Formation of the early Christian theology of arithmetic number symbolism in the late second and early third century

THE CATHOLIC UNIVERSITY OF AMERICA

Formation of the Early Christian Theology of Arithmetic Number Symbolism in the Late Second and Early Third Century

A DISSERTATION

Submitted to the Faculty of the Department of Early Christian Studies School of Arts and Sciences Of the Catholic University of America In Partial Fulfillment of the Requirements For the Degree Doctor of Philosophy

By Joel Kalvesmaki

Washington, D.C.

2006

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UMI Number: 3214679

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Formation of the Early Christian Theology of Arithmetic Number Symbolism in the Late Second and Early Third Century

Joel Kalvesmaki, Ph.D.

Director: William McCarthy, Ph.D.

Numbers were widely used in antiquity to symbolize reality and to structure theological and philosophical systems. Early Christian authors embraced this practice, but not without controversy. In the late second century there emerged distinct Christian movements that used Pythagorean number symbolism to structure their ideas about the godhead. Notable were the various Valentinian schools (including Marcus "Magus" and Colarbasus), Mono·imus, and later followers of Simon "Magus." Contemporary orthodox authors, such as Irenaeus and Clement of Alexandria, opposed them, particularly for undermining the Trinitarian doctrine received in the churches. But Irenaeus and Clement do not approach the matter identically. Irenaeus criticizes the Valentinians directly, and without squaring everything in his critique with his own number symbolism. Clement criticizes such groups indirectly, and uses his own well-developed number symbolism to illustrate the proper way to approach the subject. The Christian debates have striking parallels in roughly contemporary non-Christian texts. Marsanes, Plutarch, and Theodore of Asine show that non-Christians too debated these matters. All of these figures - Christian and non-Christian -illustrate the tensions that

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existed between those who used number symbolism to shape theological and philosophical traditions and those who used their traditions to shape their number symbolism. The orthodox theology of arithmetic formed not a single position but rather a defense against arbitrary number symbolism that justified departures from the received tradition. I argue for several important ancillary points. Pythagoreanism was reinvented during the late Roman Republic, and the number symbolism that emerged in the following centuries had a traceable history. The distinction between hen and monad, the popular formulation of the quadrivium, and numerology and the use of psephy (gematria) all have their genesis in this period . Older traditions of number symbolism, such as the distinction between male and female numbers and the importance of the tetraktys, all received new life. I outline the historical development of each of these trends and classify and describe the major types of Greek numerological prognostication. Furthermore, I argue for a new sequence to Irenaeus' s Against Heresies, and I challenge scholars' dependence upon the dichotomies eastern versus western, and monadic versus dyadic Valentinianism.

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This dissertation by Joel Kalvesmaki fulfills the dissertation requirement for the doctoral degree in Early Christian Studies approved by William McCarthy, Ph.D., as Director, and by Philip Rousseau, Ph.D., Christoph Markschies, Ph.D., and Susan Wessel, Ph.D., as Reade�s.

l Philip Rousseau, Ph.D., Reader

Christoph Markschies, Ph.D., Reader

�Gi)wjJ

/ Susan Wessel, Ph.D., Reader

11

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To my parents

iii

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CONTENTS 1

Introduction

1

2 The Valentinians

10

Marcus "Magus"

79

3

4 Mono!mus 5

The Paraphrase of the Apophasis Megale

6 Colarbasus 7 Irenaeus 8

1 05

132

140

Clement of Alexandria

9 Platonism

118

182

225

10 Numeri ex regula 262

EXCURSUSES A

Pythagoreanism in Outline

B

Themes in Pythagorean Number Symbolism

273

1

One Versus One: The Hierarchy of the Hen and the Monad

2

Odd and Even Numbers as Male and Female

284

296

3 The Tetraktys 305 4 The Quadrivium

310

5 The Number Five: Marriage 321 C

The Elements and History of Psephy (Gematria)

D

Types of Greek Numerology

325

343 IV

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E

The Original Sequence of Irenaeus, Against Heresies 1 : Another Suggestion

F

Italian versus Eastern Valentinianisrn?

G

The Structure of Clement of Alexandria's Excursus on the Decalogue

395 404

Abbreviations 412 Bibliography

415

v

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380

1 Introduction

Read any of Origen's commentaries on Scripture and you will note that at the appearance in the Bible of a bird, a plant, a color, the time of day, even a definite article, is apt to be interpreted symbolically. Origen's fascination with the world of symbols was shared throughout the Greco-Roman antiquity by Christians, Jews, Mithraites, polytheists, and others. Such symbols were key parts of their cultural and intellectual world. Certain classes of symbols were more significant than others. For such symbols handbooks and treatises were written to capture and transmit the relevant lore. Names became the basic subject matter of ancient onomastica; animals, of bestiaries; minerals, of commentaries on the meaning of stones discussed in Scripture; time, of meteorological prognostication; and numbers, of treatises on the decad. These popular tractates began to appear in the Hellenistic period, were systematized in late antiquity, and were enlarged and enriched in the medieval period. Other, less significant, symbols were systematized in handbooks, but this was done only in the medieval period: color & light, geometrical shapes, anatomy & anthropology, music, clothing, geography, smells, and food. Numbers are among the oldest and most important symbols in antiquity. From the three legs of an oracle's tripod, to the twenty-four books of The Iliad, to the shadowy Pythagorean tetraktys; up to the twelve apostles, the one hundred fifty-three fish, and the

1

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2 seven seals; Christianity, like other Mediterranean religions, used numbers to plot symbolically the world of divine and human. Of course, not all ancient authors show an equal interest in number symbolism. Varro' s treatise On the Hebdomad is far more attuned to number symbolism than, say, Julius Caesar's Civil Wars. In early Christian literature, Revelation has many more aspects of number symbolism than does the Epistle of James; the

Shepherd of Hermas has more - albeit subtle and opaque- than does Clement of Rome. The proper role of number symbolism became a point of substantive debate in the late second and third centuries, when some Christians began to use numbers in theology in radically different ways, and to new degrees of intensity. How to apply arithmetic to theology and the interpretation of the Scriptures was important to these various competitors, since numbers formed the grid upon which someone either organized the cosmos or, to their opponent, distorted it. In this study, I focus on this early Christian debate by treating several different authors and texts whose theology is marked by a special interest in number symbolism: classical Valentinian authors, Marcus (given the epithet

Magus), Colarbasus, Monolmus, the author of the paraphrase of the Apophasis Megale, Irenaeus, and Clement of Alexandria. The author of Marsanes was not Christian, nor was any other Platonist author I discuss in chapter 9, but the parallels they furnish are an important complement to the Christian material I cover. Ideally, this study would constitute the fourth of a five-volume introduction to ancient number symbolism. The first volume would cover prehistoric number symbolism and the invention of literary symbolic numbers in Babylonia and Egypt. The second volume, presented in two parts, would introduce the number symbolism of ancient Greek and ancient Hebrew societies. The third - the prelude to this study -would survey the

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3 reemergence of Pythagoreanism in the Roman Empire and the transformation of Hellenistic and Jewish number symbolism. The fifth and final volume would explore the habits of number symbolism in Christianity, Islam, and Judaism of the late antique and early medieval periods. This would bring the story to the eleventh century, or so, just before the vocabulary of number symbolism dramatically shifted once again, through Kabbalistic and other medieval literature, into new, highly elaborate, numerical composition, and other new ways of playing with numbers. These ideal five volumes would be reciprocally explanatory. The vast quantity of ancient number symbolism, and our often-speculative efforts to understand it, require us to read later texts to interpret earlier ones, and to read just as closely earlier texts to see if the later texts have not introduced new paradigms. Unfortunately, the other volumes do not exist. Aspects of number symbolism that are critical to understand my argument, but go beyond the chronological boundaries of this study, I explore in the footnotes and excursuses. I have not written chapters on either Philo or the New Testament. Both are fundamental to any explanation of the origins of the Christian debates in the second and third centuries over numbers. But to treat them properly requires extensive discussion, well beyond the scope of this study. In addition, they have little immediate explanatory value for the systems I discuss, systems that appear to be crafted independent of any predecessors. Likewise, I have not dealt with the number symbolism of Origen, Jerome, and - seemingly everyone's favorite -Augustine. In my conclusion I suggest some trends in the emergent orthodox use of numbers. As we shall see, Irenaeus provides a rationale as to what orthodox number symbolism ought to be. To determine how closely the later tradition adhered to

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4 Irenaeus' s vision would be enlightening. Hopefully my study will provide the impetus and basis for further analysis. To get to the heart of my argument, I have had to omit a number of elementary, introductory explanations. I must assume, for instance, that you have already read, or plan to read concurrent to this study, Irenaeus' s Against Heresies, Hippolytus' s Refutation of All

Heresies, large parts of Clement's Stromateis, and the Nag Hammadi texts. I have summarized the relevant content of these texts, but these summaries are meant only to reorient you to treatises you have already read, not replace them. Whenever I can, I signal studies that are a good first stop for anyone needing further introductory material. It will also help to be familiar with some of the basic texts used in Greek number symbolism and mathematics, such as the anonymous Theology of Arithmetic (the namesake of my study), Theon of Smyrna's Mathematics Useful for Reading Plato, and Nicomachus' s Introduction to

Arithmetic. Of all these various texts, Irenaeus' s and Hippolytus' s especially should be close at hand. As for secondary studies, I try to summarize, not recreate, the state of research on various subjects dealing with early Christian theology, the Greek philosophical tradition, and other broad subjects. On occasion, I have found that modern scholarship on a given topic is inadequate, difficult, or cannot be navigated easily. For example, there are very few studies that competently treat the historical contours of psephy (gematira). In the course of my research I have developed new ideas about when and how this literary phenomenon arose. Such a thesis is important but somewhat tangential to the overall direction of this study, so appears as an excursus.

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5 Some of my terminology needs a brief explanation. For instance, I tend to avoid the term gnostic, which has been greatly abused over the last century. Thankfully, it has been increasingly recognized that gnostic does not describe a coherent category when applied wholesale to the groups Irenaeus refutes or the texts in the Nag Hammadi library.1 Rather than apply the term entirely to a number of early Christian theologies or traditions, I use it only for those specific groups that I believe are called so in the primary sources. It may seem that by focusing on groups traditionally thought of as gnostic, and by setting them in opposition to Irenaeus and his followers, I reaffirm the substance if not the labels of the difference between heretical and orthodox, between gnostic and orthodox. This would be a hasty judgment. The opposition between Irenaeus and these various groups is not the premise but the thesis of this study. I shall argue, not assume, that the two have very different views of the role of numbers. Furthermore, a number of texts and authors conventionally labeled gnostic fail to make the list since not all systems of gnosis had an interest in number symbolism. Prominently missing from our list are Simon Magus, Marcion, Basilides, "Sethian" texts, and Valentinus himself. This is not to say that numbers do not occasionally crop up in these authors' texts as symbols or literary devices, but they are less frequent and important as they are in other texts. To describe Valentinian systems the term protology (and derivatives) has been recently coined.2 The neologism is helpful, since it points to the arithmetical character of V alentinian theories of how everything began, a nuance missing in similes such as

metaphysics, philosophy, and theology. But protology can be misleading, too, since it implies that 1 Foremost of these studies is Williams, Rethinking "Gnosticism " 2 Orbe, Cristologia, 1:484 n. 198, reinforced throughout Thomassen, Spiritual Seed.

