considering the “one” per se as a whole, Aristotle appears to be alluding to the first heaven, whereby the stars or unmoved movers move according to one single motion, whereas the subsequent spheres move according to a different arrangement of movement (see De Caelo II 12, 291b29–32; 292b25–26; and II 4, 287a23 ff.). Aristotle, moreover, writes in the De Anima that Democritus was of the opinion that the indivisible spheres—the spherical atoms—put the entire cosmos into motion. Democritus “says that the spherical atoms, as they move because it is their nature never to remain still, draw the whole body with them and so move it” (DA I 3, 406b20–23). Contra Democritus, Aristotle advances a different sense of the indivisible, referring to the external sphere. This is confirmed in De Caelo II 6, 288a24 ff. Furthermore, Aristotle adds that the first heaven is to be considered as a divine substance, unlike the lifeless qualities of inanimate matter: “We think of the stars as mere bodies, and as units with a serial order indeed but entirely inanimate; but we should rather conceive them as enjoying life and action” (De Caelo II 12, 292a18; see also lines 20 ff ). The movement of the outer sphere is whole, homogeneous, and simple, for the outer sphere does not require place and, as a result, the limitations of a body5 (see Phys. IV 5, 212b11–22). Similarly, the outer sphere or first heaven is beyond time and,

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as a result, eternal. To say, then, that the movement of the first heaven or the whole is indivisible in time, is to assert that it possesses nothing prior or posterior to it (see De Caelo II 8). Finally, the circular movement of the first heaven functions as a measure of the other subordinate moving arrangements in the cosmos. “Again, if the motion of the heaven is the measure of all movements in virtue of being alone continuous and regular and eternal, and if, in each kind, the measure is the minimum, and the minimum movement is the swiftest, then the movement of the heaven must be the swiftest of all movements” (De Caelo II 5, 287a23–26). The concept of measure is central to Aristotle’s philosophy and will prove to be important in our study of the unity and plurality of the cosmos and of his doctrine of nou:V.6 Regarding the third characterization of the “one,” Aristotle writes, “ta; me;n dh; ou{twV e}n h|/ sunece;V h] o{lon, ta; de; w{n a]n oJ lovgoV ei|V h\/, toiau:ta de; w|n hJ novhsiV miva, toiau:ta de; w|n ajdiaivretoV, ajdiaivretoV de; tou: ajdiairevtou ei[dei h] ajriqmw:/.” “Of this sort [sc. a thing’s definition is one] are the things the thought of which is one, i.e. those the thought of which is indivisible” (Met. I 1, 1052a29–30). That which is one qua indivisible in number is considered to be the individual: “In number, then, the individual is indivisible”7 (Met. I 1, 1052a33). In Met. D 6, Aristotle includes in his list of characterizations of the “one” per se the aspect of intuition or novhsiV, which is indivisible: “In general those things the thought of whose essence is indivisible, and cannot separate them either in time or in place or in definition, are most of all one, and of these especially those which are substances” [o{lwV de; w|n hJ novhsiV ajdiaivretoV hJ noou:sa to; tiv h\n ei\nai, kai; mh; duvnatai cwrivsai mhvte crovnw/ mhvte topw/ mhvte lovgw/] (Met. D 6, 1016b1–3).8 Only the intellectual content of an examined substance is novhsiV—a term that closely resembles Plato’s conception of intuition.9 This doctrine of novhsiV is also found in Anal. Post. II 19, where it is said that novhsiV guarantees the emergence of scientific thought, that it provides the conditions for the emergence of universals, whereby the indivisibles (ta; ajmerh:)—that is, the One and its species (see Met. D 6, 1014b6 and 1084b14) are grasped by novhsiV. In 1052a33, however, Aristotle rejects the affiliation with a transcendental One in order to guarantee indivisibility and unity.10 Finally, the fourth characteristic states that those objects that are indivisible in kind are also indivisible in intelligibility and in knowledge (tw:/ gnwstw:/) or in science (th:/ ejpisthvmh/), such that what causes a substance to become one— namely, the form—“must be one in the primary sense”11 (Met. I 1, 1052a34). Cleary also highlights the parallel definition of the one with “cause” and “element,” as is discussed in Met. I, 1052b15 ff. Here it is essential to note that what is called one refers primarily to the

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first measure of each genus and, most properly, of quantity; for it is from this that it has been extended to others. . . . Now in all these the measure (metron) and principle (arche) is something which is one and indivisible (hen ti kai adiaireton), since even in lines we treat the length of one foot as indivisible. For everywhere we seek as a measure something which is one and indivisible, and this is something which is simple either in quality or in quantity. The measure of a number is the most accurate (akribestaton) because the unit is posited as indivisible in all respects (1053a1). In conclusion, Aristotle claims (1053b4ff ) that it is evident that to be one, if we describe it according to name, is to be some measure, most properly of quantity, and then of quality. And it will be such if, in the first case, it is indivisible with respect to quantity, and in the second, indivisible with respect to quality. Hence the one is indivisible, either simply (haplos) or qua one (hei hen).12

In Met. I 2, Aristotle expands his reflection of the “one” as a measure to a discussion of the “one” as being undivided, as having a general meaning.13 In this chapter, Aristotle clearly articulates his opposition to the Pythagorean and Platonic conceptions of a transcendent One (see Met. I 2, 1053b9–16). The “one” is, rather, an attribute or property of a substance. This assertion was alluded to in Aristotle’s critique of Speusippus but is spelled out in greater detail in Met. I I. 2. The “one,” as with being, is a universal, and no universal can assume the status of a substance. As a result, the “one” is not a substance (see Met. I 2, 1053b17–23; 1054a10–19). Paramount in this section is Aristotle’s denial of substantiality to the “one.” Rather, he assigns to the one the status of a predicate. The one is as universal as being, and, as a result, it is not a separate substance.14 Thus, the “one” is a definite thing for each genus, but the unity is not unity in itself, “but just as in colours we must seek that unity as one colour; so in substances we must seek it as one substance.”15 Once again, in every genus, the unity contains a certain nature.16 In Met. I 2, 1054a5–6, Aristotle states that numbers and one are included in various items, including movement. The theme of movement plays an important role in our study of Aristotle’s doctrine of nou:V and of Plotinus’s interpretation of Aristotle’s doctrine. Plato’s conception of motion consisted of otherness (e{teron), as discussed in chapter 1. “This is evident,” says Aristotle, “from what people say. Some call it otherness and inequality and the unreal; none of these, however is necessarily moved, and further, change is not either to these or from these any more than from their opposites” (Met. K 9, 1066a10–12). The Indefinite Dyad and matter, moreover, are involved in the activity of movement in the cosmos, for in his work On the Philosophy of Archytas (frag. 2 Ross), Aristotle states that according to Plato, movement is defined as otherness within matter (see On Gener. and Corrup. I 3, 319a). In this light, Aristotle correlates movement with matter (see De Caelo II 12, 293a9). Each sphere or body generates its own par-

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ticular kind of movement, which is simultaneously affected by the movement of the first heavenly sphere, which is characterized by the causal influence of nou:V.17 The transcendence of these Platonic principles, however, is further contested and challenged by Aristotle in Met. L, to which I now turn. The purpose of this brief discussion on Aristotle’s conception of the one is to demonstrate Aristotle’s departure from the Platonic two-principle doctrine and to prepare for our discussion of Aristotle’s alternative to this two-principle doctrine.

Aristotle’s Alternative to Plato’s First Principles As seen in Met. I, Aristotle takes issue with the Platonic doctrine of a transcendent principle—namely, the One—but he has not yet provided an alternative account to Plato’s first principles. In Met. L 4–5, Aristotle provides such an account. In the early books of Met. L, we witness Aristotle once again arguing against Plato and the Platonists. Aristotle’s focus in these books is on the principles, causes, and elements of sensible, changeable substances. “Sensible substance is changeable,” says Aristotle (Met. L 2, 1069b3). This teaching echoes his doctrine in Physics I, where Aristotle states that the precise principles are those that are the contraries and a stable subject that is permanent amid all change. Strictly speaking, these various principles are different for each type of change regarding essence, quality, quantity, and place. However, all changing entities share the same principles in a general and analogical sense.18 In Met. L 2, 1069b15 ff., Aristotle reemphasizes his teaching that “being” is spoken of in two ways. In this light, Aristotle avoids the Parmenidean sanction against the generation from nonbeing by providing an account of change in terms of “that which is potentially to that which is actually,” or, using an example of the category of quality, “from potentially white to actually white” (Met. L 2, 1069b16, 17). Matter remains the constant subject throughout the change. Nonbeing, which includes matter, is furthermore expressed under three categories: potential being, privation, and matter (see Met. L 2, 1069b27–34). Each one of these senses of nonbeing is not, however, a self-subsistent entity, for each refers to actual being or form “which is a primary reality for Aristotle just as much as it was for Plato, even though they disagree about how this form should be defined and understood.”19 In the passage just cited, Aristotle refers to his conclusions in Physics I 7 regarding the causes and principles of changing substances. Privation and form or definition are contraries, leaving matter as the third principle and cause.20 In other words, the one and the same form suffices to explain change through its absence or its presence, so that something both does and does not come to be from what is not. The three kinds of substances mentioned in Met. L 1 in-

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clude sensible substance, which further undergoes change, and change implies matter, form, and privation—a subject that is adequately summarized at the end of Met. L 2. Aristotle’s discussion of first principles takes a significant turn in Met. L 4 and 5, where he discusses his account of first principles and seeks a solution to the Platonic problem of first principles. Met. L 4 recapitulates Aristotle’s conclusions from Met. L 3 about the diverse roles of matter and form at multiple levels of reality. On the one hand, the causes and principles of entities are distinct, but, on the other hand, they are the same, when considered universally and analogically (see Met. L 4, 1070a31–32). This theme is also a recapitulation of his discussion of the aporia in Met. B, where Aristotle poses the question of whether or not the principles and elements of substances and of the subsequent categories are the same or different. Strictly speaking, it is not possible that substances and the other categories share the same principles and elements, for, if this were the case, then the principles and elements would have to be common like Platonic Forms. This cannot be the case, since nothing precedes substances and the other categories. This first argument is, indeed, directed at Plato (see Met. L 4, 1070a33–1070b3). Aristotle’s second argument (1070b3–4) entails the priority of substance over relations. He asserts that substances cannot be reduced to elements of relations, nor is it possible for relations to be elevated to elements of substance, as the Platonists advocate. If the latter were possible, then the elements of relations would exist prior to a substance, which is absurd, for the relation is one category among others that are dependent on substance.21 Aristotle writes, “But again (b) substance is not an element in relative terms, nor is any of these an element in substance.” In his final argument, Aristotle begins by asking, “How can all things have the same elements?” (Met. L 4, 1070b4). He makes reference to the principles of Unity and Being, which are intelligible, precisely because they are universal and unable to be perceived by sense-perception.22 Aristotle argues that if it were the case that Unity and Being were elements of a compound, then the compound (BA) must be distinguished from each of the independent elements—namely, A and B. However, the compound in itself forms a unity and is, by implication, a kind of being. It would appear, therefore, that the compound (BA) becomes an element. For an element can be neither a substance nor a relation: “[B]ut it must be one or other. All things, then, have not the same elements” (Met. L 4, 1070b8). Aristotle, however, attempts to obviate the problem by way of accommodating both positions, that things have and do not have the same elements: “in a sense they have and in a sense they have not” (Met. L 4, 1070b10). In Met. L 4, 1070b10 ff., Aristotle advances what is perhaps the most brilliant solution to the problem—namely, that the principles and elements are the same, but only

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by way of analogy. The specific principles, such as hot and cold, apply solely to sensible entities, whereas they are inapplicable to entities of a mathematical nature, except by way of analogy. Thus, these elements and principles are not the same and are the same, only by analogy. The physical principles—form, matter, and privation—are applicable to all sensible entities, but even within the physical realm, they differ with respect to different genera; such as in the case of colors, they are white, black, and surface, whereas in the case of day and night, they are light, darkness, and air23 (see Met. L 4, 1070b15–21). Accidents, moreover, are affected by change and are also influenced by three principles.24 In Met. L 4, 1070b22, Aristotle makes a formal distinction between three elements and four principles. The three elements are different when they function as different genera, “as indeed is the ‘first cause’ which functions as a distinct moving cause for different things; e.g., the medical art is the moving cause in cases where health, disease, and the body are the elements.”25 The analogous principles indicate that form, privation, and matter are not homogeneous principles. The form appears to be the primary principle, whereas privation and matter retain their status as principles insofar as they relate to the principle of form26 (see Met. L 4, 1070b22–29). In this passage, Aristotle makes the distinction between internal and external causes. In any generation there is an external moving cause, such as a man, who produces a man a horse a horse, and so forth. (Although this passage refers to external and internal causality, one can anticipate Aristotle’s discussion of an external cause that moves all things. This external cause, or ontologically prior substance, would seem to make implicit reference to the First Mover, “which is the ultimate mover of everything in the universe.”)27 In his subsequent discussion of the nature and causal role of the moving cause, Aristotle curiously omits any mention of the final cause, though he admits to the identification of the proximate efficient cause with the formal cause of sensible substances. From the vantage point of oujsiva, Aristotle, therefore, emphasizes the three principles active in becoming—matter, form, and efficient cause—to the exclusion of final causality and privation (see Met. L 4, 1070b30–35). In addition to the specific type of causality in which the efficient causality coalesces with the formal and final causalities, Aristotle makes reference to a causality that differs fundamentally from the previous causes (see Phys. II). This reference is to the causality of the First Mover of all the cosmos, a subject to which Aristotle will return in the subsequent chapters. Met. L 5 reverts to the initial question in Met. L 4, but now in light of the doctrine of separate substances. Given the high premium on substance in general, Aristotle argues differently now for the sameness of principles and causes of all entities. “Some things can exist and some cannot, and it is the former that are substances. And therefore all things have the same causes, because, without