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6 the realm and operations of the Valentinians were wholly separate from those of orthodox writers, whose ruminations on the relationship between the Father and the Son would be more comfortably termed theology, not protology. Therefore I use the term sparingly, and only when it refers to theological or philosophical ideas of how the highest level of reality emerged. I also distinguish between arithmetic and mathematics. The former, the study of the properties and operations of discrete numbers (e.g., adding, multiplication), is a proper subset of the latter, which is the general study of all the numerical sciences. Mathematics encompasses arithmetic, geometry, music, and astronomy- the foursome known as the quadrivium (see excursus B). This classical distinction between the two words was current in English as late as the eighteenth century. The complete transformation of the sciences in the age of Newton led to our present usage, where arithmetic and mathematics are used interchangeably. For a study on ancient number symbolism, however, the distinction is helpful, especially since we often encounter the term f1et8fJ;.una, which always infers more than our modem term mathematics. I use the term numerology to connote number symbolism used either to conceal or to reveal occult knowledge. Think of it as a correlate to astrology, which today has similar connotations. All ancient numerology is number symbolism, but only some ancient number symbolism is numerology. Some ancient authors would probably be offended to find their number symbolism associated with more seedy activities, such as predicting the outcome of a marriage or determining a person's death based on the numerical value of their name. Thus, I generally prefer the neutral term number symbolism unless prognostication is at work, in which case numerology is accurate. Delatte introduced the term arithmology, which he

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7 found in an eighteenth century Greek manuscript, and it serves well to break up the monotony of the terminology, but it is unclear what the Byzantine Greek scribe meant by a�:_H8!-1oAoy(a, a hapax legomenon. The term magic has come under fire over the last number of years, mainly because the term was pejorative then, as it often is today. A person could accuse anyone of magic, but the standards used might backfire on the accuser in other contexts. One of the best alternative terms circulating today, ritual power, does not exactly roll off the tongue, but it accurately identifies the function of so-called magical texts, to ritualistically invoke the divine powers so as to prompt them to effect a change in the materia] world. Because both terms have flaws answered by the other, I use magic and ritual power interchangeably.3 The practice the terms describe, however, is not to be confused with prognostication. Magic is a proactive engagement with this world, whereas prognostication and divination attempt merely to read the future or present. Natural1y, one practice can lead to another, but we find in ancient texts that authors of one sort never try to do the work of the other. One further terminological clarification: I use psephy, psephic, and isopsephy to describe the ancient habit of reckoning the numerical value of names and words. This is more commonly known in English as gematria, but the Hebrew term it comes from was not coined until probably the sixth or seventh century. For the cultural and chronological scope of this study, the first three terms are more appropriate. I intend this to be the first, not final, word on the number symbolism of early Christian texts from the late second and early third centuries. I have not extensively 3 For the phrase ritual power see the introduction to Meyer et al., Ancient Christian Magic. For here, broad but inadequate terms must do.

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8 analyzed, for instance, the Barbeliotes, the Apocryphon of John, the so-called Ophites, the

Books offeu, the untitled text from the Bruce codex, or Pistis Sophia. Closer to Orthodox circles are the Shepherd of Hermas and the Sybilline Oracles. These and other such texts would be excellent candidates for future research. All unaccredited translations are my own. I sometimes suggest emendations to the standard editions of primary sources, oftentimes to justify or to corroborate my arguments. Such philological detours are unimportant and distracting to many, but preciously important to a few. I have tried to restrict these discussions to the footnotes or, if the argument is too extensive, an excursus. To signal such a philological discussion I mark the footnote callout with a plus sign, for example, 27+. It is traditional to the genre of the dissertation to spend several pages recounting the

status quaestionis. Forgive me for omitting this step. As far as I know, I am the first to raise exactly this quaestio. Certainly, there have been dozens of studies about individual texts and ideas I treat, and I signal these in the notes and bibliography. But no one, to my knowledge, has tried to describe and explain the scope of the late second and early third century Christian debate over number symbolism, and understand it within the much larger, longer tradition of number symbolism in the ancient Mediterranean world. I hope my study stimulates others to explore this quaestio.

Of those who have helped me in my research, the most important is my wife, Colette, who allowed me to work undisturbed, and whose curiosity in my topic provided many stimulating conversations. Robin Darling Young was the first to suggest that number symbolism would be a fertile subject for a dissertation; her intuition was correct, probably

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9 far more than even she knew. Michael Williams read an early draft of several chapters and encouraged me in my research. Janet Timbie provided excellent advice on my arguments concerning Coptic texts. John Nesbitt provided helpful suggestions for chapter eight. Stephen Chrisomalis suggested ideas about the development of Greek numeration, thereby enhancing excursus C. Einar Thomassen's excellent criticisms of a conference paper I delivered in 2005 helped me avoid glaring errors in an early version of chapter two. Finally, I thank my committee, William McCarthy, Philip Rousseau, Christoph Markschies, and Susan Wessel, all of whose suggestions and criticism I value.

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2 The Valentinians

As will become evident in the course of this study, many Christian authors and movements in the late second and early third centuries used numbers as important symbols for their theology and Scriptural exegesis. The most important of these groups are the Valentinians, with whom these next two chapters pertain. Valentinus flourished in Rome in the 1 40s and 150s, arriving there possibly from Alexandria, where he is said to have been born and educated. In Rome Valentinus was involved in church life until he left for Cyprus around 1 60, a departure possibly occasioned by his not being elected to ecclesiastical office. That he developed a school or some kind of following in Rome seems clear from a very early reference, around 155, to "Valentinians."1 Ever since Markschies's landmark study, scholars have increasingly recognized the difficulty of reconstructing Valentinus's system. The most reliable fragments and testimonies suggest that Valentinus, at least in the early stages of his career, did not hold to

1 Irenaeus, Against Heresies 3.4.3; Epiphanius, Panarion 31 .2.3; Tertullian, Against the Valentinians 4.1;

Justin Martyr, Dialogue with Trypho 35.6. For more on Valentinus's life, see Thomassen, Spiritual Seed, 41 7-22.

10

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11 the doctrines later espoused b y Ptolemy, Secundus, and other later Valentinians.2 Although Markschies hesitates to declare outright that Valentinus did not teach the doctrines his followers embraced, he emphasizes that the absence of such doctrines in his authentic fragments suggests that credit (or blame, depending on your perspective) must be given to the next generation or two of Valentinian teachers for introducing and developing the doctrines on which Irenaeus focuses. This resembles the view of Tertullian. Synthesizing the views of four second-century apologists, he regards Ptolemy, not Valentinus, as the inventor of the reified and arithmetically arranged aeons that form the Pleroma. Markschies and Tertullian's tones and purposes are diametrically opposed, but they both agree that Valentinus' s followers diverged substantially from their teacher's original teaching.3 I have nothing to say about Valentinus's use of number symbolism, a silence that corroborates their thesis. None of his fragments exhibit any interest, aside from the probably spurious report in book one, chapter eleven of Irenaeus's Against Heresies, discussed below. The number symbolism that is so prominent in Valentinianism belongs either to systems Irenaeus, Hippolytus, and others identify with later disciples, or to Nag Hammadi texts that do not name their authors. By using the amorphous terms Valentinianism and Valentinians, I mean to imply not that Valentinus is the originator of these doctrines but that the teachings belong to his successors.4

2 Markschies, Valentinus Gnosticus; idem, TRE 34:495-500. Nineteenth- and early twentieth-century

scholars were also skeptical, but a new optimism was introduced by Sagnard, Gnose valentinienne (1947). See Stead, "In Search of Valentinus," 75-76. 3 Tertullian, Against the Valentinians 4.2, 5.1. Note that Tertullian does not call his treatise Against Valentinus. 4 The term Valentinian is used by the heresiologists, not by the Valentinians themselves, at least in the scraps of texts that remain. Thomassen, Spiritual Seed, 4, regards the term as pejorative, and therefore

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12 Among Valentinus's most famous pupils were Ptolemy and Heracleon, both of whose authentic fragments depict theological systems that contrast somewhat with the Valentinianism exposed by Irenaeus.5 Ptolemy's Letter to Flora does not mention the doctrine of the aeons, and Heracleon's shows traces of it, but nothing that can be reconstructed with certainty .6 In any case, the protologies with the most developed system of aeons, the systems of special concern in this chapter, belong to the followers of Valentinus and Ptolemy, probably to be dated to the 1 60s and 170s. Many scholars assign this to western, or Italian, Valentinians, as opposed to the eastern ones. I am skeptical that this was a real division (see Excursus E). But even if the division was real, we know so little about it that it should not be used to classify various Valentinian doctrines, teachers, or groups.

sets it in scare quotes. But supposing that the term was derogatory, it does not follow that the Valentinians didn't embrace it. One person's slur could be the other's badge of pride. We shall see below that Irenaeus uses Valentinian association with Pythagoreanism as an insult, but they embraced it. 5 Hippolytus, Refutation of All Heresies 6.35.6. 6 On Ptolemy's letter, preserved in Epiphanius, Panarion 33.3-8, see below, 43-44, where I suggest there may be a doctrine of the aeons lurking behind Ptolemy's comments. This differs somewhat from the conclusions drawn by Lohr, "Doctrine de Dieu," and Markschies, "Valentinian Gnosticism," 429. Two very different assessments of Heracleon have been recently written: Castellano, Exegesis de Origenes, and Wucherpfennig, Heracleon Philologus. Based on the fragments, Castellano argues for and explores Heracleon's Valentinian connections. Wucherpfennig, following in the wake of Markschies (and the same series), argues on the basis of the same fragments that Heracleon was not a proponent of gnosis, and not even a Valentinian. Much of the force of his argument rests on the seeming Jack of overt Valentinian doctrine in the extant fragments of Heracleon. But Castellano's research, apparently unknown to Wucherpfennig, shows that Origen, u pon whom we depend for most of the fragments, cites Heracleon in order to show his philological and exegetical, not theological, deficiency. Although theology is not prominent in the Heracleon fragments, Castellano identifies Valentinian themes in them. I find Castellano's case more persuasive. Michael Kaler's observation (pers. comm.), however, that Origen never calls Heracleon a Valentinian, suggests that research on Heracleon is yet in its early stages. For more on Heracleon, see below, pp. 1 93-195 and 203.

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13 There are two types o f sources for Valentinianism, sympathetic and hostile. Of the first group, the earliest representatives are Valentinus, Ptolemy, and Heracleon. Some of the anonymous Valentinus wrote letters and hymns, and revised his sermons for publication. Ptolemy's letter and Heracleon's commentary on John suggest they belonged to a literary circle of broad interests. Absent these fragments, the bulk of sympathetic Valentinian sources are found in the Nag Hammadi texts, some of which may originate from this earlier period. The hostile sources are, of course, the orthodox heresiologists, whose concern for doctrinal purity determines what and how they quote from the Valentinians. Those who would prefer to reconstruct Valentinianism on the basis of nonhostile sources are faced with the conundrum, that any attempt to determine what Nag Hammadi texts are Valentinian must begin with a typology informed by the Fathers. To the same degree the Fathers have misunderstood the main, distinguishing features of Valentinianism, we too have probably mischaracterized what in the Nag Hammadi library is Valentinian. Like it or not, we must begin with Irenaeus and the heresiologists, but read them carefully, to determine what Valentinianism was all about and where it is best represented in the Nag Hammadi material? Not that we should accept everything the heresiologists report. As should be evident in my analysis, we must be vigilant against inconsistencies and rhetorical exaggeration. But there is no other way to learn about the Valentinians than by starting with those who wrote about them. The Nag Hammadi texts do no such thing. Thus, I treat first the orthodox authors' testimonies of Valentinianism, then the Nag Hammadi material, and attempt to synthesize afterwards the two types of evidence into a

7 Desjardins, "Sources for Valentinian Gnosticism."

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14 single, coherent picture. I have accepted the current consensus concerning what Nag Hammadi texts are probably or certainly Valentinian, and used them for the second part of my analysis.8 Marcus Magus, whom most ancient sources associate with Valentinian circles, has an unusual, highly developed number symbolism, so I treat him separately, in the next chapter. There are a few systems that seem typologically related to the theology of the Valentinians, but no ancient texts explicitly make the connection. Most notable are the socalled Barbelo-Gnostics and the Ophites.9 There are some theological and mythological similarities between the Barbelo-Gnostics and Valentinians, less so between the Ophites and the Valentinians, and scholars are disinclined to suggest with any confidence a line of descent from Valentinus to either system. The same applies to the number symbolism found in all three systems: the Barbelo-Gnostics' number symbolism has a few striking similarities with the Valentinians', but the Ophites, less so. Nevertheless, both Barbelo-Gnostic and Ophite systems involve intricate, albeit disparate, number symbolism. A full exploration of these arithmological systems, interesting in their own right, goes beyond the present study. I hope that what little material I present here of the Barbelo-Gnostic system will provide the impetus for a future, more detailed investigation.