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substances, modifications and movements do not exist. Further, these causes will probably be soul and body, or reason and desire and body” (Met. L 5, 1070b36– 1071a4). As Cleary states, the ontological priority of substance over accidents entails the “criterion of non-reciprocal dependence,” which justifies “the claim that the causes of substances are the causes of accidents.”28 Significant to our discussion of the inner nature of nou:V is Aristotle’s subsequent attempt at accounting for the analogical sameness of principles in all things: that of actuality and potentiality. “And in yet another way, analogically identical things are principles, i.e., actuality and potency” (Met. L 5, 1071a5–6). However, Aristotle is quick to assert that the same entity in question is, on the one hand, actual, while, on the other hand, potential: “but these are not only different for different things but also apply in different ways to them. For in some cases the same thing exists at one time actually and at another potentially, e.g. wine or flesh or man does so”29 (Met. L 5, 1071a6–7). The subsequent lines contrast form and the composite of form and matter as states of actuality versus matter, which is always in a state of potentiality, for it is only matter that has the capacity to be formed or to become anything by virtue of the form or its privation. “For the form exists actually, if it can exist apart, and so does the complex of form and matter, and the privation, e.g. darkness or disease; but the matter exists potentially; for this is that which can become qualified either by the form or by the privation”30 (Met. L 5, 1071a8–11). Aristotle provides another example of the manner in which potentiality and actuality differ—that is, for entities “whose matter is not the same.”31 Neither is the form the same, given Aristotle’s new development of the argument. It would appear that Aristotle is suggesting that actuality can be different in kind (see Met. L 5, 1071a11–17). The same kind of matter—namely, flesh and bones—exists, on the one hand, in a state of potentiality, such as in the case of an embryo or a young child, whereas, on the other hand, it is in a state of actuality, as is seen in the adult. In (3), Aristotle wishes to preserve the hierarchy of causes in the Scala Naturae; the man in question is a moving cause, and the sun and its oblique course are distant moving causes on the man’s activities, contrasting within the man the material and formal causes, which consist of the proximate moving (efficient) cause of man. The actuality of the sun and its oblique course, therefore, is different in kind from the actuality of the man.32 The subsequent section of chapter 5 (1071a17 ff.) highlights the necessity of specifying the way in which causes are spoken of universally. This theme relates to Aristotle’s general question, which is whether or not the principles and causes of all entities are the same or different. While in Met. L 4 Aristotle asserts that the principles and causes are spoken of universally and analogically, in Met. L 5 Aristotle refines his notion of universality, which is his attempt at obviating

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the Platonic problem of the sameness of causes when speaking of first principles universally. Universally, a primary principle is a “this” (tode ti), which is always actual and also potential. Actuality and potentiality are the primary principles in every case.33 Essentially, as Aristotle’s subsequent section (1071a24 ff.) demonstrates, individuals within a genus are not specified by their species but rather by their individuality: “[A]nd those of things in the same species are different, not in species, but in the sense that the causes of different individuals are different, your matter and form and moving cause being different from mine, while in their universal definition they are the same” (Met. L 5, 1071a27–29). While it may appear, however, that Aristotle’s solution to first principles has fallen short of providing a “unifying vision of the cosmos which we might have expected from a first philosophy that is also a theology,”34 the passages 1071a29–1071b2 provide the elements of a global or unifying vision of the cosmos (see Met. L 5, 1071a29– 1071b2). In this passage, according to Cleary, Aristotle provides two and perhaps three attempts at a general inquiry into the principles and elements of all entities, which can overcome the lacunae mentioned above. In the first attempt, Aristotle recapitulates his claim that principles and elements of all things are the same by way of analogy only. In this manner, one can speak about “matter, form, privation, and the moving cause” in diverse genera. The principles of each category alter, but as Cleary rightly expresses, the “identity of the relationship is retained just as the same proportion may be said to hold between ratios that are filled out in different ways.”35 In the second attempt, Aristotle again places a high premium on substance, to which the categories are attached and subordinate. In a sense, says Aristotle, the causes of substances can be considered to be the causes of all entities, which leads Aristotle to discuss briefly his third attempt, that of the ontological priority of substance or “that which is first in respect of complete reality is the cause of all things,” as cited above. Although it still remains ambiguous as to how substances are the causes of all things, Cleary provides a plausible conjecture by linking the priority of substance with the fact that terms like “principle” and “element” are said in many ways. . . . Therefore, I think that the third possibility hinted at by Aristotle here is that terms like “principle” and “element” can have logical structure of pros hen equivocals or “focal meaning.” The principal or primary meaning of such terms as form, privation, and matter, is given with reference to substance and this, in turn, determines their application within other categories. In the present context, the significance of focal meaning is not simply its unifying linguistic function but rather its deep metaphysical implications for Aristotle. With regard to the question of XII 4 & 5, it provides an alternative way (other than proportional analogy) in which the principles and

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causes of all things can be the same. Since the inquiry is about being, whose central and focal meaning is substance, then the principles and causes of substance range over all the categories of being.36

Met. L 5 ends the first section of book L, in which the principles and elements are discussed in light of sensible substances. Met. L 6 makes a swift transition into a discussion and an account of suprasensible substances—a transition that has caused much controversy among commentators with respect to Aristotle’s justification for such a transition.37 Prior to discussing the essential nature of suprasensible substance, especially of divine nou:V, the questions of causality and duvnamiV and ejnevrgeia must be examined in order to set up the conceptual framework for our discussion of nou:V as a simple substance and final cause.

Conclusion In this chapter, I emphasized the Aristotelian rejection of Plato’s transcendent conception of the One. Aristotle affirms, rather, that the “one” is a pros hen equivocal. This led my discussion to Aristotle’s alternative solution and the replacement of Plato’s principles. In light of Met. L 4–5, we find that Aristotle, in analyzing the principles of sensible substance, concludes that these are analogous principles, which consist of form, privation, and matter. However, for separate or suprasensible substances, simplicity and actuality characterize these substances. That is, in Met. L 4–5, Aristotle presents the three principles—form, privation, and matter—as analogous principles of all sensible substances. These principles can be applied universally to all sensible substances. The application of these principles to separate substances will lead to an analysis of Aristotle’s doctrine of the simplicity of nou:V. Prior to this discussion, which will be presented in chapter 5, the conceptual framework of Aristotle’s metaphysics must be established. In chapter 4, I will present the question of Causality, the four causes, and the twofold doctrine of Being according to actuality and potentiality. Chapter 5 will analyze in detail Aristotle’s doctrine of the absolute simplicity and priority of nou:V as presented in Met. L 7 and 9, and De Anima III. 4–5. The main purpose of this fourth section is to dismiss any claim that divine nou:V is composite—a claim that would admit a degree of potentiality within nou:V. Divine nou:V has immediate knowledge of itself. I wish to argue, however, that this claim does not preclude nou:V from having knowledge of the world. While nou:V exercises final causality and possesses knowledge of the world, this kind of knowledge does not introduce multiplicity or a composition within nou:V. This latter claim will be essential for our analysis of Plotinus’s criticism of Aristotle’s doctrine, which we will see in the subsequent chapters. In his noetic doctrine, Aristotle wishes to preserve a unity of nou:V, while maintaining a strict duality between nou:V and

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the world, in spite of the commendable efforts of the Immanentist tradition of Aristotelians, who argue that nou:V operates as the soul of the world, introducing formal causality into nou:V.

Notes   1.  Elders, Aristotle’s Theory of the One, 59–60. See also Cleary, “Aristotle’s Criticism of Plato’s Theory of Form Numbers,” 16–25.   2.  Elders, Aristotle’s Theory of the One, 61.   3.  Elders, Aristotle’s Theory of the One, 61.   4.  In Met. D 6, Aristotle writes, as the second characteristic of the “one,” that things are called one when their undergirding substratum does not differ in kind (see Met. D 6, 1016a18–24).   5.  See V. Goldschmidt, La Théorie Aristotélicienne du Lieu, in Mélanges A. Diès (Paris: Vrin, 1956), 97 and 104, where it is remarked that the outer sphere is to the observer merely a “potentia divisibilis.” See Elders, Aristotle’s Theory of the One, 62, fn.3.   6.  See Elders, Aristotle’s Theory of the One, 63, fn.1, for an insightful connection between Aristotle’s use of the term kukloforiva (circular movement). This term, used in Met. I, indicates further his departure from the Platonic cosmology, for in his earlier work, such as in De Caelo, Aristotle employed the expression hJ kuvklw/ periforav, which approximates more to platonic terminology. Elders suggests that “the ‘whole’ here stands in the first place for the first heaven. . . . Aristotle uses elsewhere ‘whole’ with the same sense, e.g., in Meteor. 341a2 th:/ tou: o{lou perifora:/.”   7.  In D 6, Aristotle states as his third characteristic that a thing is called one when the genus is continuous, even if it differs by “opposite differentiae” (1016a26), or, as Cleary articulates it, “[T]hings are called one if the formula of their essence cannot be divided into another formula which also signifies the same essence” (J. Cleary, Unpublished version of “Aristotle’s Criticism of Plato’s First Principles”). (I am very grateful to Professor Cleary for having allowed me to survey and cite from his unpublished work on this topic.) Finally, the essence of what is to be one is to be an ajrchv or principle of Number, for it functions as the ultimate measure: “The essence of what is one is to be some kind of beginning of number; for the first measure is the beginning, since that by which we first know each class is the first measure of the class; the one, then, is the beginning of the knowable regarding each class. But the one is not the same in all classes” (Met. D 6, 1016b18–22). Cleary adds, “[T]he first measure in each genus is that by which we know its number” (Cleary, unpublished version of “Aristotle’s Criticism of Plato’s First Principles”). Cleary concludes, “Therefore, the one is the principle of the knowable in each case, although the one is not the same in all genera” (Cleary, unpublished version of “Aristotle’s Criticism of Plato’s First Principles”). (See Met. D 6, 1016b32–1017a3.)   8.  H. G. Apostle makes a very helpful suggestion regarding this passage. To perceive the substance at different angles is to lose sight of its oneness or unity. This claim is comparable to Aristotle’s assertion that the highest species of substances are the highest beings that there are in nature. “Just as the ultimate species of substances are beings in the

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highest degree above all, so they are indivisible (or are one as stated) in the highest degree. If one thinks of each part of a substance at different times, then he does not think of the substance itself as one at any of those times, and so he does not think of the substance as one at all” (Aristotle’s Metaphysics, trans. and commentary H. Apostle [Bloomington and London: Indiana University Press, 1966], 302, fn.23).   9.  See F. Cornford, “Mathematics and Dialectic in the Republic VI-VII,” Mind 41 (1932): 37–52, 173–190: 37 ff., for further discussion of the significance of novhsiV in the work of Plato. One characteristic of novhsiV is its upward movement of the intellect, its inductive pathway, which is contrary to a deductive or downward movement from an initial principle. (Plotinus will, however, adopt both, and this inclusion of novhsiV as possessing an upward and downward motion will furnish us with greater insight into his conception of nou:V.) 10.  Elders, Aristotle’s Theory of the One, 65. This original position of Aristotle’s, as was mentioned, is articulated transparently in his doctrine of novhsiV in Anal. Post. II. 19, 100b10–17. For further information on this topic, see J. M. Le Blond, Logique et méthode chez Aristote: Étude sur la recherché des principes dans la physique aristotélicienne (Paris: Librairie Philosophique J. Vrin, 1970), 131–39; O. Hamelin, Système d’Aristote, 3rd ed. (Paris: Vrin, 1976), 258; H. Bonitz, Index Aristotelicus, 2nd ed. (Berlin: Akademische Druck- U. Verlagsanstalt Graz, 1955), 490b45–491b34; C. H. Kahn, “The Role of NOUS in the Cognition of First Principles in Posterior Analytics II.19,” in Aristotle on Science: The “Posterior Analytics,” Proceedings of the Eighth Symposium Aristotelicum, ed. E. Berti (Padua: Antenore, 1981), 385–414; L. A. Kosman, “Understanding, Explanation, and Insight in Aristotle’s Posterior Analytics,” in Exegesis and Argument: Studies in Greek Philosophy Presented to Gregory Vlastos, ed. E. N. Lee, A. P. D. Mourelatos, and R. M. Rorty (Assen, The Netherlands: Van Gorcum & Comp. B.V., 1973); and J. H. Lesher, “The Meaning of NOUS in the Posterior Analytics,” Phronesis 18 (1973): 44–68. 11.  Cleary further writes in his unpublished version of “Aristotle’s Criticism of Plato’s First Principles”: “In summary (1052a33–6), those things are one which are continuous by nature (to suneches phusei), and the whole (to holon), and the individual (to kath hekaston) and the universal (katholou). All these are one in view of the fact that they are indivisible (toi adiaireton); some in motion, and others in thought or in their formula (ton logon).” 12.  Cleary, unpublished version of “Aristotle’s Criticism of Plato’s First Principles.” 13.  See Elders, Aristotle’s Theory of the One, 80. 14.  As Cleary says, it “cannot be a substance which is one and apart from the many (hen ti para ta polla)—for it is common to all—so it must be a predicate” (Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 13). 15.  Cleary, unpublished version of “Aristotle’s Criticism of Plato’s First Principles.” 16.  Cleary concludes, “Aristotle resists the Pythagorean-Platonic tendency to make numbers the substances of things because they can be counted, and insists that they are always the numbers of something; i.e. predicates not substances” (Cleary, unpublished version of “Aristotle’s Criticism of Plato’s First Principles”). Cleary adds, “In the jargon of

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medieval philosophy, we can conclude that for Aristotle both one and being are transcendental predicates and not independent substances. Unity, as with Being, is related to each category within a genus and, as a result, it and they are not located within the category of whatness (ti esti) only, nor inequality only” (Cleary, unpublished version of “Aristotle’s Criticism of Plato’s First Principles”). 17.  See Elders, Aristotle’s Theory of the One, 87–89, for further discussion of this topic. Elders rightly concludes his remarks about Plato’s conception of motion by saying that “it would seem that motion pervades all being with the exception of the first principle, and that we must distinguish sharply between two degrees of being, the material and the immaterial, each of which possesses its own characteristic movement.” 18.  See Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 84. 19.  Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 84. 20.  See Metaphysics N 1–2, especially 1089a25 and Met. Q 10, 1051a34. 21.  Cleary captures this brief argument well when he writes, “The implicit rationale seems to be that, if relations were the elements of substance (as the Platonists held?), then they would be prior in existence to substances, which is impossible according to his categories because relations are dependent attributes of substance. On the other hand, relations cannot be composed of substances because such a composite would be itself a substance, which is again contrary to his categories” (Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 86). 22.  See Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 86. 23.  See also L. Elders, Aristotle’s Theology: A Commentary on Book L of the Metaphysics (Assen, The Netherlands: Van Gorcum & Comp. N.V., 1972), 118: “Sensible bodies (touvtwn) have the same elements (viz. the hot and the cold and matter), but we cannot say that all categories (substances, qualities, activity . . .) have identical principles: their principles (form, privation, matter) are the same by analogy.” 24.  “He substantifies them,” says Elders, Aristotle’s Theology, 119. 25.  Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 87. 26.  See Elders, Aristotle’s Theology, 119. See also the excellent chapter by J. Vuillemin, De la logique à la théologie; cinq études sur Aristote (Paris: Flammarion, 1967), 12–22, especially 19–21. 27.  Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 87. 28.  Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 89. See also Cleary’s reconstruction of this argument on page 89. 29.  With respect to this example, see Cleary: “The examples given of such cases are wine, flesh, and man, but I think that the last two are to be taken as distinct entities, each of which is at one time potential and at another time actual. Thus, prior to the constitution of flesh from its material elements, they are potentially flesh and then they become flesh when these elements have been structured according to the appropriate ratio” (Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 90). 30.  See Elders, Aristotle’s Theology, 126–27. Moreover, actuality is predisposed to become its opposite (i.e., another actuality). It is, therefore, both actual and potential at the same time.

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31.  Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 90. 32.  See Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 91. 33.  However, these principles are universals. See Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 91. See also Elders, Aristotle’s Theology, 130–31. 34.  Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 92. 35.  Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 93. 36.  Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 94. 37.  I give Cleary the last word on this topic. His suggestion at explaining such a transition is extremely helpful and insightful. A parallel can be found in Metaphysics VI 1 (1026a30–31) where Aristotle claims that first philosophy is both a special science and also universal precisely because it is first. It is a peculiar characteristic of the logical structure called a pros hen equivocal that its primary instance is both particular and universal. This has an important bearing on the perennial problem in Aristotelian scholarship about whether the special science of theology can be integrated into a general science of being qua being. Despite the absence of this description of metaphysics from Lambda, I think there is some evidence that such a conception is present in both the analogical and focal meanings of being. For instance, these two meanings are presented as two ways in which we can say that the principles and causes of all things are the same. While the analogical sameness of the principles seems to hold only in a general manner, it would appear that pros hen sameness holds for both particular and universal. The latter kind of sameness provides the crucial connection between theology and general ontology, even though Aristotle does not here spell out the details. Still I think that this is the perspective from which we should view XII 6 with its sudden transition to an inquiry into supersensible substance. Since Aristotle does not stop to explain this transition, commentators have often been puzzled as to how the previous inquiry into the principles of sensible substance fits with what follows. The conclusion of XII 5 contains a typical survey of his results about the principles of sensible things—what they are and how many, how they are the same and how they are different. The challenge for Aristotelian scholars is to make sense of the fact that he uses these conclusions as if they were stepping-stones into the realm of supersensible substances. (Cleary, “Aristotle’s Criticism of Plato’s First Principles,” 94–95)

c h a pte r f o u r

The Anatomy of Aristotle’s Metaphysics

Introduction: The Question of Causality Aristotle’s cosmology is governed and ordered by material and formal causality, which, when analyzed, consists of a fourfold causal doctrine: material, formal, efficient, and final causality.1 Aristotle’s doctrine of four causes is his answer to the perennial question, “What are the causes of the cosmos?”2 In Metaphysics A, Aristotle claims that, contrary to his predecessors, only he has completely captured all the causes of the cosmos.3 The Greek terms aijtiva and ai[tioV refer to Aristotle’s notion of cause. The term aijtiva is an adjective that is used substantively, and it means “that on which legal responsibility for a given state of affairs can be laid.” In its substantive use, ai[tion refers to the “ ‘credit’ for good or bad, the legal ‘responsibility’ for an act.”4 With respect to Aristotle’s cosmology, aijtiva refers to the rational explanation of the factual structure of the cosmos, and of why particular objects in the cosmos come into being and can be defined by the intellect.5 Causes are not merely conceptually based; they relate to the real events in the cosmos. Each of the four Aristotelian causes provides partial explanations for the order of the cosmos. An analysis of the twofold causality of matter and form creates the conceptual framework for the subsequent analysis of the fourfold causal doctrine. For both Plato and Aristotle, all scientific inquiry requires the study of causes, the reason why Nature is structured the way it is. Moreover, to know causes entails a degree of stability of form, which the intellect apprehends from the sensible object. However, the difference between Plato’s and Aristotle’s theories 73

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of science rests upon the status each one gives to the intellect’s object. According to Aristotle, Plato taught that real objects of knowledge can be defined, yet remain separate, from the perceptible objects. The Forms maintain a transcendent, immutable, and eternal status in relation to the physical world’s transient objects, each of which has a correlating Form;6 the Forms are eternal patterns against which the natural world is fashioned by the dhmiourgovV (Demiurge) and preserved by the causes of Nature. Aristotle’s main charge against Plato, which was seen in chapter 1, is that Plato’s theory of Forms is ineffective: “Again, it must be held to be impossible that the substance, and that of which it is the substance, should exist apart; how, therefore, can the Ideas, being the substance of things, exist apart?” (Met. A 1, 991b1–3; see also Met. M 9, 1086b5–10). The controversy surrounds Aristotle’s interpretation of Plato’s rendering of the term cwrismovV and, thus, concerns the status of the Forms. Does the Forms’ cwrismovV necessarily entail merely their conceptual independence, or strictly their ontological independence? In the Parmenides, 130b, Plato clearly argues for the separability of the Forms. However, he does not provide a detailed explanation of this proposed doctrine. (Nor, in fact, does Aristotle provide an explanation for his criticism of Plato.)7 This debate also is widespread in the French-speaking world. Yannis Prélorentzos asserts that when referring to the Rep. 509d–511e, it is inappropriate to speak of two “Worlds.” Rather, one should speak of “deux domaines d’un seul et même monde (Socrate parle de deux ‘lieux’ ou ‘genres’).”8 Monique Dixsaut sympathizes with this view; the Forms are not separate in another world, but the separation entails two dimensions of a same world.9 Luc Brisson, however, does not endorse this theory. It is clear for him that Plato makes a radical, ontological separation between the Forms and the sensible world, since only an intelligible principle distinct from the sensible thing can provide a proper measure of the thing’s intelligibility.10 Yvon Lafrance follows the interpretation of Brisson.11 In fact, both Brisson and Lafrance follow Harold Cherniss.12 According to Cherniss, Brisson, and Lafrance, the cwrismovV is the heart of Plato’s philosophy of transcendence. It is difficult for analytic philosophers, such as Vlastos, Kraut, and Fine, to accept this transcendent status of the Forms, since analytic philosophy itself does not permit such a dimension to philosophy. Aristotle’s critique of Plato is of Plato’s assertion of the real and universal status of Forms. In the early part of Plato’s Parmenides, Plato argues that the Form is not a concept as such, novhma, but is beyond a concept. Analytic philosophers, however, tend to view Plato’s Forms as concepts and, therefore, deny the transcendent nature of the Forms. It is, however, beyond the scope of this project to explore further the ramifications of either position. In this section, I wish merely to accentuate Aristotle’s conviction that

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Plato advances a doctrine of the separation of the Forms and that, according to Aristotle, Plato’s theory is ineffective. The Aristotelian legacy consists of affirming the intelligibility of the transient, physical world. Aristotle’s comments on Plato’s description of the Forms are clear: they are but “empty words and poetic metaphors,” since they do not contribute to the scientific inquiry of knowledge.13 Although Aristotle refutes the cwrismovV of Plato’s Forms, he steadfastly adheres to Plato’s vision of the universe as an organized hierarchy of beings, and of the grades of perfection that ensue from the ontological development and surpassing of one stage to another.14 Aristotle maintains that philosophy is the attempt to explain the causes of Nature not by reference to a transcendent, separate cause (i.e., the Platonic Forms), but to the immanent activity of form in matter. Every sensible substance is characterized by the causal unit of matter and form. In reality, form and matter in sensible substances are inseparable, in that the form is the intrinsic, universal principle that defines a sensible substance, and must “cooperate” with matter, since matter individualizes form. The sensible substance is the matter organized and determined by the formal principle. Thus, to posit a separation between form and matter is absurd, since one would have to account for the unity of a thing by first asserting its divisible components. Only logically is form separable, since it can be abstracted and considered apart from matter by the human intellect. However, Aristotle remains sympathetic to the Platonic teaching that scientific knowledge is possible, but is attained by the intellect’s apprehension of the form inherent in the transiency of matter. Ultimately, Aristotle labored to explain the phenomenon of motion or change,15 which, he claims, Plato’s Forms were unable to account for (see Met. A 1, 991a8–10). Within the fluctuating material cosmos, form is the stable, intelligible principle. The Aristotelian form, then, is unchangeable and responsible for the intelligibility of each individual sensible substance in the natural world. Thus, the universal principle, form, is located within the individual substance.16 Although form has its logical inherence in the human mind, it must exist extra-mentally in the material object itself; otherwise, the material object cannot be considered as an individual unity of matter and form. Insofar as the material object is informed, it is a real thing. Thus, contrary to Plato’s claim that the Form is transcendent to the object, Aristotle argues that form is inherent and immanently operative within it, and accounts for the intelligibility and realness of the material object. Aristotle’s sensible universe is characterized by substances that are in change or fluctuation in four ways: change of substance, of quality, of quantity, and of place.17 Change entails a beginning, an end, and a subject that endures throughout the change (see Phys., V 1, 224a34–b4).