IRENAEUS'S VALENTINIAN REPORT Irenaeus begins his expose of the Valentinian school by discussing at length the doctrines of one particular group or text. Roughly one third of book one of Against Heresies recapitulates s

Thomassen, "Notes pour la delimitation," and "L'histoire du valentinisme."

9 Irenaeus, Against Heresies 1 .29-30; Apocryphon ofJohn.

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15 this group's doctrine and exegesis. Although many scholars frequently refer to this group as

Ptolemaean or as the grand or main system, it is likely that both labels read too much into Irenaeus's language. Irenaeus mentions the school of Ptolemy in the preface to book one, but does not explicitly connect it with the first system he discusses.10 He never says who was responsible for this first Valentinian system. Further, Irenaeus does not explicitly call it the

main group, or any other label that suggests them to be the Valentinians par excellence. True, Irenaeus discusses them first, and to the greatest length, but this does not mean that he regards them as the most important or most advanced group of Valentinians. Indeed, Irenaeus's later discussion about Marcus-explored in the next chapter-shows that he regards this first system as but one school of Valentinian thought. All we can say with certainty is that the person or persons behind this system were Valentinians whom Irenaeus thought both typified the error of the movement in its later stages, and were especially useful for beginning his treatise.1 1 Throughout this study, I refer to this group of 1o Markschies, "New Research," 251; Irenaeus, Against Heresies 1 .pr .2 . Markschies notes that in the

preface to book one Irenaeus promises to treat the Ptolemaeans only as far as he is able; i.e., he could only treat them briefly, at Irenaeus, Against Heresies 1 .12. Thomassen, Spiritual Seed, 18 and passim, regards Against Heresies 1.1-9 as Ptolemaean, but he does not deal with Markschies' s arguments, which are, in my view, more compelling. One other point convinces me that it is misleading to refer to chapters 1 through 9 as Ptolemaean: the section mentions no proper names. This contrasts with the rest of Against Heresies; Irenaeus regularly reminds readers of the specific group or teacher he is discussing. It seems to me that, had Irenaeus known the source of chapters 1 through 9 was Ptolemaean, he would have made the most of this point, to answer the teaser in the preface. 1 1 Pace Thomassen, Spiritual Seed, who unjustly charges Irenaeus with inconsistent definitions of the term Valentinian (see, e.g., pp. 13-15). Thomassen (ibid., e.g., 15-17) also unfairly accuses Irenaeus of inconsistency in his two claims, that the Valentinians (1) have a common false doctrine and (2) constantly disagree with each other, each variation being a lie. There is no contradiction in these two theses. Consider, for instance, a biologist in our own age, who might argue in similar lines against conservative Christians, that they all (1) share a false doctrine of the origins of the physical world yet (2) cannot agree on whether Genesis teaches a young earth, an old-earth, or any other of the dozens of variations taught by Christians. Irenaeus pursues a similar line of attack against the Valentinians.

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16 Valentinians- the group behind chapters one through nine of Against Heresies book one- as the first group, not the main group or Ptolemaeans. Irenaeus' s first group of Valentinians hold to a theology that is marked by reified abstractions (termed aeons) whose associations with each other form the basis of intricate mythologies. The system is difficult to grasp without multiple readings. This obscurity is not due to the language barrier; fluent Greek speakers would have found the system just as impenetrable without several careful, slow readings. My summary here merely epitomizes the system. Readers who have never before encountered Valentinianism will find the next several pages incomprehensible without reading very carefully chapters one through nine of Against Heresies book one. In that system, the pre-existent, transcendent aeon, called Forefather- also called Foresource and Depth-coexists with his consort, Thought - also called Grace and Silence (figure 1 ).12 Depth impregnates Silence, and she brings forth Mind - also called Only Begotten, Father, and Source of All. At the same time Mind is generated, so too is his

12 Irenaeus, Against Heresies 1 .1 . 1 . Foresource I Forefather I Depth = DQOlXQXTJ I DQonaTWQ I Bu8o<;;

Thought I Grace I Silence = "Evvow: I XaQL<; I I:tyf]. Throughout this study I refer to the aeon by its name in English translation, capitalized. I indicate the underlying Greek in the notes and the figures. Figure 1 helps also to clarify the nomenclature in this system, which can be confusing. One aeon may have several names or only one, and one name may apply to more than one aeon. Many names that to Irenaeus, Hippolytus, and other orthodox writers apply to a single subject (e.g., Son of God, Word of God, Christ, and Jesus) often designate different entities in Valentinian thought. I have also capitalized the names of the various groups of aeons: Tetrad, Ogdoad, Decad, Dodecad, and Triacontad. Even if it is not clear whether these were intended to be proper nouns, they are certainly specialized terms, and capitalization helps mark that.

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17

poapxl) I Foresource llponcinvp I Forefather Bt!eos I Depth ·Evvota I Thought Xcipts I G
Noiis I Mind Movoy€111\S I Only &gotten lldTT)p I Father 'Apxi) Twv miVTwv I Source of all

o

0.9�

'AA1)9eta I Truth

Aoyos 1 Word
-

-

-

·

-

·

-

·

-.

Zwl) I Life

Av9pwnos I Man

•

Bt!ews

M ittS

Profound

!"<:'\ Ageless 1...-<..J

'Ayl)paTos

'AVTo<j>vl)s 'AKt VTJTOS

Faith

"Evwcrts

llaTplKOS

Union

Paremal

!"<:'\ 'H&ovl)

Self-engendered 1,...-<..J

Immoveable

fl(ans

Copulation

MTJTplKOS Maternal

Pleasure

!"<:'\

l:(ryKpacrts 1...-<..J Intercourse

'Ae(vovs Ever-Mindful

Movoyevl)s !"<:'\ MaKap(a Only Begotten 1...-<..J Bliss

' EKKAT)(JlQ(JTlKOS Churchly 9€ATJTOS Desired

XptaTOS (1st)/ Christ

/ .

0

0

0

'ID.n(s

()

g

Hope

'AycitrTJ Love

0 0 [> 0 (

l:vveats Und(a

I

W.sdom -

llVEVJ.La"Aytov

I� ·fl I� . " "

·

/Holy Sp,rit

'

;�d

Project ,;.,;t by all30 aeons (.A.H 1.26, 145)

[>

'hJ(JOVs I Jesus L.mjp I Savior XptcrnSs (2nd) I Christ Aoyos I Word lldVTa I All napaKATJTOS I Comforter

Figure 1. The Valentinian Pleroma, according to lrenaeus, Against Heresies 1 . 1 -9. Male aeons are assigned (arbitrarily) triangles; females, circles. Hollow triangles and circles represent the original 30 aeons. Arrows indicate lines of projection. The large hexagon represents Limit, who is assigned six names and is said to be hexagonal (ill. by author)

consort, Truth. Thus, Irenaeus claims, Depth, Silence, Mind, and Truth are the first, original Pythagorean tetraktys, and are what they call "the root of all."13 1 3 Ibid. Mind I Only Begotten I Father I Source of all = Nove; I Movoynrr'Jc; I ncn:rw I AQXJl TWV ru:XvTwv. Truth = AAr']Sna. On the term tetraktys, see excursus B3.

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18 Whether this quartet of aeons is truly equivalent to a Pythagorean tetraktys remains to be seen, but their arrangement in a hierarchy of one male-female pair over another provides the model for subsequent emanations. Mind begets Word and his consort Life; Word and Life beget Man and Church.14 Thus is formed the Ogdoad, made up of two Tetrads, one over the other. Word and Life, after begetting Man and Church, project another five pairs of aeons, called the Decad. Man and Church themselves project six pairs of aeons, the Dodecad. Thus, all the emanations combined - the Pleroma - constitute the Triacontad, arranged in three groups: Odgoad, Decad, and Dodecad. The Father- that is, the Forefather, not Mind (who also goes by this name) -then projects through Only Begotten yet another entity, Limit. Limit, who has no consort, is called by five other names: Cross, Redeemer, Fruitbearer, Limiter, and Transferrer. The entity is thought of as a hexagon that delimits and supports the internal Pleroma. Limit has two powers, a stabilizing one and a divisive one.15 Insofar as Limit stabilizes, it is the Cross; in its dividing activity it acts as Limit proper. Thus, Limit and Cross are opposite functions of the same entity. Limit is described very differently than the emanations are. It is not called an aeon. That it is called a power means that Limit is an entity of some sort, but exactly what is not specified. Its role is only somewhat less obscure. In the myth about the fall of Wisdom, the thirtieth aeon, Limit is the boundary beyond which she nearly strays in her desire to know the transcendent Forefather. Limit stabilizes the Pleroma and guards against anything on 14 Irenaeus, Against Heresies 1 .1 .1 . Word = Aoyoc:; Life = Zwfj; Man = "Av6Qwnoc:; Church = 'EKKAYJata. 1 5 Ibid. 1 .2.4. Limit = "OQoc:; Cross = LTlXVQOC:; Redeemer = AVTQWTr'jc:; Fruitbearer = KaQmmr']c:;

Limiter = 0Qo6ETTjC:; Transferrer = Mnaywyn)c:. Limit as hexagon: ibid. 1 .3.1; Limit's powers: ibid. 1 .3.5.