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With respect to changes of quality, of quantity, and of place, a substance persists throughout the change. Yet the substance cannot evidently persist throughout its change when change means generation or destruction; Socrates cannot persist throughout his own birth and death. Thus, in the Scala Naturae, Aristotle presents the generation and destruction of substance as a unique type of change. Aristotle presents a formless matter at the bottom of the cosmos, and at the farthest extreme of the cosmos, he posits a matterless form. Prior to the complexity of material beings, prime matter (prwvth u{lh), at the lowest level of the cosmos, remains the simplest matter and, ultimately, the primary condition of change in the fluctuating world.18 Uninformed matter cannot exist per se. In other words, prime matter, matter in itself, is a logical inference that Aristotle postulates in order to consider an indeterminate condition for change to take place in beings.19 Therefore, its priority is at the level of logic. Indeterminate as it is, prime matter is the underlying substrate of changing substances, logically considered. Yet, although indeterminate, prime matter is determinable, since it is potentially any thing. Prime matter merely requires the impression of a universal principle—namely, form—to enable matter to become some particular thing. Thus, matter and form are correlative terms that must cooperate to create the unity of a sensible thing.20 After prime matter there appear the four elements, and then the mixtures of these elements: earth, water, air, and fire. (This relationship between proximate matter and remote matter also exemplifies such an increasing level of determination.) Yet these elements are not indeterminate, as their simple nature would suggest, but they are already determined bodies through the activity of form. Collectively and duly proportioned at the lowest level of the cosmos, they form minerals, which become the material for plants and animals. Ascending the hierarchy, the human being presupposes the material and formal complexity of the preceding stages. The human is the most highly organized being of animals, because of the human’s capacity to reason, especially active reason. Surpassing the human being are the pure intelligent substances devoid of matter. At the summit of the hierarchy stands a single, simple substance of pure form—nou:V—which will be discussed in the next chapter.21

The Four Causes As mentioned above, the sensible substance is composed of the inseparable causal unit of matter and form. In the cosmos, the composite level of matter and form is located in the concrete, transient conditions of sensible reality (i.e., earth), a stage below that of the sublunary sphere that contains only rotating, immaterial forms—the “gods.” Whereas the material cause (u{lh)22 is the material fabric

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out of which something is produced,23 the formal cause (ei[doV) is the inner, animating principle of change that clearly defines a sensible substance as such and distinguishes it from another kind of substance—namely, the species. The status of matter correlates to the four levels of change, and change itself correlates to four kinds of matter: local matter or matter for locomotion, matter for alteration, matter for change of size, and matter for generation and destruction. Change presupposes matter. Matter is the indeterminate dimension of a substance that acquires more determination in proportion to the increase of formal influence. With respect to the formal cause, Aristotle, in Phys. II 3, 194b27, considers form as the “archetype, i.e., the definition [logos] of the essence, and its genera, [which are] called causes” (Phys. II 3, 194b27). The form of a thing, as the inner, animating principle of alteration, provides the essence of a thing. The logos of the essence is what Aristotle refers to as the structure or “order” of the essence, which is particularized, or “instantiated,” in matter, thus rendering the thing intelligible.24 Both the form and the essence are required to provide an intelligent account of things. The subsequent two causes, efficient (to; o{qen hJ kivnhsiV) and final, are two necessary dimensions to the causal order of the cosmos, establishing, in relation to the material and formal causes, a fourfold causal doctrine. They coalesce in that “the changer will always introduce a form . . . which, when it moves, will be the principle and cause of the change. For instance, an actual man makes what is potentially a man into a man” (Phys. III.2, 202a9–12). The formal cause is inseparable from the efficient and final causes.25 These causes are conceptually separable, and, in fact, the efficient cause is usually separate from the formal, final cause at the level of the individual, though this is not the case at the level of species. The efficient cause refers to the being in actuality that initiates movement; it refers to the primary source of change (see Phys. II 3, 194b29–30), the agent of change in a substance26 (see Phys. II 1, 193b2). Again, the efficient and formal causes are not mutually exclusive. The principal agent of change is, therefore, identified with that which introduces the form. As a primary principle of change, the efficient cause is fully actual. Only form is actual. Therefore, efficient cause coalesces with, and is an expression of, formal causality, logically speaking.27 The final cause, “that for the sake of which” [to; ou{ e{neka] (Phys. II 3, 194b32–3), is the end or purpose (tevloV) for which the thing is brought into being,28 or the goal to which the growth development is directed.29 The final cause rightly characterizes Aristotle’s philosophy as teleological, since the emphasis is on the purpose or end, which is immanently operative in the thing during its development. Aristotle alludes to the fact that the final cause is not logically, but really, different from the formal cause and is an expression of form (see Phys. II 8, 199a30–2).

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Although the form is necessarily a realized state (i.e., the necessary condition of its assuming the role of the primary principle of motion), it is a state relatively realized in relation to a higher, simpler stage with less matter. Of course, such a form is fully realized in the appropriate matter and not in a separate state, which is another point all together. However, the separate form, and its distance from the form/matter composite, provides the comprehensive view of causality within the cosmos. The separate form provides the measure of the status of each level of form and the final cause. Physical forms like man may clearly reach their end, but in the comprehensive view of form and final causality, this man’s form is not absolute, but rather is relative to the form of a separate substance. (This is clearly seen in Aristotle’s De Anima, in which Aristotle presents an ascending scale of actuality and form within substances. This will be discussed below.) Each stage yearns or strives for a higher form.30 At each stage of the sensible substance’s development, its form is achieving increasingly full actualization, moving toward its end (tevloV). Paradoxically, the end to which each thing aspires is inherent in the thing itself from the very beginning. The end is not severed from the growth process of the natural object. It is form that is the propelling force or power inherently operative in each thing, and as its moving principle, it is considered the thing’s end. It is form in its actual state that functions as the final cause. As actuality precedes potency (Met. H 1, 1049b5), the end (tevloV) precedes the actualized state of the thing, absolutely speaking. The tevloV is the force actualizing the substance’s potencies. Again, the end is the form in its realized state.31 Therefore, to render the process intelligible, form must be expressed as a final cause.32 With respect to matter, form is actual; however, in relation to the final tevloV, form is, in this present state of development, potential. Hence, whereas form in the process of self-actualization is potential, form realized (tevloV) is form fully actual.33 The end is only present potentially, as an oak is potentially present in the acorn, and actually present when the acorn becomes an oak. Development or growth entails the emergence of the actualization from that which is potential. Yet development does not imply the emergence of something new, since the end is already inherent in the thing itself; the tevloV already governs the developing process of the thing’s actualization. Development does not entail the changing of one infima species into another. In the Categories, Aristotle argues that each genus includes its unchanging infima species, and that development occurs only within the particular specimen, the substance, of the species. However, in his later works, Aristotle suggests that the infima species, and not the specimen, is the true substance. The genus alone is too abstract, indeterminate, and universal to be a substance. Yet its development—its concrete determination through the admixture of diverse differentiae—enables the genus to become in the infima species an “indivisible (‘atomic’) unity of universal and individual.”34

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duvnamiV and ejnevrgeia The original meaning of the concept of ejnevrgeia, and, moreover, its rapport with duvnamiV and ejntelevceia, have been discussed philosophically and philologically for many generations, resulting in a lively debate that has yet to see closure. The debate centers around the fact that the concept of ejnevrgeia has different meanings. It is generally accepted by scholars that the Protrepticus is Aristotle’s earliest work and that it is a reflection of his adherence to Plato’s metaphysics. In the Protrepticus, Aristotle makes a significant distinction between two kinds of “living,” one with respect to power (kata; duvnamin) and also to activity (kat= ejnevrgeian): Things are said to be alive in two senses, in virtue of a potentiality and in virtue of an actuality; for we describe as seeing both those animals which have sight and are naturally capable of seeing, even if they happen to have their eyes shut, and those which are using this faculty and are looking at something. Similarly with knowing and cognition: we sometimes mean by it the use of the faculty and contemplation, sometimes the possession of the faculty and having knowledge. If, then, we distinguish life from non-life by the possession of perception, and perceiving has two senses—properly of using one’s senses, in another way of being able to use them (it is for this reason, it seems, that we say even of a sleeping man that he perceives)—it is clear that living will correspondingly be taken in two senses: a waking man must be said to live in the true and proper sense; as for a sleeping man, because he is capable of passing into the activity in virtue of which we say that a man is waking and perceiving something, it is for this reason and with reference to this that we describe him as living. When, therefore, each of two things is called by the same term, the one by being active the other by being passive, we shall say that the former possesses the property to a greater degree; e.g., we shall say that a man who uses knowledge knows to a greater degree than a man who possesses knowledge, and that a man who is looking at something sees to a greater degree than one who can do so. (See Iamblichus Protrepticus 56.13–59.17 Pistelli, in Barnes; [B79 and 81] or 14, Ross)

The distinction prepares the ground for Aristotle’s development of the concept of ejnevrgeia, which, as we shall see, was originally meant to signify “activity” but was later altered to signify “actuality.”35 With respect to the concept duvnamiV, Aristotle explains in his philosophical lexicon (Met. D 12) that duvnamiV has various meanings. With respect to ejnevrgeia, the attempt at defining the concept becomes more complicated. In his Index Aristotelicus, H. Bonitz writes about the concept ejnevrgeia: Quoniam potentiae vel opponitur is motus et actus, quo res ad perfectionem naturae suae perducitur, vel ipsa illa perfectio ejnergeiva/ levgetai ta; me;n wJV kivnhsiV

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pro;V duvnamin, ta; d= wJV oujsi;a provV tina u{lhn (Met. Q 6, 1048b8). Quod discrimen quamquam non potest ubique accurate observari, tamen ad perlustrandam varietatem usus aptum est. (Vol. V 251a-21–27)

While this distinction remains useful, it does not reflect the various ways in which ejnevrgeia is used in the Aristotelian corpus.36 In Met. Q, Aristotle introduces the terms duvnamiV and ejnevrgeia as corollaries to the matter-form distinction in order to further explain real development (i.e., change) in the cosmos.37 The concept of ejnevrgeia in this case is used in the sense of the traditional term, actuality. As a result, ejnevrgeia corresponds with the concept duvnamiV, taken as potentiality. Thus, ejnevrgeia and duvnamiV are a pair of principles that are applicable to the entire range of being analogously, as we have seen above (see Met. L 4–5). However, ejnevrgeia (actuality) and duvnamiV differ from matter and form in that the latter pair does not properly analyze the real movement of a thing, whereas the former pair relates to the dynamic changes occurring in real, particular substances and their modes of existence. The concepts of ejnevrgeia as actuality and duvnamiV include teleological aspects, which the matter-form pair does not include.38 As one considers the ascending order of the cosmos, one can only conceptually perceive an increase in form and a decrease in matter. Whereas when the sensible thing changes, matter and form per se do not change, since matter and form remain abstract causal principles in any sensible substance. Consequently, the matter-form distinction remains an abstraction from the changing, sensible thing, and insofar as the distinction is an abstraction, it is reduced to a static representation of the sensible phenomena.39 Thus, ejnevrgeia and duvnamiV render a more precise account of change in real sensible substances, for they include a teleological aspect.40 More specifically, ejnevrgeia and duvnamiV are two senses of being, whereas matter and form are two kinds of cause.41 Aristotle is, in fact, the inventor of the distinction between ejnevrgeia and duvnamiV. While Aristotle credits Plato for the matter-form distinction, as seen at Physics I 9, where Aristotle provides a solution to Parmenides’ challenge to the possibility of generation and states that “some others [Plato] have also touched on [matter], but not sufficiently” (Physics I 9, 191b35–36, trans. Menn), he does not credit Plato for the ejnevrgeia-duvnamiV distinction.42 In fact, Aristotle does not even credit Plato for the Aristotelian (nominative) use of the concept duvnamiV. Plato appears to have used the concept dunavmei adverbially in the Statesman 266b3 and in the Timaeus 54b4–5.43 Aristotle’s use of to; o]n dunavmei does not refer back to the adverbial sense, but rather to the noun duvnamiV. Plato uses the concept to mean active and passive powers (see Sophist 247e3–4), and Aristotle appears to accept these powers to move and to be moved as the initial

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meaning of the concept duvnamiV (see Met. Q 1, 1045b35–1046a2). However, in his philosophical lexicon, Met. D 12, where Aristotle discusses the many senses of duvnamiV, Aristotle does not mention to; o]n dunavmei. There must, then, be an original and primary (nominative) meaning of to; o]n dunavmei to which Aristotle refers, if at all. Aristotle’s reflections on the concept duvnamiV, considered as an ability to do or suffer, elucidates the more central concept of an ability in general and, Menn proposes, “extends duvnamiV and the dunatovn by analogy, from the ability (or what is able) to do or suffer, to the ability (or what is able) to be.”44 However, this explanation does not provide an adequate reason for the correlation between duvnamiV and ejnevrgeia. Aristotle’s use of the correlative concept, ejnevrgeia, may provide the necessary clue to the Aristotelian picture of the doctrine of duvnamiV and ejnevrgeia. The concept of ejnevrgeia is not found in the pre-Socratics or in Plato, and we may conclude, then, that Aristotle invented the concept.45 However, the etymology of the concept does not correspond with what is traditionally translated as “actuality.” Rather, it refers to “activity.” To complicate matters even more, in addition to using the concept ejnevrgeia, Aristotle uses yet another term to designate “actuality”—namely, ejntelevceia, which is used sparingly throughout the Aristotelian corpus, but which always means “actuality” when it is employed, whereas ejnevrgeia can mean either “activity” or “actuality,” depending on the context. The question that has been raised is this: “Why does Aristotle invent two concepts for ‘actuality’ and, subsequently, why did he, on the one hand, invent a new concept for ‘actuality,’ and, on the other, employ the concept of ejnevrgeia for what can be translated into English as ‘activity’?”46 Within his works, Aristotle appears to be ambiguous about the meaning of ejnevrgeia, whether it translates as “actuality” or “activity,” but by the concept ejntelevceia, Aristotle always means actuality. At Met. Q 3, Aristotle states that in addition to its application to ejntelevceia, ejnevrgeia is extended to motion or change, since motion or change appears to be ejnevrgeia [hJ pro;V th;n ejntelevceian suntiqemevnh] (see Met. Q 3, 1047a30–32). However, Aristotle states that ejnevrgeia are also in the activity of, for example, God’s acting on the heavens, and this involves no motion in the ejnergou:n. Thus ejnevrgeia, according to Aristotle, is applicable to actual existence (ejntelevceia) within the categories of substance and its accidents, which are not said to be in motion. Aristotle, however, claims that the most obvious reflections of ejnevrgeia are motions. As a result, Aristotle’s starting point is that of the concept of ejnevrgeia considered as activity—the kind of activity that indicates motion and by analogy incorporates all the categories. However, ejntelevceia is always employed for “actuality.”47 Nor can Bonitz’s explanation help, as I have cited it above, for he

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fails to reveal how the different meanings of ejnevrgeia, of actuality and activity, are related, and he states only that, like ejnevrgeia, ejntelevceia opposes duvnamiV, and that these concepts are interchangeable. There is, however, a firm relationship between Aristotle’s conception of activity and of actuality, given Aristotle’s liberal employment of the concept of ejnevrgeia for these two terms, and the unique concept of duvnamiV as their correlative.48 There are two ways in which we can reconstruct this connection. On the one hand, we can affirm that activity is a derivative of actuality and that ejnevrgeia is better translated as “actuality,” for, in this case, activity would be an instantiation or a unique extension of actuality. On the other hand, we may assert the opposite claim, that actuality is a derivative of activity, rendering “activity” the better translation of ejnevrgeia, and by doing so, we interpret the “actual existence of a thing (in any category including substance) as itself an activity, in the Thomist phrase of an “act of being,” as Kosman has argued. The problem is expressed very well by Menn: either (i) Aristotle recognizes by reflection on the concept of activity that this is a special application of the more abstract modal concept of actuality, which may be called ejnevrgeia from its most obvious case; or (ii) Aristotle recognizes, by reflection on the existence of different kinds of things, that actual existence in each case consists in the appropriate activity, that “to be for living things is to live” (De Anima 415b13), so that every actuality is an instance of ejnevrgeia.49

We can track, therefore, the origins of Aristotle’s concept of ejnevrgeia, beginning with the assumption that the concept of ejnevrgeia was first understood as “activity” and then, as Menn states, developed into a new conception of the opposition of being-in-potentiality and being-in-actuality. The concept of activity remains fundamental, and never becomes a specialization of an abstract concept of actuality; at the same time, while the concept of actuality is derivative from the concept of activity, actuality is not an instance of activity, and there is no “act of being.”50

As mentioned above, Aristotle makes a subtle distinction between ejnevrgeia and ejntelevceia—a distinction that has caused controversy in Aristotelian scholarship, due to the lack of a precise definition of ejntelevceia. Several recent attempts by scholars have been made to clarify this difference, but no consensus has been reached. By way of approaching this topic, G. Blair,51 for instance, has disputed and rejected the traditional argument that Aristotle introduced the distinction between duvnamiV and ejnevrgeia as an explanatory theory of change.52 He argues that Aristotle invented the concept ejnevrgeia, rather, because the activity of thinking is not a type of process (i.e., no change is involved in the

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activity of thinking, but only in the states leading up to thinking).53 Therefore, kivnhsiV only explains the active essence of ejnevrgeia, but it cannot replace it, for kivnhsiV corresponds properly to duvnamiV, as we shall see in more detail below. Thus, Blair54 attempts to define and interpret ejnevrgeia not as actuality, but rather as “internal activity.” In Met. Q 3, Aristotle argues against the Megarians, who assert that only when an entity is in activity can it be said to be capable.55 Aristotle disputes this assertion and defends the reality of duvnamiV, for duvnamiV explains change (kivnhsiV), unlike the Megarians’ position, which attempts at denying reality to change and generation, for it entails the incapacity of that which is not fully and actually occurring (see Met. Q 3, 1047a10–23). In order for philosophy adequately to reflect our commonsense experience, Aristotle draws the fundamental distinction between duvnamiV and ejnevrgeia, against the Megarians, who make potentiality and actuality the same. Line 24 provides a tentative definition of duvnamiV as that which is “capable of doing something if there will be nothing impossible in its having the actuality of that of which it is said to have the capacity” (Met. Q 3, 1047a24). Prima facie this definition seems to be circular, for it presupposes a third term—namely, activity—in order to render it intelligible.56 What remains interesting from the standpoint of the distinction between duvnamiV and ejnevrgeia is Aristotle’s qualification or introduction of a new concept—namely, ejntelevceia. Lines 30–32 highlight a distinction between ejnevrgeia and ejntelevceia, and in this distinction, Aristotle aligns ejnevrgeia with kivnesiV. “The word ‘actuality’ [ejnevrgeia], which we connect with ‘complete reality’ [ejntelevceia], has, in the main, been extended from movements to other things; for actuality in the strict sense is thought to be identical with movement”; ejlhvluqe d= hJ ejnevrgeia tou[noma, hJ pro;V th;n ejntelevceian suntiqemevnh, kai; ejpi; ta; a[lla ejk tw:n kinhvsewn mavlista` (Met. Q 3, 1047a30–32). In this light, Aristotle argues against thinkers, possibly Plato, who do not ascribe movement (kinei:sqai) to nonexisting entities (see Met. Q 3, 1047a33–35). Only the Megarians would claim that entities that move (kinouvmena) do not possess existence. Again, Aristotle introduces at this point the distinction between ejnevrgeia and ejntelevceia in order to provide the correlative terms for duvnamiV.57 Aristotle’s reason is given in the next line: “For of non-existent things some exist potentially; but they do not exist, because they do not exist in complete reality”; tw:n ga;r mh; o[ntwn ei[nia dunavmei ejstin` oujk e[sti dev, o{ti oujk ejnteleceiva/ ejstivn (Met. Q 3, 1047b1–2). This does not provide us, however, with a clear definition of ejntelevceia. Once again, scholars are divided over the exact meaning of Aristotle’s concept ejntelevceia. D. Graham has argued that Aristotle mistakenly derives ejntelevceia from ejntevlwV e[cein.58 G. Blair, however, has made a strong case for the inter-

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pretation of ejntelevceia in light of the meaning of ejnevrgeia, the en- signifying “having the end within,” as opposed to self-sufficiency or completeness. As a result, Blair prefers to translate ejntelevceia as “internal-end-having” or “having the end within,” contrary to having the end from without.59 Given that duvnamiV has two meanings, the capacity to do something and the capacity to be something, Blair argues that the invention of ejntelevceia was to account for the second correlate of duvnamiV, and to provide a justification for how a thing is capable of changing into another.60 This argument caught the eye of some scholars, such as J. Cleary, who writes of this that it “is an attractively clear and testable hypothesis because it implies that Aristotle should use the term ejnevrgeia in contexts where he is discussing the active sense of duvnamiV associated in particular with living things, while using the term ejntelevceia where the topic is the passive sense of duvnamiV that is linked with change.”61 Both Blair and Cleary agree that Aristotle, however, does not use ejntelevceia in any consistent way that would reveal a pattern of his thought. We continue to be at a loss as to what ejntelevceia can mean, since Aristotle provides no definition of the concept. S. Menn, however, provides a viable solution to this problem. According to Menn, ejntelevceia has always meant “actuality,” whereas ejnevrgeia initially meant “activity” and meant “actuality” only later, in his mature works—an analogical extension that was not discussed in the Physics or in the first seven books of the Metaphysics. In Met. Q and L, however, Aristotle uses ejnevrgeia in place of ejntelevceia in order to account for actuality.62 Aristotle’s intention behind such a strategy, according to Menn, is to demonstrate that ejnevrgeia is prior to duvnamiV, thereby establishing the ontological priority of the unmoved Mover, considered as the first principle, pure ejnevrgeia free of any duvnamiV, which will be discussed below.63 Aristotle prefaces his discussion of being in Met. Q 1 by considering the two central modes of being: potentiality and actuality (ejntelevceia, 1045b35). His primary task is to highlight the various ways in which potentiality is used (see Met. Q 1, 1045b33–1046a4). Aristotle provides two senses of the term duvnamiV64 (see Met. Q 1, 1045b35– 1046a11, and Met. D 12). The first sense of duvnamiV refers to the power that one substance possesses in order to influence the movement of another. “For one kind is a potency of being acted on, i.e., the originative source, in the very thing acted on, of its being passively changed by another thing or by itself qua other” (Met. Q 1, 1045b35). The second sense refers to the capacity of a material substance to receive a form. “[A]nd another kind is a state of insusceptibility to change for the worse and to destruction by another thing or by the thing itself qua other by virtue of an originative source of change” (Met. Q 1, 1046a13–15).

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The first sense may be called an active potency, and the latter a passive potency.65 An active potency entails the actualization or realization of a potency, prior to which state it remained passive. Thus, the active potency can effect change in individual substances by actualizing their potencies. Potency, then, cannot be defined by abstract concepts: it is merely observed in a particular, individual substance.66 Potency characterizes the real change or development of a substance.67 However, potency alone cannot fully explain change, since nothing develops from passive potency to active potency without the agency of an actual thing.68 A being’s full development into maturity entails not only two states of potency, but also an agent already fully actual that is responsible for influencing movement in the substance. Therefore, the actual state of the agent is the necessary condition for the actualization of the two states of potencies in any sensible substance. (The three ways in which Aristotle identifies the priority of ejnevrgeia over duvnamiV will be discussed more carefully below.) With this distinction of potency and actuality, Aristotle now provides a stricter definition of change. It is the actuality of the potential qua potential. “[I]t is the fulfillment of what is potential as potential that is [change]. So this, precisely, is [change]”; hJ tou: dunatou: h: dunatovn ejntelevceia fanero;n o{ti kivnhsivV ejstin` (Phys. III 1, 201b4–5; see 401a10–12). Change is commonly interpreted as the development or process by which the potentiality of the elements of a substance are actualized or realized, according to the tevloV of the substance. Ross69 has argued that ejntelevceia must signify actualization, as opposed to actuality, given that change refers to the transition or passage from potentiality to actuality. A. Kosman, however, disagrees with Ross, and rightly so. According to Kosman, Ross’s reading renders the definition circular, given that it presupposes the very concept of the process of actualization in its definition of change. Moreover, Kosman states, Aristotle uses ejntelevceia, as opposed to ejnevrgeia, which he could have used in order to emphasize the process of change as opposed to a completed condition.70 The challenge, therefore, is to interpret the “as such” or “qua” in Aristotle’s definition so as to circumvent circularity. R. Heinaman has challenged Kosman’s criticism of Ross and argues in favor of Aristotle’s definition being circular.71 Cleary highlights the problem very well: If we are to avoid circularity, this cannot be understood as the actuality of the potentiality for being in motion; e.g., the process by which bricks and stones begin to be built into a house. For one thing Aristotle always insisted that the beginning of motion cannot itself be a motion, since there is no period of time in which motion begins. Furthermore, he thinks of change as the potentiality to be something rather than to become something. For example, it is the bronze qua potentially a statue that is change rather than the bronze qua potentially being made into a statue. But then the problem becomes one of identifying some actuality that is

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not identical with the result of the change, which later only comes into existence when the change is finished.72

Moreover, Cleary takes issue with Kosman’s claim that change is the activity manifested by a subject at the first level with regard to its goal—that is, “the activity of an object that is potentially other than it actually is. But in that case Aristotle’s definition would not apply to the subject at rest, which is not exercising its potentiality to be other than it is.”73 By “first level,” Cleary refers to the first level of duvnamiV as presented in Aristotle’s De Anima II 5, which refers, for example, to a human being, who has from birth the capacity for language, in contrast to the second level of duvnamiV, which entails the process of habituation for this person to become a native speaker of a particular language. The second level of duvnamiV is no longer a capacity, but is rather a disposition, a e{xiV. With respect to the qua-phrase in the definition of change, therefore, we must understand the potentiality of the deprived subject in Phys. III 1 alongside the second-level knower in De Anima II 5. M. L. Gill has also criticized Kosman’s argument on the grounds that, given that the subject undergoing the change is deprived of the essential trait that orientates the subject to overcome that lack, the subject itself cannot initiate this change. Thus, an external agent must provide this orientation toward her goal—that is, the change implies that there is an external mover. In this light, Gill has argued that Phys. III 1 is an incomplete account of the nature of change. Only in Phys. III 3 do we find the complete account of change, for in this chapter, Aristotle indicates that change is due to the common actuality of a moving agent and the recipient patient, which is found in the patient. Change occurs, therefore, when the external agent provides the tevloV for the patient, whose development depends on its reaction and orientation toward this tevloV74 (see Phys. III 3, 202a12–22). Thus, there is only a single actuality of both the mover and the patient. Change, then, is perceived as an active production or a passive reaction, but remains a single actuality.75 It is especially for this reason that Cleary cannot accept Blair’s definition of ejntelevceia as “having its end within,” for change is not an end in itself and is, therefore, incomplete, since change is defined by an external limit, by an external mover. Change must be seen as an incomplete ejnevrgeia, unlike the complete ejnevrgeia of seeing and thinking. There is, therefore, an eminent type of ejnevrgeia that precedes duvnamiV and that must be considered in order to appreciate Aristotle’s noetic doctrine in the De Anima III 4–5 and Metaphysics L 7–9, which will be discussed below. The nature and role of duvnamiV was discussed in Met. Q 1–5 and D 12, but at Q 6, Aristotle begins to discuss the nature (tiv e[sti) and the sort of ejnevrgeia (activity) in relation to duvnamiV and kivnhsiV76 (see Met. Q 6, 1048a25–30).