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19 the outside. I t forms the boundary between the Triacontad and the subsequent events that unfold as a result of Wisdom's errors. Wisdom is the last and youngest emanation of the Dodecad and, by extension, of the Triacontad . She undergoes a passion that does not involve her male consort, Desired, and she seeks after the Forefather, who is known only to Mind.16 In her journey into the vastness and inscrutability of the Father, Wisdom is nearly annihilated by the Father's sweetness, but - Irenaeus here repeats himself- she is saved by Limit, who eventually restores her to her consort. Her attempt, however, to know the Father has repercussions. As she repents, she abandons "her former Resolution, along with the passion that carne with that astonishing wonder."17 This act of repentance and Wisdom's passion, Irenaeus continues, are turned by some into an elaborate rnythology.18 In her vain effort to apprehend the Forefather, Wisdom begets a "shapeless essence" (ova(av cti-!OQcpov), the kind of nature a woman would beget, were she acting on her own. (This alludes to the commonly held belief that in all acts of procreation, the male provided the form, whereas the woman supplied the rnatter.) 19 Recognizing what has happened, Wisdom experiences first pain, then fear, and finally distress, which leads her to supplicate the Forefather. She is restored, but her Resolution and passion remain outside Lirnit.2° 1 6 Ibid. 1 .2.2. Wisdom L:o¢[a; Desired = E>u\rrr6c;. 17 Ibid. 1 .2.2, 1 .2.4. Resolution = 'Ev8Uf1T]OLc;. Passion ( rra8oc;) may be an aeon too, although Rousseau and Doutreleau do not capitalize it here in their edition. See lrenaeus's critique at 2.20.5 and my discussion below, p. 156. 1s Against Heresies 1 .2.3. 1 9 See, e.g., Aristotle, On the Generation of Animals, and Plutarch, Isis and Osiris 53-54 (372E-373A). The notion was common in Pythagorean and Platonist theology of the time. See Thomassen, Spiritual Seed, 270-91 . 2o Irenaeus, Against Heresies 1 .2.4. =

=

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20 To prevent this from occurring to any other aeon, Only Begotten projects another syzygy through the foresight of the Father: Christ and the Holy Spirit, who fasten and support the Pleroma by teaching the aeons about their syzygies, about the incomprehensibility of the Father, and about thanksgiving and true rest.2 1 With the restoration of harmony, all the aeons in the Pleroma collectively project an emanation to the honor of Depth. This emanation has several names: Jesus, Savior, Word, Christ, and AllP Along with this second Christ the angels are projected. This entity, Savior, opens up the womb of Wisdom's Resolution, who is called a second ogdoad, the external pleroma (figure 2).23 This Resolution - also called Achamoth is stranded outside the Pleroma with her passion, and is visited by the first Christ, who, via the Cross, provides the exile with the form she lacks, and she takes on two names, Wisdom and Holy Spirit. With her new form Wisdom seeks to reenter the Pleroma, but Limit prevents her, because she is still entangled by her passion. Christ returns to the Pleroma and sends along with the angels the Savior-Comforter, the entity generated by all the Pleroma.24 Resolution-Achamoth, after veiling herself, runs to the Savior and takes from him strength and a form relevant to knowledge, which frees her of her passion, and a new pregnancy of a spiritual embryo is formed in the image of the Savior.

2 1 Ibid. 1 .2.5-1 .2.6. Stead, "Valentinian Myth of Sophia," 79, notes that the generation of Christ and the

Holy Spirit produce a Pleroma of 32, not 30, aeons, which suggests that lrenaeus is introducing into a dyadi c Valentinian system elements of a monadic one. The inconcinnity is noteworthy, but recourse to the monadic/dyadic dichotomy cannot resolve the difficulty. See below, pp. 55-60. 22 Jesus = J11 aovs; Savior = Lw'rfJQ; Word = i\oyos; Christ = XQLG'ros; All = DavTa. Later (Irenaeus, Against Heresies 1 .4.5) he is called Comforter (= DaQctKAll'rOs). 23 Irenaeus, Against Heresies 1 .3.5, 1 .4.1 . 24 Ibid. 1 .4.5. '

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21 Pleroma

Savior Jesus

Christ

Christ Comforter

(1) Extension: provides , essential shape I!Op<j>wat v/

(+angels)

rr)v KaT'

oOOlav

(AH 1.4.1)

(3) Sent by Christ

·

-

' (2) Return

!

:

--

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-

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••

116pwow n)v KaTa yvwmv·--­ alhi11aTa (AH 1.5.1) = 11

ofl'spting born through pregnancy

Spiritual offspring =

Church, antitype of upper church

Soulish offspring

Demmrge * God the Father

called Ml)TpomiTwp, 'AmiTwp, l1l)l!l0Vpy6s-

.Material substance

nght

left

earth

heaven upper

lowe.r

light

heavy

animals

demons devil

men

four elements

Figure 2. The Valentinian emanation of the lower realms, according to lrenaeus,

Against Heresies

1 . 1 -9.

Male aeons are (arbitrarily) assigned triangles; females, circles. Broken lines indicate activity; solid arrows, generation. The directions right and left are those of Inclination, not the reader (illustration by author).

This encounter between the Savior and Achamoth results in a tripartition of reality outside the Pleroma. Through her passion comes matter; through her repentance, the soulish realm; through her pregnancy, the spirituaJ.25 Of these three things, she is able to zs

Ibid. 1 .5.1. These offspring are depicted in figure 2.

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22 shape only two of them, the soulish and the material, since she is not superior to spiritual substance. She takes the lessons- �J-a8r'J1-HX'W, the mathematics, if you will- imparted to her by the Savior, and shapes out of the soulish material an entity called God the Father. This is the king of all things, both the soulish and the material, corresponding to the right and left sides. Unaware that he is being moved by his mother, this Father, whom they also call Mother-Father, Fatherless, and Demiurge, creates soulish things on the right and material things on the left, becoming father to the former, and to the latter, king.2 6 The resultant material creation is Resolution's attempt to honor the Pleroma of aeons. Out of the soulish substance the Demiurge creates heavenly things and things that are light and lofty. The Demiurge, for creating the seven heavens, is called the Hebdomad, and Achamoth is called the Ogdoad, thus "preserving the number of the original, first Ogdoad of the Pleroma."27 As the Ogdoad, she is also the Intermediate Region, bridging the material universe and the Pleroma.28 Out of material substance, the Demiurge creates earthly things, and things that are heavy and lowly. From the three emotional extremes Resolution experienced while outside the Pleroma -fear, grief, and astonishmentperplexity - come the creatures and the material elements of the universe. From fear come the souls of men and animals; from grief, the devil and his demons. From astonishmentperplexity comes earth; from fear, water; from grief, air. Just as ignorance is latent in all three emotions, so fire, the fourth material element, is latent in all three elements. In the

26 Father = Da:Ti]Q; Mother-Father = MllTQ07Hhwg; Fatherless = ArHhwg; Demiurge L1llflLOUQy6c;. 27 Ibid. 1 .5.2. The same sentiment seems to underlie Clement of Alexandria, Excerpts from Theodotus 47.1, where Prov 9.1 - "Wisdom has built for herself a house and has established seven pillars" - is taken by the Valentinians to refer to Wisdom and the Demiurge. 28 Irenaeus, Against Heresies 1 .5.3--4. Intermediate Region = flECYOTlls· =

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23 creation, that of the creatures and the elements, the Demiurge acts without reflecting on or knowing what he is creating, since it is Achamoth who initiates and governs the creation. The Demiurge' s ignorance is so profound that he is unaware of the spiritual realms, and so considers himself to be the only god: "I am God, there is none besides me.''29 When the Demiurge creates men, he takes the dregs of material substance and breathes into it soulishness. Achamoth uses the Demiurge' s act of implanting the soul to sneak in the spiritual component, since the Demiurge is ignorant of spiritual things. Thus, man is a tripartite creature composed of body, soul, and spirit, derived from earth, the Demiurge, and Achamoth, respectively.30 Of these three parts, the material body is destined to perish, and the soulish component is to be cultivated to become more spiritual, since the spiritual aspect is the only one that hastens the consummation of all things. Reflecting this tripartite structure, human beings fall into grades, too. Spiritual people - Irenaeus says the Valentinians regard themselves as forming this class- are initiated into the mysteries of Achamoth.31 Soulish people are the ordinary rank and file in the Church; they lack perfect knowledge and must rely upon good works and bare faith. Earthly people-those outside the Church -have no prospect of salvation. These three grades correspond to Seth, Abel, and Cain, respectively _32 When the seeds of spiritual matter are perfected, Achamoth, the Mother, is to transcend the place of the intermediate region, to enter the Pleroma, and to be wed to the Savior. Thus, the Savior, the sole male entity engendered by the entire Triacontad, will unite 29 Ibid. 1 .5.2, 4-5; citation from Is 45.5, 46.9. 30 Irenaeus, Against Heresies 1 .5.5-6. 31 Ibid. 1 .6.1 . 32 Ibid. 1 .6.2, 1 .7.5.

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24 with the formerly abandoned Resolution of Wisdom to take up their new marriage in the bridal chamber of the Pleroma. Replacing the Mother in the intermediate region will be the Demiurge and the souls of the righteous. All material substance will be consumed by fire and be annihilated.33 According to Irenaeus, in this same circle of thought there are those who teach that the Savior sent forth a soulish being who passed through Mary as if she were a pipe channeling water.34 They say that the Savior descended upon this Christ in the form of a dove, and thereby forged in the Lord a tetrad, reflecting the first, primal Tetrad in the Pleroma. The elements of the Lord's tetrad are the soulish and the spiritual aspects (aspects provided by Achamoth and the Demiurge, respectively), the dispensation (prepared by an ineffable art), and the Savior (who was the dove who descended on him).35 That is, the Lord consists of spirit, soul, body, and a higher aeonic nature, but these natures work independently of each other.36 Thus, Jesus consists of four disjointed parts, and different episodes in his life reflect these different modalities.

I have summarized only the main points in Irenaeus' s treatment of this first Valentinian system, but it is thorough enough to show the general character of its theology and to discuss those aspects that most depend upon mathematics and ancient number symbolism. The system of emanations lends itself well to schematization, such as that of

33 Ibid. 1 .7.1, 5. 34 Ibid. 1 .7.2. 35 Dispensation: oiKOVOf1L£X, a term used by the orthodox to describe the Incarnation of God the Word. 36 This is Tertullian's interpretation: Against the Valentinians 27.2. Irenaeus's "ineffable" dispensation Tertullian takes to be the bodily aspect, and Tertullian turns Irenaeus's EK mu I:w-rf]Qoc; into Sotericiana, i .e., the [higher, aeonic] nature of the Savior.

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25 figures 1 and 2, which portray the mathematical symmetries inherent in Valentinian theology. To be noted are the emphases on pairs, quartets, octets, and the hexagon formed by Limit. The patterns in the names given to the aeons augment the mathematical symbolism. The name of the first element- the male partner - of every syzygy in the Decad and Dodecad is a masculine adjective. Female aeons, which take up the even-numbered ranks, are named with female abstract nouns.37 Further, the masculine aeons in the Decad have names that describe characteristics of the Forefather; the female aeons' names are terms for sexual intercourse. In the Dodecad, the masculine aeons' names describe some of the functions of Mind; the female aeons' names describe virtues of the mind. The names of the aeons in the Decad and the Dodecad make clear that these entities were first inside the Forefather and Mind, the ground of their being. The groups of emanations also show that the Pleroma has been organized around a mathematical principle. The most fundamental series, 8-10-12, is an arithmetical progression. The series (1)-1-2-4, found within the Ogdoad, is a geometrical progression. A harmonic progression, 6-8-12, can be identified with Limit-Ogdoad-Dodecad, but this association does not follow the narrative as closely as the other two progressions do. Thus, two of the three chief mathematical ratios, found in Euclid and Nicomachus of Gerasa, are prominent in the main configuration of the Pleroma. The assignment of odd-numbered aeons to males and even-numbered to females draws from the Pythagorean symbolic associations of gender with odd and even (see excursus B2). By naming each of the male and female aeons the Valentinians allude to the ancient practice, attested in Philolaus, Xenocrates, and others, of assigning to the numbers 37 See Against the Valentinians 6.1, where Tertullian complains that the gender of the names cannot be

replicated in Latin translation. See also ibid. 1 1 .2.