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In this preface, Aristotle proposes to examine potentiality as a different kind of duvnamiV, in addition to his previous examination of duvnamiV, whose nature it is to change another or to be changed by another. Aristotle attempts to explain this new sense of duvnamiV by examining particular instances by way of grasping the analogy, because we are not able to grasp its meaning by definition, given its universality (see Met. Q 6, 1048a35–1048b5). Each of these five examples illustrates the second schema of duvnamiV that Aristotle relates to kivnhsiV, by contrast with the first schema of duvnamiV, which consists of two kinds of actualities: 1) the complete actuality or the result of the activity, and 2) the incomplete actuality or the change that produces this result. With respect to the first schema, some actualities relate to potentiality in the same way that change is related to potentiality, and, moreover, as substance (i.e., the product) is related to preexisting matter. Given this, Gill has argued that Aristotle’s presentation of the second schema was refined by employing aspects of the first schema.77 The second schema entails two sorts of actualities: the first pertains to actuality as it is related to potentiality, as seeing is to that which has sight but whose eyes are shut; and the second pertains to substance that is related to a kind of generic matter, or, for example, that which has been isolated from matter as it is related to its generic matter. Thus, kivnhsiV refers not to the strict and narrow technical sense, but rather to the general sense, for it refers to a substance awake and seeing, and as a result, it is a general concept that pertains to change in the strict sense and to activity in the sense of motion in the second schema. Aristotle appears to be arguing that as in the first schema, the second one emphasizes an actuality that is characterized as a kivnhsiV and another that is the product. What makes the second schema different, among other factors, is that kivnhsiV is not equivalent to change in the strict sense, but is rather an activity. However, given that these schemata are parallel, the second schema presupposes a motion and a product qua actualities, in addition to the two kinds of potentialities, the one active and the other passive.78 This is expressed in Met. Q 6, 1048b6–9. In Met. Q, the relation between the different senses of duvnamiV is less cohesive than in Met. D 12, given Aristotle’s new distinction between a complete and an incomplete ejnevrgeia.79 In Met. Q 8, Aristotle discusses the various ways in which activity (ejnevrgeia) is prior to duvnamiV, in the general sense of potentiality as the origin of change in another or in itself as other and as “one primary kind,” as he highlights in chapter 180 (Met. Q 8, 1046a11). Most specifically, ejnevrgeia precedes duvnamiV in three ways: 1) in formula or definition and 2) in substance; whereas 3) in time, it is only prior in one way and not in the other way. With respect to the priority in formula (tw:/ lovgw/) of ejnevrgeia to duvnamiV, Aristotle states that what is potential in the primary sense is potential given that it possesses the possibil-

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ity to become active. The example he gives is that the “capability of building” entails that which can build, “capable of seeing” signifies that which can see, and “visible” signifies that which can be seen. Therefore, the formula and the knowledge of each activity must precede the knowledge of the other (see Met. Q 8, 1049b13–18). With respect to the priority in substance, ejnevrgeia is prior to duvnamiV in two ways. First, it is prior because of those things that are posterior in coming to be in form and in substantiality, such as a man who is prior to a child and a human being to seed. And second, it is prior because these things that come into being move toward a principle, an end (tevloV), and the ejnevrgeia is this end, “and it is for the sake of this that the potency is acquired” (Met. Q 8, 1050a9). Cleary summarizes this argument very well: “Since the final cause is a first principle and the coming-to-be is for the sake of the completion, and the activity is the completion, it is for the sake of this that the potentiality is acquired.”81 Given these two levels of priority, Aristotle concludes (1050b2) that substance and form are activity (ejnevrgeia). “According to this argument, then, it is obvious that ejnevrgeia is prior in substantial being to potency; and as we have said, one ejnevrgeia always precedes another in time right back to the ejnevrgeia of the eternal prime mover” (Met. Q 8, 1050b3–5). Thus, ejnevrgeia is prior to duvnamiV in the sense that that which is active (to; ejnergou:n)—which is identical with the species (tw:/ ei[dei)—is prior to the thing that it can produce. Only with respect to time does Aristotle acknowledge that duvnamiV is prior to ejnevrgeia, in the sense that the particular, already existing man, for instance, is in actuality, but the matter that exists potentially, but not yet actually, is prior in time (see Met. Q 8, 1049b18–23). This final claim reinforces Aristotle’s ultimate claim that, generally speaking, ejnevrgeia precedes duvnamiV.

Conclusion The anatomy of Aristotle’s Metaphysics and the clarification of terms enable us to grasp the causal relation among the four causes and the precedence of ejnevrgeia to duvnamiV, which have created the conceptual horizon against which we are better able to study Aristotle’s doctrine of the simplicity of nou:V. This priority on the levels of formula and substance is clearly manifested and illustrated in the De Anima and Metaphysics L, to which I turn now.82

Notes   1.  See Physics II 3, 194b17–195a4.   2.  The question in Greek philosophy originated with the Ionians (Thales, Anaximander, and Anaximenes) and the Pythagoreans. The speculative inquiries

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concerned the general structure of the cosmos. Whereas the Ionians, in the east of Greece, sought for scientific foundations upon which the cosmos is established, the Pythagoreans, in the west of Greece, aspired for a religious fraternity based on the mathematical principles inherently operative in the cosmos. These two complementary beginnings to philosophy were bequeathed to Socrates, Plato, and Aristotle. See W. K. C. Guthrie, The Greek Philosophers: From Thales to Aristotle (New York: Harper & Row, 1975), 22.   3.  In Met. A.1, Aristotle analyzes at length the trajectory of the four causes. He concludes that no other philosopher prior to himself has systematically captured the four causes that furnish the cosmos: matter, form, efficient, and final.   4.  A. E. Taylor, Aristotle (New York: Dover Publications, 1955), 50; Liddell & Scott define aijtiva as follows: “the occasion of something bad, a charge, accusation, blame, a fault,” and, moreover, as “causing, occasioning; hence chargeable with a thing: but mostly in bad sense, causing ill, blamable, guilty . . . the party to be blamed, the culprit” (Liddell & Scott, Greek-English Lexicon, abridged [Oxford: Clarendon Press, 1958]).   5.  A. H. Armstrong, An Introduction to Ancient Philosophy (repr., Lanham, MD: Rowman & Littlefield Publishers, 1989), 82.   6.  Plato, Republic, trans. P. Shorey (Cambridge, MA: Harvard University Press, 1987), 596a ff: “We are in a habit, I take it, of positing a single idea or form in the case of the various multiplicities to which we give the same name”; see also Rep., 507a–b: “We predicate ‘to be’ of many beautiful things and many good things, saying of them severally that they are, and so define them in our speech. . . . And again, we speak of a self-beautiful and of a good that is only and merely good, and so, in the case of all the things that we then posited as many, we turn about and posit each as a single idea or aspect, assuming it to be a unity and call it that which each really is. . . . And the one class of things we say can be seen but not thought, while the ideas can be thought but not seen.” See also Guthrie, The Greek Philosophers, 88.   7.  For a short summary, see R. Kraut, “Introduction to the Study of Plato,” in The Cambridge Companion to Plato, ed. R. Kraut (New York: Cambridge University Press, 1996), 41, fns.34 and 123. For a more detailed discussion of this debate, see G. Fine, “Separation,” Oxford Studies in Ancient Philosophy 2 (1984): 31–87; G. Vlastos, Socrates, in The Philosophy of Socrates, ed. G. Vlastos (Garden City, NY: Anchor Books, 1971), 256–65. Sir David Ross questions Aristotle’s criticism of Plato: It may be doubted whether Plato thus “separated” the universal from its particulars. To distinguish the universal from its particulars is in a sense to separate it. It is to think of it as a distinct entity. Whether Plato also thought of it as a separately existing entity, it is hard to say. Much of his language lends itself to the charge, but it is possible that he may only be putting in an emphatic and picturesque way the doctrine that particulars always imply a universal. (D. Ross, Aristotle, 5th ed. [London: Methuen & Co, 1964], 158)

  8.  Y. Prélorentzos, La République (Livre VII) (Paris: Hatier, 1993), 13.   9.  M. Dixsaut, Le naturel philosophe, Essai sur les dialogues de Platon (Paris: J. Vrin, 1985).

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10.  L. Brisson, “Une nouvelle interprétation du Parménides de Platon,” in Platon et l’objet de la science. Textes réunis et présentés par P.-M. Morel (Bordeaux: Presses Universitaires de Bordeaux, 1996), 80. 11.  See Y. Lafrance, La Théorie Platonicienne de la Dovxa (Montréal: Bellarmin, 1981). 12.  H. Cherniss, Aristotle’s Criticism of Plato and the Academy (Baltimore: Johns Hopkins University Press, 1944). 13.  Met. A 1, 991a12–13: The Forms “help in no wise towards the knowledge of the other things (for they are not even the substance of these, else they would have been in them)”; see also Guthrie, The Greek Philosophers, 125. 14.  The hierarchy of stages is primarily seen in Met. A.1 and De Anima II. 15.  See Guthrie, The Greek Philosophers, 128; Guthrie elucidates the problem: “How to bring within the compass of philosophic knowledge a world of unstable phenomena, always changing, never the same for two instants together? Where is that stability which . . . the human mind demands?” 16.  As aforementioned, Plato’s Forms are universal but separate from the sensible object, whereas Aristotle’s are, while still universal, operative within the sensible object. According to Aristotle, the universal form renders a substance into an individual thing— a this. Generally, Aristotle speaks of substances as sensible things composed of matter and form. However, in the De Anima and Metaphysics, he speaks of nou:V as an unperceived, albeit individual, substance, since it is devoid of matter, a topic that will be addressed later in this chapter. See J. Barnes, Aristotle (Oxford: Oxford University Press, 1982), 45–46. It should be noted that this is one of the most debated issues among Aristotelian scholars. It is beyond the scope of this book to explore and develop this theme. 17.  Change in substance entails the birth and death of a natural organism and includes the generation and destruction of an artifact; change in quality means the alteration of the properties of a substance (i.e., water alters when it is exposed to freezing or boiling conditions); change in quantity refers to the growth and diminution of a substance; and change in place refers to motion. See Barnes, Aristotle, 46–47. 18.  It should be noted that Aristotle rarely uses the concept of prw:th u{lh. His disciples, however, considered it to be one of the most important doctrines in Aristotle’s philosophy. See Ross, Aristotle, 168. It should be noted that W. Charlton and M. L. Gill question the existence of such a doctrine in Aristotle. See W. Charlton, Aristotle’s Physics I and II (Oxford: Clarendon Press, 1992); and M. L. Gill, Aristotle on Substance: The Paradox of Unity (Princeton, NJ: Princeton University Press, 1989). 19.  Prime matter is logically postulated in order to understand the added and juxtaposed properties or accidents in a substance. See Phys. I.8, 191a31–2 and II.1, 193a29. 20.  See Ross, Aristotle, 168. 21.  Ross, Aristotle, 168–69. 22.  In fact, u{lh literally means timber, the timber of a boat. See Taylor, Aristotle, 45. 23.  The material substance that is produced is a configuration of the four material elements—earth, air, water, and fire—which are duly proportioned by the formal cause. This teaching is found in Plato’s works, especially the Timaeus, where the four elements are duly proportioned into a determinate measure by the dhmiourgovV. See Timaeus,

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31c–32c, especially 32c, which provides the reason for the activity of the dhmiourgovV to harmonize the elements of the cosmos—namely, to ensure the cosmos’s unity: “For these reasons and out of these materials, such in kind and four in number, the body of the Cosmos was harmonized by proportion and brought into existence. These conditions secured for it Amity, so that being united in identity with itself it became indissoluble by any agent other than Him who had bound it together” (Plato, Timaeus, trans. R. G. Bury [Cambridge, MA: Harvard University Press, 1987]). The four elements in the Timaeus are derived from Empedocles. 24.  Jonathan Lear, Aristotle: The Desire to Understand (New York: Cambridge University Press, 1988), 28. J. Lear captures the relation between formal cause and the essence of a thing very well: “Because the form of a natural organism or artifact gives us what it is to be that thing, the why and the what converge . . . for the why of something is its essence” (Lear, Aristotle, 29). 25.  See Lear, Aristotle, 28. 26.  See also Lear, Aristotle, 29. 27.  “Therefore,” Lear concludes, “the primary source of change is form. The actual primary source is an active state” (Lear, Aristotle, 35). 28.  Armstrong, Introduction to Ancient Philosophy, 82. For a discussion on the tevloV of Nature, see Henri-Paul Cunningham, “Téléologie, nature et esprit,” in La question de Dieu selon Aristote et Hegel. Published under the direction of Th. De Koninck and G. Planty-Bonjour (Paris: Presses Universitaires de France, 1991), 25–35. 29.  Aristotle, Selections, trans. Terence Irwin and Gail Fine (Indianapolis: Hackett Publishing Company, 1995), Glossary, 564–622, especially 582; see Phys. II.3, 194a35 and Met. L 7, 1072b2. 30.  In fact, Aristotle will say that movement in Nature is caused by the Prime Mover, which functions as an object of love, toward which the whole of Nature aspires. The Prime Mover is the unmoved Mover. “On such a principle, then, depend the heavens and the world of nature” (Met. L 7, 1072b14). This will be discussed below. 31.  ”The end, the form in its realized state,” comments Lear, “is none other than a successful striving” (Lear, Aristotle, 35). 32.  ”For Aristotle,” continues Lear, “the reason one has to cite the form in its final, realized state is that it is only by reference to that form that one can understand teleological behavior” (Lear, Aristotle, 36). 33.  Lear further writes that the “form of a developing organism . . . is not merely its achieved structure, it is a force in the organism for attaining even higher levels of organization until the organism achieves its mature form” (Lear, Aristotle, 39). 34.  G. R. G. Mure, Foreword to F. W. Weiss, Hegel’s Critique of Aristotle’s Philosophy of Mind (Martinus Nijhoff: The Hague, 1969), xiv. 35.  The question concerning many scholars is, how reliable is the Protrepticus with respect to expressing the duvnamiV-ejnevrgeia distinction, as we see it in Met. D 12. See P. Gohlke, Die Entstehung der aristotelischen Prinzipienlehre (Tübingen: Mohr, 1954), 7–8; M. Wundt, Untersuchungen zur Metaphysik des Aristoteles (Stuttgart: W. Kohlhammer Verlag, 1953), 18–19; and recently D. W. Graham, Aristotle’s Two Systems (Oxford:

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Clarendon Press, 1987), 203, fn.41, who responds to Gohlke and Wundt. The distinction can, moreover, be accepted based on the evidence of the Protrepticus and still maintain that this evidence (i.e., the absence of a definition of duvnamiV of the kind that correlates with ejnevrgeia in Met. D 12) indicates an early period in Aristotle’s career, when the concept of ejnevrgeia was not created. On this topic, see A. Smeets, Act en Potentie in de Metaphysica van Aristoteles (Louvain: Leuvense Universitaire Uitgaven, 1952). This claim, however, was challenged by Graham, Aristotle’s Two Systems, 204–5 and fn.48; and D. W. Graham, “The Development of Aristotle’s Concept of Actuality: Comments on a Reconstruction by Stephen Menn,” Ancient Philosophy 15 (1995): 553–54. 36.  See C.-H. Chen, “Different Meanings of the Term Energeia in the Philosophy of Aristotle,” Philosophy and Phenomenological Research 17 (1956): 57 ff. Chen has uncovered ten different ways in which Aristotle employs the concept of ejnevrgeia. I will, however, limit my discussion to a couple of meanings, insofar as they pertain to our theme—namely, was the concept of ejnevrgeia first used by Aristotle to mean “activity” or “actuality”? 37.  For an excellent discussion of the use of duvnamiV as far back as Homer and Hesiod, and its usage in epic poetry and in Plato’s philosophy, see J. Cleary, “‘Powers that Be’: The Concept of Potency in Plato and Aristotle,” Méthexis 11 (1998): 19–64, esp. 19–25; see also P. Pritchard, “The Meaning of ‘Dunamis’ at Timaeus 31c,” Phronesis 335 (1990): 182–93; S. Menn, “The Origins of Aristotle’s Concept of =Enevrgeia: =Enevrgeia and DuvnamiV,” Ancient Philosophy 14 (1994): 73–114, esp. 81–82, who has argued that Plato anticipated Aristotle’s distinction between duvnamiV and ejnevrgeia through a corresponding distinction between possession and use in the Euthydemus (277e–278a and 280b5–282a6) and Theaetetus (197a8–b1); and Z. Bechler, Aristotle’s Theory of Actuality (Albany, NY: SUNY Press, 1995), 23–25. For further research on the distinction between duvnamiV and ejnevrgeia, see G. Blair, “Unfortunately, It Is a Bit More Complex: Reflections on =Enevrgeia,” Ancient Philosophy 15 (1995): 565–80, who has challenged both Menn and Graham on their recent reflections on ejnevrgeia; W. Charlton, “Aristotle and the Uses of Actuality,” Proceedings of the Boston Area Colloquium in Ancient Philosophy 5 (1989): 1–22; C.-H. Chen, “Different Meanings of the Term Energeia in the Philosophy of Aristotle,” Philosophy and Phenomenological Research 17 (1956): 56–65; and L. A. Kosman, “Substance, Being and Energeia,” Oxford Studies in Ancient Philosophy 2 (1984): 121–49. 38.  Chen, “Different Meanings of the Term Energeia in the Philosophy of Aristotle,” 57. 39.  See Taylor, Aristotle, 47. 40.  C.-H. Chen adds to the concept of duvnamiV as potentiality: “In the Aristotelian concepts of dynamis . . . at least the following teleological moments are involved: 1. Matter is according to [Aristotle] the carrier of dynamis in this sense. If something is potentially something else, its dynamis is owing to its material constituent. Matter has then a natural tendency towards form; it aims at being actually so and so determined as the form is. So in his concept of potentiality finality is an important moment. 2. This actual determination is the end of the matter. A seed of a certain tree, for example, aims at becoming such a tree actually. If the conditions required for this change are fulfilled, it develops into such a one. Thus the basis of the development is the dynamis in the sense

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of potentiality. It forms the second important moment of his concept of potentiality. The same teleological moments are involved in his concept of actuality. For actuality is that state in which potentiality is actualized” (Chen, “Different Meanings of the Term Energeia in the Philosophy of Aristotle,” 57, fn.8). 41.  See Menn, “The Origins of Aristotle’s Concept of =Enevrgeia: =Enevrgeia and DuvnamiV,” 73. 42.  See Menn, “The Origins of Aristotle’s Concept of =Enevrgeia: =Enevrgeia and DuvnamiV,” 74. 43.  Menn, “The Origins of Aristotle’s Concept of =Enevrgeia: =Enevrgeia and DuvnamiV,” 74; see also Pritchard, “The Meaning of ‘Dunamis’ at Timaeus 31c,” 182–93, esp. 190–92; and Cleary, “‘Powers that Be’: The Concept of Potency in Plato and Aristotle,” 20–25. 44.  See Menn, “The Origins of Aristotle’s Concept of =Enevrgeia: =Enevrgeia and DuvnamiV,” 75. 45.  See Menn, “The Origins of Aristotle’s Concept of =Enevrgeia: =Enevrgeia and DuvnamiV,” 75 and fn.3. Graham, however, does suggest that Aristotle’s concept of ejnevrgeia is developed out of the metaphysical foundation prepared by Plato. See Graham, “The Development of Aristotle’s Concept of Actuality,” 553–55. 46.  Menn, “The Origins of Aristotle’s Concept of =Enevrgeia: =Enevrgeia and DuvnamiV,” 75. 47.  See Menn, “The Origins of Aristotle’s Concept of =Enevrgeia: =Enevrgeia and DuvnamiV,” 76, and fn.5. 48.  Menn, “The Origins of Aristotle’s Concept of =Enevrgeia: =Enevrgeia and DuvnamiV,” 77. 49.  Menn, “The Origins of Aristotle’s Concept of =Enevrgeia: =Enevrgeia and DuvnamiV,” 77–78. 50.  Menn, “The Origins of Aristotle’s Concept of =Enevrgeia: =Enevrgeia and DuvnamiV,” 78. 51.  See G. Blair. Energeia and Entelecheia: “Act” in Aristotle (Ottawa: University of Ottawa Press, 1992), 18–20. See also his article “The Meaning of ‘Energeia’ and ‘Entelecheia’ in Aristotle,” International Philosophical Quarterly 7 (1967): 110–17. See also D. Graham, “The Etymology of ejntelevceia,” American Journal of Philology 110 (1989): 73–80, who has aligned his interpretation with that of the philologist H. Diels, while rejecting the interpretation of K. von Fritz. Diels is known for rejecting R. Hirzel’s claim that Aristotle invented the word ejntelevceia as a contrast with Plato’s ejndelevceia (74–76) (H. Diels, “Etymologica: 3. =Entelevceia,” Zeitschrift für vergleichende Sprachforschung 47 [1916]: 200–203; R. Hirzel, “Über Entelechie und Endelechie,” Rheinisches Museum 39 [1884]: 169–208). See G. Blair, “Aristotle on Entelecheia: A Reply to Daniel Graham,” American Journal of Philology 114 (1993): 91–97, where Blair reacts against Graham’s interpretation of ejntelevceia. See also Graham, “The Development of Aristotle’s Concept of Actuality,” 551–64. In his evaluation of Menn’s argument, Graham has praised Menn’s accurate analysis that in the earliest appearance, ejnevrgeia and its opposition to duvnamiV refer to “activity” (553). Moreover, Menn is correct, according to Graham, to attribute

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this earliest evidence for the concept ejnevrgeia to Plato—a claim that has been ignored by many modern scholars but was first developed by Jaeger in “Review of P. Gohlke,” Varia Gnomon 4 (1928): 625–37, arguing that the concept of ejnevrgeia was already used in the Protrepticus. See also J. Rist, The Mind of Aristotle: A Study in Philosophical Growth (Toronto: University of Toronto Press, 1989), 105–6. However, Graham highlights and develops his detailed criticism of Menn’s argument on pp. 555–63. 52.  Blair, Energeia and Entelecheia: “Act” in Aristotle, 24–25: “Something, therefore, to erase from one’s mind here is the all-to-common notion that Aristotle’s theory of Act and Potency was developed as a way to explain change. What he is after is a distinction, not how one gets from one condition into the other.” 53.  See Blair, Energeia and Entelecheia: “Act” in Aristotle, 27. 54.  See Blair, Energeia and Entelecheia: “Act” in Aristotle, 18–19. 55.  It should be noted that many scholars have leveled a serious criticism about Aristotle’s authenticity in reporting the exact teachings of the Megarians. As a result, his “solution” appears, according to them, at best, dubious. See B. Calvert, “Aristotle and the Megarians on the Potentiality-Actuality Distinction,” Apeiron 10 (1976): 277–89; and S. Rosen, “Dynamis, Energeia and the Megarians,” Philosophical Inquiry 1 (1979): 105–19. See also Bechler, Aristotle’s Theory of Actuality, 21–23, who perhaps exaggerates by arguing that Aristotle’s discussion of potentiality and actuality is reducible to and resembles the general position of the Megarians. 56.  See Cleary, “‘Powers that Be’: The Concept of Potency in Plato and Aristotle,” 27, and also R. Heinaman, “Is Aristotle’s Definition of Change Circular?,” Apeiron 27 (1994a): 25–37. 57.  See Cleary, “‘Powers that Be’: The Concept of Potency in Aristotle and Plato,” 28: “The reason . . . is that some things which are not (yet) in energeia will be in energeia; and among non-beings some things are in potency (dunavmei) but are not (yet) beings because they are not in entelecheia. It is still not clear what this means in plain English. . . . But what is clear is that for Aristotle the problem of being and non-being can only be resolved satisfactorily by means of the distinction between dynamis and energeia.” 58.  See Graham, Aristotle’s Two Systems, 184, fn.5. 59.  Blair, Energeia and Entelecheia: “Act” in Aristotle, 79. 60.  Blair, Energeia and Entelecheia: “Act” in Aristotle, 31. 61.  Cleary, “‘Powers that Be’: The Concept of Potency in Plato and Aristotle,” 29. 62.  See Menn, “The Origins of Aristotle’s Concept of =Enevrgeia: =Enevrgeia and DuvnamiV,” 105. 63.  This hypothesis, incidentally, is accepted and is approved by Cleary, “‘Powers that Be’: The Concept of Potency in Plato and Aristotle,” 30. Incidentally, Taylor has argued that ejnevrgeia refers to the completed process of growth of the form itself in a substance (i.e., the realization of form), whereas ejntelevceia strictly refers to the appearance or manifestation of the realized form. See Taylor, Aristotle, 49. See also C. Witt, Ways of Being: Potentiality and Actuality in Aristotle (Ithaca, NY: Cornell University Press, 2003). 64.  On the two senses of duvnamiV in Aristotle, see M. Frede, “Aristotle’s Notion of Potentiality in Metaphysics Q,” in Unity, Identity, and Explanation in Aristotle’s Meta-