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26 one through ten to various gods and goddesses, based partly on the criterion of gendered number.38 The Valentinians describe aeonic projection as a sexual function. This imagery plays upon and reinforces the Pythagorean tendency to describe in sexual terms the relationship between the monad and the dyad, or the intercourse between odd and even numbers.39 We need not concern ourselves here with a lengthy explanation of how the Valentinians, Irenaeus's first group specifically, constructed gender per se; our main purpose is to note merely that Pythagorean arithmetic, along with its sexual vocabulary, occupies a central place. Also noteworthy is the Valentinian emphasis on fours, and on the tetraktys, a term drawn from Pythagorean arithmology (see excursus B3). The Ogdoad consists of two tetrads, one above the other, and a succession of four syzygies. That is, the Ogdoad has two structures, each of which is built upon the symbolic number four. And in imitation of the Tetrad the Lord who descends for the salvation of Achamoth's offspring takes on a fourfold character, probably intended to contrast with humanity's threefold nature (on which, see below). The importance to Valentinians of the number four as a principle of organizing both the upper realm of the Pleroma and the Lord's mission of salvation prompts Irenaeus to recall the Pythagorean association. The first Tetrad of Depth, Thought, Mind, and Truth, Irenaeus claims, "is the first and original Pythagorean tetraktys, which they also call 'the root of all' . "40

38 See below, pp. 301-302. 39 See below, pp. 303-304. 40 Against Heresies 1 . 1 . 1 .

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27 It is difficult to tell if Pythagorean tetraktys is Irenaeus' s comment, or his opponents' own explanation. Irenaeus states directly that they call the first four aeons the "root of all," but the interpretation immediately following - that this root is the Pythagorean tetraktyscould be either Irenaeus' s editorial comment or his paraphrase of his source, continued on from the previous sentences.4 1 Both scenarios fit the evidence well: Irenaeus generally holds that theology should not be beholden to any philosophy other than the rule of faith given to the Church; the Valentinians seem to offer a theology that relishes Pythagorean number symbolism. Determining the source of Pythagorean tetraktys requires first deciding if the epithet is a slander (as Irenaeus probably saw it), an honorific title (as might be expected from a school that was attempting to wed theology and Pythagorean symbolism), or both. I shall explore this question later. But note that all options are viable. After all, the term root of all- certainly a Valentinian phrase- to describe the first four aeons does nothing but encourage association with the tetraktys, described in the Pythagorean Golden Poem as "possessing roots of everlasting nature."42 And, according to Irenaeus, the Valentinians used the term tetraktys in other contexts.43 Less related to Pythagorean arithmology is the number eight, enshrined in the topmost Ogdoad of the Pleroma. Just as the primary Tetrad is reflected in the lower regions in the person(s) of the Lord, so too the upper Ogdoad is mirrored in the lower regions by the seven heavens - embodied in the Demiurge- and the mother Achamoth as the eighth. One 41 Cf. Tertullian, Against the Valentinians 6.6, where the first Valentinian tetrad is called quadriga, a four-horse chariot, not a tetraktys. Thus, the term root need not be interpreted exclusively as a Pythagorean symbol. 42 See below, p. 306. 43 Against Heresies 1 .18. 1 .

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28 of the themes in Valentinian salvation is the need to move from the lower regions of the Demiurge into the eighth, middle region, from which further advancement into the Pleroma can occur. The important idea of transition from the seventh to the eighth realms recurs throughout early Christian sources, and I shall touch on this theme intermittently in this chapter, reserving for later a more complete exploration (fittingly, chapter 8). But why eight? The number was not extraordinarily popular, either with Pythagoreans or with other Greeks who used number symbolism. In the late antique handbook The Theology of

Arithmetic the entry for the number eight is the shortest. One answer suggests itself, that the Valentinians were influenced to some degree by the ancient Egyptian cult at Hermopolis, where an ogdoad of divinities were worshipped. The ogdoad at Hermopolis consisted of four male deities and their female consorts. But the parallel ends there. There is no evidence that Egyptian religion exercised direct or indirect influence on the Valentinian doctrine of the Ogdoad.44 There too many structural differences between the two. The ogdoad of Hermopolis was actually an ennead, since the god Thoth reigned over the other eight.45 Unlike those in the Valentinian ogdoad, the female deities in Hermopolis' s ogdoad have the feminine forms of their male consorts' names. Considering how stylized and patterned the names of the Valentinian aeons are, it would be a strange 44 There is nothing to suggest that the ancient cult of Hermopolis was known to non-Egyptians in the 2nd century CE. There was an awareness of the connection between Thoth, the city's main deity, and Hermes Trimegistus, and knowledge of other parts of the city's lore (Meautis, Hermoupolis-la-Grande, 21, 24-25), but little about its ogdoad. 45 Meautis, Hermoupolis-la-Grande, 20. If in Isis and Osiris 3 Plutarch refers in veiled terms to Hermopolis's ogdoad, the enneadic structure is confirmed, since he makes Isis/Justice the head of the nine muses, i .e., the nine gods of Hermopolis. Even then, however, Plutarch's analogy does not correspond to the ancient ogdoad, thereby reinforcing my earlier point, that non-Egyptians really didn't know about the ogdoad of Hermopolis. See Gwyn Griffiths, De Iside et Osiride, 264-65.

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29 omission not to follow the same naming conventions as those found in the ogdoad of Hermopolis, were the latter the template for the former. That the deities of the Hermopolis ogdoad do not project other deities is yet another stark difference, as is the lack of any Egyptian parallels elsewhere in Valentinian mythology. My own explanation is that the Ogdoad is a natural consequence of the expansion of the primary Tetrad, just as the Decad, the Dodecad, and the full Triacontad are the result of the expansion of the Ogdoad. This is not the only explanation. The number eight was clearly an early Christian symbol, enshrined in Christ's day of resurrection and other ancient Christian symbols.46 As will become more evident as this study progresses, the Valentinians merged the Christian symbol with Pythagorean lore, thereby creating at the center of their system an Ogdoad that had two sources. Another important number in Irenaeus's first Valentinian scheme is three, used to depict the projections that emerge from Wisdom's Resolution-Achamoth. She projects three kinds of offspring, resulting in spiritual, soulish, and material substance. This tripartition leads to the creation both of the human being, who consists of all three parts, and more generally of humanity, which falls into three classes: the elect, the Church, and those without hope of salvation.47 These three categories of humankind correspond to Seth (spiritual and receptive of the seed of salvation), Abel (soulish and not receptive of the seed of salvation), and Cain (earthly, material, and wicked).48 The threefold division seems to have played a part in the Valentinians' claim that baptism belonged to the soulish members

46 Extensively documented in Quacguarelli, L 'ogdoade patristica. 47 Irenaeus, Against Heresies 1 .5.1, 1 .6.1, 1 .7.5. 48 Ibid. 1.7.5.

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30 of the Church whereas redemption belonged to the spiritual. If baptism is a barrier between the world and the Church, then the sacrament of redemption forms the second barrier between the Church and the elect, thereby creating three groups.49 Even the material world, which was normal1y in the ancient world divided into four elements, is tripartitioned in the V alentinian system. There are three passions of the Mother Achamoth: fear, pain, and perplexity. These three passions become the basis for reorganizing the four elements into three, with fire intermixed with water, air, and earth.50 The emphases on divisions of three in the lower realm suggest it is a condition meant to contrast with the upper realms of the Pleroma, where pairs and tetrads mark its harmonious composition. The point is never made explicit, but the number three, used as an organizing principle, serves as an arithmological counterweight to the twos and fours in the upper Pleroma.51 Thus, the Valentinian notion of the three parts of the human being is far more than a simple borrowing from the Platonic tradition, which often espoused a tripartitioned anthropology.52 Rather, it reinvents the Platonic theme, and makes the transformed doctrine a central part of its mathematical theology.

49 Ibid. 1 .21 .2. On this so-called redemption see Thomassen, Spiritual Seed, 360-64, 401-2 5o Ibid. 1 .5.4. See also Clement of Alexandria, Excerpts from Theodotus 48.4. 51 Irenaeus claims (Against Heresies 2.15.2, discussed below, p. 151) that the Pleroma was also trisected

into Ogdoad, Decad, and Dodecad, but this is his observation, not their claim. But not all Valentinians held to a 3-versus-4 typology. See Clement of Alexandria, Excerpts from Theodotus 80.3: "For he who has been sealed by Father, Son, and Holy Spirit is beyond the threats of every other power and by the three Names has been released from the whole triad of corruption." But see ibid . 28, where the "third and fourth" generations of Dt 5.4 refers, according to the Valentinians, to the 3 places on the left and their offspring, but 1 0,000 to whom mercy is given, to things on the right. 52 See Stead, "In Search of Valentinus," 92-94.

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31 Other Valentinians generally appealed to the world around them to corroborate their system of aeons. According to Valentinian group, the four elements - fire, water, earth, and air- are all projected, and as such are an image of the first Tetrad. The second Tetrad is signified by the "energies" of the elements: heat and cold, dry and wet. Thus, the universe encodes the Ogdoad.53 The Decad is indicated by seven circular bodies, an eighth heaven encircling them, and the sun and moon.54 The zodiac indicates the Dodecad.55 And since the highest heaven is "yoked against" the orbit of the totalities, it goes from sign to sign in thirty years.56 This motion of the heavens is an icon of Limit, which encompasses the Triacontad. The extra examples illustrating the mathematical organization of the aeons are numerous: the moon's circuit is thirty days; that of the sun, twelve months; the day is divided into twelve hours; each twelfth part of a full day is further divided into thirty parts; and the earth is divided into twelve zones. Just as they could use the heavens to illustrate the Pleroma, Valentinians used the human being, too. A person consists of a single source, the head, in which are rooted four senses, like the Tetrad: sight, hearing, smell, and taste.57 Each of these four senses have two organs (two eyes, two ears, two nostrils, and the tongue, divided into bitter and sweet

53 Irenaeus, Against Heresies 1 .1 7.1 . 54 Ibid. Is this a contradiction? In antiquity the sun and moon were ranked among the seven planets, so this list has counted them doubly. Possibly "sun and moon" here is a euphemism for other celestial entities. The sources do not elucidate this problem. 55 Ibid. See also Clement of Alexandria, Excerpts from Theodotus 71, which reproduces notes by a Valentinian who relates the 12 zodiac signs to circumstances in life. 56 Irenaeus, Against Heresies 1 .17.1. This seems to refer to procession by positing a 1 o movement of the axis against the stars every 30 years, which is about twice the actual speed of procession. 57 Irenaeus, Against Heresies 1 .18.1 . This list follows, importantly, the traditional order of the senses. See below, p. 129 n. 48.

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32 parts), and so indicate the Ogdoad. An ineffable, unseen ogdoad is thought to reside in our innards.58 In our two hands is indicated the blossoming of the Decad, and the whole body is divided into twelve parts.59 Thus, collectively, the entire human being is an icon of the Triacontad. All these themes in Valentinian number symbolism suggest that Pythagorean and Platonic number symbolism, combined with a popular view of science, is the main formative influence. The parallels are too numerous and too central to ignore. But what about Scriptural influences? How much of the Valentinian system of number symbolism depends upon Biblical exegesis? As I have already noted in the introduction, it is beyond my purpose here to speculate on the first-century roots of second-century number symbolism. It is important, however, to note how the Valentinians read Scripture and used it to inform and justify the number symbolism in their theology. Fortunately, Irenaeus preserves several examples of the Valentinian use of the Bible and its numbers.60 The entire system of aeons, the Valentinians suggest, was "not spoken of openly because not everyone could comprehend knowledge of them. But they were mentioned mysteriously by the Savior through parables to those so able to understand."61 Thus, any

58 Irenaeus, Against Heresies 1 .1 8.1. I have been unable to determine the basis in ancient science for this observation. 59 Ibid. The twelve parts of the body is prominent in Marcus. See below, p. 86. 6o There are four sections of book 1 devoted to Valentinian exegesis. These areAgainst Heresies 1.1 .3, 1 .3, 1 .8.2-5, and 1 .18. The first 3 come from Irenaeus's first Valentinian group. The fourth, however, comes after Irenaeus's discussion of Marcus, and it summarizes features that apply to all the various Valentinian groups. Strictly speaking ,the exegesis reported in chapter 18 does not belong to the longer Valentinian system. Nevertheless, I synthesize here all 4 sections, since they all share the same Scriptural exegesis. It all likely comes from a single source. See below, p. 160 n. 67. 61 Irenaeus, Against Heresies 1 .3.1.

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33 instance of aeon (aiwv) in the New Testament, such as Paul's "to all generations of the aeon of aeons" in E phesians 3.21, or even in the liturgical celebration of the Eucharist, was to be read as a cryptic allusion to the system.62 Paul supposedly taught about the syzygies in Ephesians 5.32, where, speaking about "the syzygy of life," he says, "This mystery is great, and I am speaking about Christ and the Church."63 According to the Valentinians, Paul used the analogy of marriage to refer mysteriously to the doctrine of syzygies in the Pleroma. The prologue of the Gospel of John mentions the upper Ogdoad, according to the Valentinians. They argue that John, intending to discuss the generation of all that exists, distinguished at verse one God the Father from the Beginning and from the Word.64 But when John conflates them in verse two, he shows how one is the projection of the other. Verse four introduces Life, the consort of the Word. A phrase in the same verse, "the life was the light of men," alludes to Man and Church, insofar as av8Qwnwv, being plural, must refer to someone other than Man. Thus, the entire second Tetrad is referred to. The first Tetrad is discussed in verse fourteen, where Father, Grace, Only Begotten, and Truth are all mentioned. So, John presents the primary Ogdoad in the prologue of his gospel. The lower ogdoad, that of Achamoth, is represented most especially by the prophetess Anna, who lived for seven years with her husband, then alone afterwards.65

62 Ibid . 1 3.1 . 63 Ibid. 1 .8.4. .

Ibid. 1 .8.5. Beginning refers to Jn 1 .1's cXQXTl, which the Valentinians take to be shorthand for AQXTJ TWV navTwv, the Source of all, one of Mind's alternate names. 65 Lk 2.36-38; Irenaeus, Against Heresies 1 .8.4. 64

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34 The Tetrads and Ogdoad are indicated too in Genesis, where Moses refers to them with the terms God, beginning, heaven, and earth.66 The second Tetrad, the offspring of the first, Moses refers to with the terms abyss, darkness, water, and spirit. And in honor of the Tetrad the sun was made in the fourth day, the tabernacle was made with four colors of fabric, and the stones on the high priest's robe were arranged in four rowsP According to some Valentinians, man was fashioned on the eighth day, because of the Ogdoad.68 This too explains Noah's ark, which carried eight people, David's place as the eighth brother, and circumcision on the eighth day.69 The Decad is also mentioned by virtue of the iota, the first letter in the name Jesus ('Irpouc;). This connection is alluded to in Matthew 5.1 8, the promise that not one iota would fall away before all was fulfilled. The iota as a number symbol for ten is common throughout early Christianity?0 The Decad is proclaimed also in Genesis, in the creation account, where one finds the ten terms light, day, night, firmament, evening, morning, dry, sea,

plant, and wood?1 In the rest of Genesis the Decad is alluded to in the following: the ten nations whose territory God promised the Hebrews possession, Sarra's giving her slave to Abraham after ten years, Abraham's servant giving ten golden bracelets to Rebecca,

66 Irenaeus, Against Heresies 1 .1 8.1, Gen 1 . 1 . 67 Gen 1 .14-19. Irenaeus, Against Heresies 1 . 18.2, E x 26.1 . E x 28.17. 68 Gen 2.7. See Against Heresies 1 .1 8.2 for Irenaeus's explanation of the differences among Valentinians on whether man was created on the sixth or eighth day. 69 Gen 7, 1 Pt 3.20; 1 Sam 16.10-1 1; Irenaeus, Against Heresies 1 .18.3, Gen 17.12. 70 Ibid. 1 .3.2. See below, pp. 94, 1 69, 192, 340 n. 37. On the Greek system of using letters for numbers, see excursus C. 71 Ibid. 1 .18.1 . Gen 1 .3; 1 .5; 1 .5; 1 .6; 1 .5, 8, 13; 1 .5, 8, 13; 1 .9; 1 .1 0; 1 .11; 1 . 1 1 . See below, p. 187.

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35 Rebecca's delay for ten days, and the ten sons of Jacob who go to Egypt to buy grain?2 Elsewhere in the Old Testament, Jeroboam assumes reign of the ten kingdoms, the Tabernacle has ten courtyards, and the gates measure ten cubits.73 After the Lord's Resurrection, he reveals himself to the ten disciples (Thomas in absentia) who were hidden, just as the Decad is unseen?4 The Dodecad is revealed in Scripture, too: The Lord was twelve years old when he spoke with the teachers of the Law, and he selected twelve apostles?5 The mishaps of Wisdom, the twelfth aeon, are alluded to in the apostasy of Judas, in Christ's passion occurring in the twelfth month of the year of his preaching ministry, and in the woman who had a flow of blood for twelve years?6 A further example is the twelve-year-old daughter of the head of the synagogue the Lord raised from the dead, an event reminiscent of the salvation of Achamoth.77 Just as Moses names the members of the Decad in the creation account, so he does with the Dodecad: sun, moon, stars, seasons, years, whales, fish, serpents,

birds, quadrupeds, beasts, and man - twelve terms in all?8 The twelve sons of Jacob and the twelve tribes also signal the Dodecad?9 So too, the twelve stones on the breastplate and the

72 Irenaeus, Against Heresies 1 .18.3; Gen 15.19-21 (here dependent upon the Hebrew: the LXX lists 11 nations); 16.2-3; 24.22; 24.55; 42.3. 73 3 Ki 11 .31; Ex 26.1, 26.16. 74 Jn 20.19-24. 75 Lk 2.42-46, Mt 1 0.2, Lk 6.13. Irenaeus, Against Heresies 1 .3.2, 1 .1 8.4, Clement of Alexandria, Excerpts from Theodotus 25.2. 76 Irenaeus, Against Heresies 1 .3.3, Mt 9.20, Lk 8.44. 77 Irenaeus, Against Heresies 1 .8.2; Lk 8.41-42. 78 Irenaeus, Against Heresies 1 .1 8.1, Gen 1 .14-16; 1 .14-16; 1 .1 6; 1 .14; 1 .14; 1 .21; 1.21; 1 .20; 1.20; 1 .24; 1 .24; 1 .26. Unlike the exegesis of the Decad (see above), this does not follow the order given in Genesis. Also, ilAtoc;, m:ATJVTJ, and ix8uEc; are never used in Gen 1 LXX, and must be inferred. 79 Irenaeus, Against Heresies 1 .18.4; Gen 35.22-26; 49.28.

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36 twelve bells.80 Moses and Joshua built altars made of twelve stones, twelve men carried the ark of the covenant across the Jordan, and Elisha placed twelve stones around the bull when he contended with the priests of Baal.81 Absent the Dodecad, the rest of the eighteen aeons are made clear by the eighteen months the Lord spent with the disciples after the Resurrection, and from Lll, the first two letters of his name.82 The entire group of thirty aeons illumines the Savior's not doing anything visibly for thirty years, in demonstration of the mystery of the aeons.83 The Triacontad is especially clearly evinced in the parable of the vineyard, where workers come at the first, third, sixth, ninth, and eleventh hours. The sum of the hours is, of course, thirty. So too there are the thirty cubits of height in Noah's ark, the thirty elect men among whom Samuel put Saul first, thirty days David hid in the field, thirty who entered the cave with David, and thirty cubits to the breadth of the holy tabemacle.84 For the tripartition of humanity the Valentinians point to the parable of the woman and the three measures of grain.85 They identify the woman in the parable with Wisdom, and the yeast, with the Savior. Paul too, they say, discusses all three classes of human beings.86

8o Ex 28.21, 36.2 1 . The twelve bells are not mentioned in the Bible. See, however, Justin Martyr, Dialogue with Trypho 42.1 and the comments of Rousseau and Doutreleau, 1 .1 (SC 263): 262. 81 Ex 24.4; Jos 4.9, 4.20, 3.12; 3 Ki 18.31. 82 Irenaeus, Against Heresies 1 .3.2. s3 Ibid., 1 .1 .3, 1 .3.1 . 84 Ibid. 1.1 .3, 1 .3.1; 1 Sam 9.22 (Hebrew: LXX has 70 elect); 1 Sam 20 (but inexactly: 3 days in both Hebrew and Greek; the Valentinian exegete might have extrapolated 30 from 3); 2 Sam 23.13 (somewhat loosely: 3 of 30 came to David, in both LXX and Hebrew); Ex 26.8. 85 Irenaeus, Against Heresies 1 .8.3, Mt 13.33, Lk 13.20-21 . 86 Irenaeus, Against Heresies 1 .8.3, 1 Cor 2.14-15, 15.48.

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37 Despite this wide array of Scriptures, it is unclear that these were for the V alentinians the foundations of their system, Biblical proof texts, if you will. Irenaeus' s paraphrase of their language suggests that they did not consider these verses to prove their teaching, or to be the source or foundation of it. The Bible is said to "reveal" or "make clear," implying that the insight would not be apparent to the ordinary reader. Induction into the Valentinian system is a prerequisite. As already mentioned above, the Valentinians did not regard the doctrine of the aeons as self-evident, and any allusions or teachings about it in Scripture were hidden and needed to be made manifest. That manifestation could be made only to those capable of understanding. The Valentinian schools' emphasis on the hidden messages of Scripture mirrors their belief that from the lower realms-particularly from the Demiurge and his acts of creation -was hidden any knowledge of the aeons of the Pleroma.87 Indeed, the Valentinian tradition, according to Irenaeus, was revealed only to initiates and remained hidden from anyone outside their circle, a charge that probably had some truth to it, but not for the nefarious ends Irenaeus insinuates.88 Thus, the Valentinians claimed, not that the Scriptures are the origin for or the basis of their doctrines, but that the doctrines and knowledge thereof explain and unlock the Scriptures. So what did the Valentinians claim to be the source and basis of their doctrines? How did they claim to get the system? The answer is not made explicit in Irenaeus's testimony.89 But we need not assume that they thought it came from the Scriptures or from the earliest apostolic traditions, the sources claimed by the orthodox apologists. Rather, Scripture was the place 87 See, e.g., Irenaeus, Against Heresies 1 .20. See, e.g., ibid. 1 .Pref.2, 1 .21 . 1 . 89 Not, a t least, in this first Valentinian group. W e shall see i n chapter 3 a possible exception t o this rule: Marcus receives knowledge of his doctrines by direct revelation. 88

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38 where initiates could go and discover the hidden references to the Pleroma. How this attitude compares with other writers will become more evident throughout this study.