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physics, ed. T. Scaltsas, D. Charles, and M. L. Gill (Oxford: Oxford University Press, 1994), 173–93; M. Wiener, “Potency and Potentiality in Aristotle,” New Scholasticism 44 (1970): 515–34; Bechler, Aristotle’s Theory of Actuality, 11–23; and Cleary, “‘Powers that Be’: The Concept of Potency in Plato and Aristotle,” 19–64. 65.  It should be noted that Met. D 12 does not mention ejnevrgeia and ejntelevceia as correlates to the two uses of duvnamiV, but it does highlight these uses of duvnamiV in a similar way to Met. Q 1. The first kind of potency is characterized as an active potency, for it refers to a principle of motion or of change, which operates within a being that is different than the moved or altered being or is in the same being qua other. “‘Potency’ means (1) a source of movement or change, which is in another thing than the thing moved or in the same thing qua other; e.g., the art of building is a potency which is not in the thing built, while the art of healing, which is a potency, may be in the man healed, but not in him qua healed. ‘Potency’ then means the source, in general, of change or movement in another thing or in the same thing qua other” (see Met. D 12, 1019a15–20). The second sense of potency is characterized as a “capacity,” for it refers to the principle of being moved or of being changed by another being or by the being itself qua other. “[A]nd also, (2) the source of a thing’s being moved by another thing or by itself qua other. For in virtue of that principle, in virtue of which a patient suffers anything, we call it ‘capable’ of suffering; and this we do sometimes if it suffers anything at all, sometimes not in respect of everything it suffers, but only if it suffers a change for the better” (Met. D 12, 1019a20–24). Thus, this second sense of duvnamiV possesses a disposition (diavqesiV) to function as a cause or principle of being affected. (See also Cleary, “‘Powers that Be’: The Concept of Potency in Plato and Aristotle,” 33.) 66.  Aristotle, says Ross, “sees clearly that the notion of potency is indefinable; he can only indicate its nature by pointing to particular instances” (Ross, Aristotle, 176). 67.  See Cleary, “‘Powers that Be’: The Concept of Potency in Plato and Aristotle,” 34: “Even though Aristotle subsequently develops and extends the notion of dynamis to make it more compatible with his theory of substance, he always insists that its primary meaning is related to change.” 68.  Ross, Aristotle, 177. 69.  Ross, Commentary on Aristotle’s Physics (1936), 537. 70.  See A. Kosman, “Aristotle’s Definition of Motion,” Phronesis 14 (1969): 41. Kosman is in clear disagreement with Ross. Ross writes that motion is “the actualization of that which is potentially, as such. That is, if there is something which is actually x and potentially y, motion is the making actual of its y-ness” (Ross, Aristotle, 81). Moreover, Ross writes in his commentary of Aristotle’s Physics, 537: “[E]jntelevceia must here mean ‘actualization’, not ‘actuality’: it is the passage from potentiality to actuality that is kivnhsiV.” Kosman is clear: “But this answer is wrong. I do not mean that Aristotle would have been unhappy with the description of motion as the actualizing of a potentiality, but only that this is not the definition which he offers at the beginning of Book III of the Physics” (Kosman, “Aristotle’s Definition of Motion,” 41). 71.  See Heinaman, “Is Aristotle’s Definition of Change Circular?,” 25–37. 72.  Cleary, “‘Powers that Be’: The Concept of Potency in Plato and Aristotle,” 36–37.

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73.  Cleary, “‘Powers that Be’: The Concept of Potency in Plato and Aristotle,” 38. 74.  See Cleary, “‘Powers that Be’: The Concept of Potency in Plato and Aristotle,” 38; see also M. L. Gill, Aristotle on Substance, 194. 75.  See Cleary, “‘Powers that Be’: The Concept of Potency in Plato and Aristotle,” 38. 76.  For further research on this relationship, see J. L. Ackrill, “Aristotle’s Distinction between Energeia and Kinesis,” in New Essays on Plato and Aristotle, ed. R. Bambrough (London: Routledge & K. Paul, 1965), 121–41; C. Hagen, “The Energeia-Kinesis Distinction and Aristotle’s Conception of Praxis,” Journal of the History of Philosophy 22 (1984): 263–80; R. Heinaman, “Kosman on Activity and Change,” Oxford Studies in Ancient Philosophy 12 (1994b): 207–18; R. Heinaman, “Aristotle on Activity and Change,” Oxford Studies in Ancient Philosophy 13 (1995): 187–216; Kosman, “Aristotle’s Definition of Motion,” 40–62; M.-Th. Liske, “Kinesis und Energeia bei Aristoteles,” Phronesis 36 (1991): 141– 59; P. S. Mamo, “Energeia and Kinesis in Metaphysics 6,” Apeiron 4 (1976): 24–34; A. P. D. Mourelatos, “Aristotle’s kinesis/energeia Distinction: A Marginal Note on Kathleen Gill’s Paper,” Canadian Journal of Philosophy 23 (1993): 385–88; M. A. Stone, “Aristotle’s Distinction between Motion and Activity,” History of Philosophy Quarterly 2 (1985): 11–20; and M. J. White, “Aristotle’s Concept of qewriva and the =EnevrgeiaKivnhsiV Distinction,” Journal of the History of Philosophy 18 (180): 253–63. 77.  Gill, Aristotle on Substance, 172–83 and 214–18. 78.  For a summary of this argument, see Cleary, “‘Powers that Be’: The Concept of Potency in Plato and Aristotle,” 41. 79.  See Cleary, “‘Powers that Be’: The Concept of Potency in Plato and Aristotle,” 42. See also R. Polansky, “Energeia in Aristotle’s Metaphysics IX,” Ancient Philosophy 3 (1983): 162–63. 80.  For further research on Aristotle’s conception of the priority of ejnevrgeia, see J. Cleary, Aristotle on the Many Senses of Priority (Carbondale: Southern Illinois University Press, 1988), 75–85; and C. Witt, “The Priority of Actuality in Aristotle,” Apeiron 27 (1994): 217–28, and her Ways of Being: Potentiality and Actuality in Aristotle (Ithaca, NY: Cornell University Press, 2003). 81.  Cleary, “‘Powers that Be’: The Concept of Potency in Plato and Aristotle,” 45. 82.  Potency does not ensure the eternity of a substance. The substance that is potentially a being is also potentially a nonbeing, while the eternal substance, that which is always actual, never ceases to be. Aristotle refers to the immaterial substances in the sublunary sphere (Met. L 8) and to nou:V (Met. L 7 & 9).

c h a pte r f i v e

The Unmoved Mover and the Simplicity and Priority of nou:V Metaphysics L 7, De Anima III.4–5, and Metaphysics L 9

Introduction The question concerning the content of the knowledge of nou:V has remained troublesome for centuries, and the Aristotelian texts in Book L are not clear about this content. However, there is enough evidence to demonstrate that nou:V does know the world, while remaining purely actual and unaltered by its content. This presentation will weigh heavily when we discuss the simple nature of nou:V and Plotinus’s general critique of Aristotle’s doctrine of the simplicity of nou:V. J. Lear introduces this problem with the following statement: What does God’s thinking himself consist in? Is this a totally empty conception, a mere solution to a puzzle? If so, how could Aristotle have believed that God was an unmoved mover of the world? . . . It is incredible that Aristotle should allow the bare solution to a dialectical puzzle to serve as one of the foundations of his entire metaphysical outlook. We do have before us a rich conception of God’s relation to the world.1

The question before us is this: Can Aristotle successfully eliminate the duality between nou:V and nohtovn, and, ultimately, of the self-knowledge that nou:V possesses and its knowledge of the world? According to Plotinus, whose arguments we will encounter in chapter 9, Aristotle’s attempt fails to overcome the duality within his own highest and most actual being—namely, nou:V—thereby leaving nou:V with a residue of potentiality. Plotinus argues that only the simplest (aJplouvstaton) principle is immune to multiplicity and potentiality.2 The Ar97

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istotelian challenge, therefore, is to prove that nou:V, while contemplating itself, remains one and indivisible.3 This topic concerns us greatly, and it will be important in this section in order to 1) set up the foundations of Aristotle’s conception of divine nou:V, and 2) properly understand Plotinus’s very rich interpretation and critique of Aristotle concerning the limitations of the divine nou:V. I wish to argue, however, that Aristotle is not unfamiliar with the argumentative step Plotinus makes, for Aristotle even discusses and anticipates the consequences of a Plotinus-like move of rendering nou:V subordinate to a more simple principle. (This will be discussed below.)

Metaphysics L 7 Metaphysics L 7 is concerned with the singular source of all movement, a source that moves without itself being moved and that must be an “eternal, substance and actuality” (Met. L 7, 1072a25–6). As seen above, the prime Mover has been mentioned by Aristotle in L 4, where Aristotle writes, “[B]esides these there is that which as first of all things moves all things” (Met. L 4, 1070b34–5). Moreover, chapter 6 demonstrates that every motion implies a cause, which must be an actual substance [hJ oujsiva ejnevrgeia] (see Met. L 6, 1071b20) and which is devoid of matter [a[neu u{lhV4] (see Met. L 7, 1071b21). Met. L 6 provides the necessary assumptions for his argument for the absolute priority of the unmoved Mover. He first states in this chapter that substances are prior to all things, and as a result, if they cease to be, then everything ceases to be. However, he adds, motion cannot be either generated or corrupted, given that it always exists, which he has argued in the Physics. Moreover, time cannot be generated or corrupted, otherwise there could never be a before and after, which would be absurd. Time cannot be generated (i.e., come into being and cease to be), for that would entail a time prior to time, or that there will be a time after time has ceased to be, which is an absurd claim. Moreover, given that time is related to motion, they are continuous and eternal in the same manner. In this light, Aristotle affirms that there must be an eternal circular motion (see Met. L 6, 1071b2–11; see also Phys. 219b1; 261a31–263a3; and 264a7–265a12). Moreover, he continues, if there is a substance that only possesses the capacity of moving things or of causally influencing them, but is not actually doing so (mh; ejnergou:n), then there could be no movement, “for that which has a potency need not exercise it” (Met. L 6, 1071b13–14). In this light, Aristotle reaffirms his criticism of his predecessors who have claimed that matter—potency—can be prior, for nothing could ever emerge out of such potential states (see Met. L 6, 1071b12–20). Therefore, Aristotle must affirm a principle that is prior in actuality, unlike Plato’s Forms, for this active principle must be responsible for

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movement, for without it there can be no motion in the cosmos. More specifically, the critique of Platonic Forms is not directed against their being less actual, but rather against their lack of causal power. Finally, this first principle cannot possess any potentiality, “for,” as cited above, “there will not be eternal movement, since that which is potentially may possibly not be. There must, then, be such a principle, whose very essence is actuality,” argues Aristotle (Met. L 6, 1071b18–20). This first principle is nothing other than the unmoved Mover.5 “There must, then, be such a principle, whose very substance is actuality. Further, then, these substances must be without matter; for they must be eternal, at least if anything else is eternal. Therefore they must be actuality” (Met. L 6, 1071b20–22). However, if it is the case that “everything that acts is able to act, but that not everything that is able to act acts, so that the potency is prior” (Met. L 6, 1071b23–25), then potentiality would appear to be prior to actuality. And, if this is the case, then how can this principle be the source of movement in the cosmos? Aristotle quickly dismisses the claim that potentiality precedes actuality, as we have seen above, in our analysis of Met. Q. Thus, Aristotle must affirm a kind of motion that is primary (see Met. L 6, 1071b37), and this primary motion is the unchanging eternal cycle of the heavens (see Met. L 6, 1072a9–18, 22–23). At this stage of his argument, Aristotle still argues in a similar way to Plato’s argument for motion, which is known as the cycle of the Same and the Different. Aristotle believes that there is a substance that always moves with perpetual motion—namely, the circular motion of the first heaven, as we have just seen. However, Aristotle must move beyond Plato here and stipulate a principle that moves even the heavenly bodies. Given that the first heaven is moved and also moves other substances, there is an intermediate, which leads Aristotle to affirm the unmoved Mover, which is an eternal and purely active substance (aji