IRENAEUS'S REPORTS ON VARIATIONS IN THE VALENTINIAN TRADITION After discussing the first Valentinian system Irenaeus details a number of variations. In chapter eleven he outlines the systems of Valentinus, Secundus, and an unnamed Valentinian (called Epiphanes by Epiphanius), and then another group identified only by the amorphous label "others." In the next chapter Irenaeus treats two groups of Ptolemaeans, the "more knowledgeable" and the "more prudent," after which he compares five different opinions among the Valentinians concerning the origin and identity of the Savior. The most significant variant of Valentinianism, the system of Marcus, follows in chapters thirteen through sixteen (discussed in chapter 3). After Marcus, the only group to have a doctrine of aeons structured on principles of arithmetic and number symbolism is the so-cal1ed Barbelo-Gnostic group of chapter twenty-one. All these systems have important differences in the numerical structures they use to describe the divine realm. The system of the aeons found in the first variation, which Irenaeus ascribes to Valentinus, is structurally the same as that found in the first Valentinian system.90 Pseudo-

Markschies (Valentinus Gnosticus ? 363-87) argues against attributing Against Heresies 1 .11.1 to Valentinus, based on a close comparison of terminology there with the same terminology in the fragments that can be securely assigned to Valentinus. The exercise has been revisited with similar results: McCree, "Gospel of Truth." I agree, this section is not likely to be by Valentinus, but I do not think the possibility is completely eliminated . There are a number of modern religious leaders who changed terminology and metaphysics as their nascent communities developed. Note, for instance, the Book of Mormon, which bears little evidence of the later doctrines of Joseph Smith. I will refer to the material in Against Heresies 1 .1 1 .1 as belonging to pseudo-Valentinus, for the sake of convenience, not conviction. 90

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39 Valentinus posits an original Dyad (Ineffable and Silence), which projects a second Dyad (Father and Truth). This Tetrad then projects the second Tetrad (assigned the same names as in the first Valentinian system). The first pair of the second Tetrad projects ten powers, and the second pair, twelve. Pseudo-Valentinus also posits two Limits, rather than one. The first is meant to bracket Depth (i.e., Ineffable) from the rest of the aeons, and the second, to separate the Pleroma from the wayward aeon, Mother. He never mentions the geometrical shape of either Limit. Aside from this and the doubling of Limit, pseudo-Valentinus and the first Valentinians use the same number symbolism to organize the upper Ogdoad. Secundus, the creator of the next variant, also holds to an upper Ogdoad, but he arranges its two tetrads into right and left, corresponding to light and darkness.91 Such an arrangement of opposites resembles the Valentinian opposition between the materia] and the soulish elements of the created world, an opposition that seems to allude to and play with the Pythagorean table of opposites.92 The paratactic arrangement of the two tetrads in Secundus' s system suggests that he thought of the projection of the aeons differently than the other Valentinians did, as a movement sideways, as well as downward. Unfortunately, Irenaeus does not supply enough information to explore the variation further. The system ascribed to Epiphanes is more peculiar.93 To him, the primal aeon, Foresource, existed before all. He calls it Mov6'rf]c;. With Foresource exists Power, designated 'Ev6'rf]c;. The two are treated as a pair that projects, in tum, Monad (also called Source of all, as in the first Valentinian system) and Hen. This second pair then projects all

91 Irenaeus, Against Heresies 1 .1 1 .2. 92 See below, pp. 300-301 . 93 Irenaeus, Against Heresies 1 .1 1 .3.

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40 the remaining aeons. The paradox here is that Epiphanes - to adopt on a provisional basis Epiphanius's nomenclature for this otherwise-anonymous author- depicts the primal Tetrad as a quartet of unities, organized internally in a hierarchy. That is, each of the four aeons' names is some variation on the word

one.

The names of these unities follow a distinct

pattern, with the root f.l OV- forming the names of the first and third (the male) entities, and £v-, that of the second and fourth (the female). Furthermore, the male aeons are called "sources," and the female, "powers." The relationship can be arranged in a square:

APXAl

�YNAMEl�

Movonv;; Movac;

'Ev6'rTJc; "Ev

Epiphanes' system draws from two important conventions in Greek mathematics. First, there is the debate, begun in the Hellenistic period, over whether the monad is metaphysically higher than the hen, or vice versa (see excursus Bl). Epiphanes falls clearly on the Pythagorean side of the debate. Second, Epiphanes' system resembles somewhat the structure that Nicomachus of Gerasa gives the four mathematical disciplines, what was later called the quadrivium (see excursus B4). Monotes and Monad are to Henotes and Hen as arithmetic and music are to geometry and astronomy. This arrangement was not unique to Epiphanes: the aeons in the Tetrad of the first Valentinian system also seem to share this kind of relationship. But Epiphanes' nomenclature makes the connection with the quadrivium more explicit.94 It also makes very clear his Pythagorean credentials.95 94 For parallels between Epiphanes and Marcus, see below, p. 93 n. 40.

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41 The fourth, anonymous group called "others" in chapter eleven posits an Ogdoad whose typology departs further from the other Valentinian Ogdoads.96 In this system,

Tipoa pxfi Foresouu:e

include) Depth and Silence. The first entity of this Ogdoad is Foresource, after whom come Inconceivable, Ineffable, and Invisible, in second through fourth places. Each of these four

5

Soun:e

'AvEWOT)TOS --....·AKaTctAT)TrTOS Inconceivable •

2 Incomprehensible 6

AppT)TOS �AVOVOIJ.G<1TOS Ineffable

there is an Ogdoad that preexists (and therefore does not

' Apxfi

---r--

3

'A6paTOS ______.... 'A)'EWT)TOS Invisible

4

7

Unnamable

Unbegotten

8

Figure 3. An anonymous Valentinian' s system, based on lrenaeus, Against Heresies 1 . 1 1 . 5 (illustration by author).

entities emits another to fill the fifth through eighth places, as weii as the first through fourth places: Source, Incomprehensible, Unnamable, and Unbegotten.97 The explanation suggests the arrangement shown on figure 3. Here the sideways motion of projection, similar to that alluded to in Secundus, is unmistakable. The primal aeon emanates downward three levels, then across, unlike emanations in the first Valentinian system: across before a downward cascade. It is also worth noting that the names of the entities reveal the intended hierarchical structure. Foresource, by virtue of its name, precedes Source. The rest of the entities' names, on both left and right, are all adjectives formed from the alpha privative, and describe properties of Foresource. This Ogdoad has vertical symmetry, as if it were a wax tablet. The anonymous Valentinian has 95 See below, pp. 308-309. 96 Irenaeus, Against Heresies 1 .1 1 .4. 97 Inconceivable awvvorrro c;; Ineffable = cXQQrrroc;; Invisible = aOQ(XTOc;; Source = cXQ Xr'J; =

Incomprehensible = aKC
=

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42 used a naming technique similar to that used in the first Valentinian system's Decad and Dodecad, but with different results. After presenting these four groups Irenaeus discusses the d ifferences among the various groups concerning whether Depth has a mate or not. These differences pertain to monadic versus dyadic models

No\Is Mind

of Valentinianism, which I discuss later, in connection

Figure 4. The "more knowledgeable"

with Hippolytus' s report on Valentinianism.

Ptolemaeans' system of the aeons, based on lrenaeus, Against Heresies 1 . 1 2 . 1 . Male

The first group mentioned in chapter twelve,

aeons are (arbitrarily) assigned triangles; females, circles (illustration by author) .

"those around Ptolemy more knowledgeable," diverges yet further in its mathematical arrangement of the upper aeons.98 Depth, first of all, is considered to have two consorts, Thought and Will, the former prior to (but also dependent on) the latter (figure 4). Thought mixes with Will, and produces Only Begotten (also called Mind) and Truth. Truth is the offspring of Thought, and Only Begotten, of Will. In this arrangement the Ptolemaeans have transformed the Valentinian Tetrad. Depth rules over a pair of female aeons, who then, in chiasm, generate the first male-female pair.99 Comparing this system with the others suggests that it elaborates upon the classic Valentinian system (and not vice versa), since it stretches and plays with the conventional odd-even and male-female number symbolism, 98 Irenaeus, Against Heresies 1 .12.1. 99 Note, Will's gender seems ambiguous. She is called, first, a consort of Depth, and is given a female abstract noun for a name. But this name is subtly changed from 8£AT)m� to the neuter cognate, 8£AT)f-1C<, and then Will is said to be the archetype for the male. This is probably an intentional transformation, and our sources do not explain its purpose.

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43 and even alters the dynamics of the upper Tetrad. It alters the traditional Valentinian notion of a syzygy, since it assigns to Depth two, instead of one, consorts, to reflect the two different stages (thinking, willing) involved in one aeon emanating another. The next group discussed in chapter twelve, "the more prudent" (that is, of those around Ptolemy) offers yet another model for the generation of the Ogdoad.100 In this system, Forefather and his Thought emanate the next six aeons all at once. This seems to conflict, however, with a subsequent clarification, that Word and Life emanate from Man and Church. It is unclear, then, if Forefather and Thought emanate all the other six aeons or only some of them. The arrangement also reverses the Valentinian system, which has Man and Church emanate from Word and Life. Our sources do not attempt to resolve the discrepancy about the projection of the Ogdoad, whether it happens all at once or progressively. In any case, this group has organized the Ogdoad in two Tetrads, and four syzygies, very much in line with the other Valentinian systems. Since we have discussed the two groups specifically called Ptolemaeans, it is worth noting some aspects of number symbolism in Ptolemy's only preserved work, his letter to Flora.101 There, Ptolemy discusses the Mosaic Law, noting that all five books have three separate authors, and that the part that is authored by God is itself tripartitioned into pure, mixed, and symbolic.102 The Ten Commandments are the most perfect of the three sections, reflected by the presence of the perfect number ten.1 03 This three-way division of the Law reflects how the very god who gave the divine part of the Law is the Demiurge, a deity that 1oo Ibid. 1 .12.2. 1 01 Preserved by Epiphanius, Panarion 33.3.1-33.7.10. w2 Ibid. 33.4.2, 14; 33.5; 33.6.1-5. 1 03 See below, n. 125. Ptolemy's observation parallels Heracleon's. See below, p. 1 94.

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44 stands between the perfect God and the DeviJ.l04 Ptolemy then presents a riddle- the unbegotten Father stands as the origin of two very different essences, the corruptible and the incorruptible-but he ends the discussion with a promise to write again and discuss further the origin of things.105 In these cryptic references Ptolemy alludes to a pattern seen in the first Valentinian system: the lower realm is tripartitioned, a symbol of its inferior status to the upper Pleroma. Ptolemy shies away from discussing the upper levels of divinity. Maybe he held to a view of the aeons similar to that found in the first Valentinian system.106 We cannot tell, but it is worth noting his interest in dividing and arranging the Scriptures and the world according to patterns found in other Valentinian systems.107

BARBELO-GNOSTICS Late in book one Irenaeus discusses one more group with a theory of aeons stamped with mathematical symbolism. These are the so-called Barbelo-Gnostics.108 Irenaeus makes no formal connection between them and the Valentinians, although later heresiologists do.1 09 The description of how they envisioned the generation of the upper realm is rather unclear, 104 Epiphanius, Panarion 33.7.3-33.7.4. 105 Ibid. 33.7.9. 106 For further evidence see below, p. 194. 107 Epiphanius makes a similar observation, at Pan arion 33.1 1 .1 0, where he calls Ptolemy a "divider

and geometer of the Law." Geometer (yEW!-!ETQT]C:) means surveyor, but here it certainly alludes to the second mathematical science, geometry. ws Throughout this study I use B arbelo- G n ostics admittedly a modern term - not just out of convenience: Irenaeus calls them, along with the members of the other two systems discussed in Against Heresies 1 .29.1-1 .31 .2, "gnostics" (see excursus E) and he dwells on their reverence for an aeon called Barbelo (Against Heresies 1 .29.1). Theodoret, Compendium of Heretical Fables 1 .13 (PC 83:361-64; Rousseau and Doutreleau, Contre les Heresies, 1 .1 [SC 263]: 328--35) calls them Barbeliotoi or Borborianoi. 109 Rather, Irenaeus or his source connects the Barbelo-Gnostics with Simon:Against Heresies 1 .29.1 . For their alleged connection with Valentinianism see Theodoret, Compendium of Heretical Fables 1 .13. -

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45 but the general structure can be tentatively reconstructed, through a judicious use of Theodoret's paraphrase of Irenaeus.110 There

·Ewma I Thought

is an aeon (the unnamable Father) who exists in a virginal Spirit, whom they call Barbelo (figure 5).m From this primal pair- the male aeon embedded within the female - the rest of the aeons emanate. The Father desires to

AirroyEvl)S I Self-

Xdp�s I Gua eEAT)<JlS I Will l:UvEO�S I Understanding pwvq
manifest himself to Barbelo, and Thought comes forth.112 Barbelo then asks the Father for Foreknowledge, who, in tum, seeks

Figure 5. Upper Pleroma of the Barbelo-Gnostics, according to lrenaeus, Against Heresies 1 . 29. 1 , with Greek terminology supplemented by Theodoret,

1 . 1 3 . Figure does not depict the aeons Adamas, Agnitio, Wood, or

Compendium of Heretical Fables

Magnitude. Male aeons are (arbitrarily) assigned

Incorruption, then "eternal Life."113 Barbelo

triangles; females, circles (illustration by author).

then begets Light, also dubbed Christ, who asks for and receives Mind. The Father then adds Word. Also in this group is Will, whose generation is not explained.114 The aeons of this group then form four pairs among themselves, and become an Ogdoad, although it is not explicitly called this.

110 Compendium of Heretical Fables 1 .13. Theodoret diverges from Irenaeus's account most significantly

by conflating Barbelo and Thought. My account in this section follows Irenaeus' s report, and I draw from Theodoret' s version mainly to clarify Irenaeus' s terms. m Barbelo = BcxQ�T]i\w8 (Theodoret) or BcxQ�T]QW/BcxQ�T]i\w (Epiphanius). 1 1 2 Both Theodoret and the various versions of theApocryphon of John, which also recounts the Barbelo-Gnostic myth, depart here from Irenaeus: Thought and Barbelo are the same aeon, thus preserving the primacy of the Father, who is called Monad. Apocryphon of John 4.26-5.4 (numeration in Layton's translation). 1 1 3 Foreknowledge = I1g6yvwmc;; Incorruption = Acp8a:gaia:; eternal Life = a:iwvia: Zwr). 11 4 Light = wc;; Will = 8ii\T]f1CX.

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46 The pattern of emanation differs considerably from other Valentinian systems. The first to emerge from Father and Barbelo are the first four female aeons, not male-female pairs of aeons. The four feminine aeons emerge not from sexual activity but from answers to requests made by other aeons. Further, the order in which the male aeons are projected does not correspond to the order of their female counterparts. For example, the male counterpart to Thought, the first female aeon, is Word, who is the penultimate to be projected. There is also very little connection between the names in the V alentinian Ogdoad and those in the Barbelo-Gnostic one. The Barbelo-Gnostic system revels in Ogdoads. After Thought and Word beget another syzygy, Self-begotten and Truth, the third and fourth syzygies (Incorruption & Christ-Light and Life & Will) generate eight luminaries to guard them.115 Incorruption and Christ-Light generate Armozel (also called Savior), Raguhel, David, and Eleleth. Life and Will generate the luminaries' female counterparts: Grace, Will, Understanding, and Prudence.11 6 In the Barbelo-Gnostic version of the myth of the fall of Wisdom yet another Ogdoad is generated. Wisdom, seeing that all the other aeons have consorts, seeks her own mate in the lower regions.m There she generates a "work" that contains Ignorance and Audacity; the work itself they call First Ruler, the creator of this world. First Ruler then unites with Audacity and generates Evil, Jealousy, Envy, Discord, and Desire.1 18 When the mother of

Self-begotten = AtnoyEvi]c;. Irenaeus, Against Heresies 1 .29.2. 1 1 6 Will = E>L\Tjmc;; Prudence = QWVT]mc;. m Irenaeus, Against Heresies 1 .29.4. m

n s Ignorance = "Ayvow; Audacity = Av8abEta; First Ruler = TIQwTciQxwv; Evil = KaKia; Jealousy =

Zi]Aoc;; Envy =
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49

naTIJp I Father Milos I Deplh

' A):r\9Eta I Trulh

Zunj I Life

t;' 1l

Bvews ProfoWld

' AytjpaTOS .-\gdess

'AVTo<jnn)s Sdf�dered

Copulation

Intercourse

Maternal

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_

I

W

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� �· rr

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lft.,

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I g.

:Euvwts

,�

..

[::8 EKKA'lOWUTtKOS MaKaptOTl)S [::8 I 8E.Al)TOS "'-- 0 :Eo<j>(a •

MaKap(a

XptOTOS (1st) I Christ

AELVOI!S

. ,:2.

' ID.rr(s

[::8

MqTptKOS

Pleasure

Immoveable

[::8

Paternal

w ' H&ovtj

LL')'Kpaats

Failh

OaTplKOS

Union

w MovoyEvtjs w

0(aTLS

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w •EVIllULS

' AKlVl)TOS

Only Begotten

OapciKATJTOS

Mi�LS

I "0 " . 8 l'ii· ()

Understanding

Churchly

Blessedness

. Desired V �

Wisdom

I

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OvEflva" AyLOv I Holy Spirit

'

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-

. -

Figure 6. Valentinianism, as reported by Hippolytus,

·

-

.

Refutation of All Heresies

I>

Kaprros 1 Fruit ' ll)OOVs / Jesus

6 . 29-36. Male aeons are

(arbitrarily) assigned triangles; females, circles. Arrows indicate which aeons project which. Unlike in figure 1, Limit is not presented as a hexagon; the circular shape is arbitrary (illustration by author) .

the monadic Father, followed by six emanations, or powers. The theological grouping of one followed by six is a recurrent structure in the theology of other groups Hippolytus discusses.123 1 23 See, e.g., the system of Mono'imus, discussed below, chapter 4. See also Stead, "Valentinian Myth," who argues that such a presentation would have appealed to a 2nd-century reader of Philo.

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50 Mind and Truth, seeing their offspring productive, present to the Father a perfect number of aeons: ten.124 According to these Valentinians the Father had to be glorified by a perfect number since he, the unbegotten Monad, is himself the most perfect. Thus, just as the Monad, in its utmost perfection, is the foremost of numbers in the Decad, so the Decad is the foremost of things that come into being in multitude.l25 Word and Life, seeing Mind and Truth glorify the Father, attempt to glorify their own parents. Because they lack the same level of paternal protection, Word and Life beget twelve aeons, a slightly less perfect number.126 Thus, there are, in total, twenty-eight aeons, not counting the Father, who transcends them.127 Hippolytus's version of the myth of Wisdom is similar in many respects to that of Irenaeus. She is the twelfth aeon, and she runs upward to be with the Father. In 1 24 Cf. Irenaeus, Against Heresies 1 .1 .2, where Word and Life, not Mind and Truth, beget the Decad, a

difference Hippolytus notes at Refutation of All Heresies 6.30.4. 1 25 Hippolytus, Refutation of All Heresies 6.29.8. Cf. Theology of Arithmetic 81 .9. Various numbers are called perfect, most notably 3, 6, 7, and 1 0, each for a different reason: 3 has beginning, middle, and end (see below, p. 257); 6 is the sum of its factors (including 1, but excluding itself); 7 has cosmological and theological perfection, especially in the Jewish and Christian traditions; and 10 is the image of 1, the most perfect number. For other ancient discussions of 10 as perfect, see Aristotle, Metaphysics 986a8, Problemata 910b31, and frag. 203 (= Alexander of Aphrodisias, Commentary on Aristotle's Metaphysics, p. 40, Hayduck ed.); Plutarch, The E at Delphi 9 (388E); anonymous, [On the Numbers] (Delatte ed., lines 20, 55); Philo, Questions and Answers on Genesis 4.110; Clement of Alexandria, Stromateis 6.1 1 .84.5 (discussed below, p . 192); Monoi·mus in Hippolytus, Refutation of All Heresies 6.24.1-2, 8.14.6 (see below, p. 1 1 2); Hippolytus, Refutation of All Heresies 1 .2.8-9, 4.51 .6, 6.23.5; Chalcidius, Commentary on the Timaeus 84.5-8; anonymous, The Mysteries of the Greek Letters (Hebbylynck's ed, 52-53). 126 Hippolytus, Refutation ofA ll Heresies 6.30.1-2. Cf. Irenaeus, Against Heresies 1 .1 .2, where Man and Church beget the Dodecad, a difference Hippolytus notes at Refutation of All Heresies 6.30.5. The comment on the relative imperfection of the Dodecad must be Hippolytus' s , since there is no indication in any of the other Valentinian systems that the number twelve was deficient. Hippolytus's other heresies are frequently obsessed with the perfection of the number ten (see below, chaps. 4 and 5), and it is likely that that concern has leaked into his report here. 127 Hippolytus, Refutation of All Heresies 6.30.3.

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51 Hippolytus's narrative, however, she tries to imitate his monadic, syzygy-less state, and does so without properly understanding the difference between the Father's transcendent nature and her own, inferior nature.128 Wisdom's projection of a shapeless essence horrifies the aeons, who plead the Father to take action before they are overcome by corruption. This prompts the Father to order Mind and Truth to project Christ and the Holy Spirit to stabilize the Pleroma. Their projection brings about the full number of aeons, thirty.129 The Father also projects another aeon, Cross, to stabilize the Pleroma, and he emerges as Limit.l3° The whole Pleroma, now peaceful and harmonious, decides to glorify Depth and so collectively project a single aeon, Fruit, also called Jesus.131 The exiled aeon Wisdom is called, as in Irenaeus's systems, Ogdoad, and the Demiurge, Hebdomad.132 Note, the only Ogdoad in Hippolytus's Valentinianism is in the lower realm. Wisdom is called an Ogdoad, but the significance of the name is not explained. Since there is no upper Ogdoad, she cannot be a reflection of it, as is found in other Valentinian systems. The lower world in Hippolytus's Valentinianism is governed by fours. Wisdom is struck by four passions, not three: fear, pain, perplexity, and (the new one) supplication.133

12s Ibi d. 6.30.6, 7. 129 Ibid. 6.31.1-3. Here Hippolytus, like Irenaeus, notes the conflicting methods the Valentinians use to

derive the quorum of thirty aeons. Hippolytus is concerned, however, with presenting a model that genuinely differs from Irenaeus's. Thus he acts as if the default Valentinian system is the one where the Father is not counted with the aeons and Christ and Holy Spirit are. 1 30 Ibid. 6.31 .6. He is also called Participant (=Maoxn)c;), possibly a corruption of Irenaeus's Transferrer (=Mnayoyn)c;). In any case, Limit in Hippolytus's Valentinian system has only three names and is not suggested to have any particular geometrical shape, like a hexagon (as in Irenaeus's first Valentinian system). Note, too, Hippolytus, unlike Irenaeus, calls Limit an aeon. See above, p. 18. 131 Hippolytus, Refutation ofAll Heresies 6.32.1-2. m Ogdoad: ibid. 6.31 .7, 6.32.9, 6.33.1, 6.34.8, 6.35.4, 6.36.1 . Hebdomad: ibid. 6.32.7, 6.36.1, 6.33.1 . 1 33 Ibid. 6.32.5. Cf. Irenaeus, Against Heresies 1 .5.4.

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52 Each of these four passions the aeon Fruit/Jesus (equivalent to the aeon Jesus in Irenaeus' s Valentinian system) takes and instantiates - that is, he endows them with essence, reifies them, if you will- separately from Wisdom.134 Her fear brings about the essence of the soul; her pain, material essence; her perplexity, the essence of demons; and her supplication, the "power of the essence of the soul." Over each of these four elements presides a ruler. The Demiurge governs the essence of the soul; the Devil (bLa�oAoc;), material essence; Beelzebul, the essence of demons; but Wisdom, higher than all three, governs the spirit.l35 This fourfold scheme of elements is, according to Hippolytus' s Valentinian, the Pythagorean tetraktys, the "source with the roots of eternal nature." In Hippolytus's Valentinian system, there is no upper Tetrad, only the six roots, all in pairs, the most fundamental number for organizing the Pleroma. This emphasis on four contrasts with Irenaeus' s V alentinian systems, which tend to subdivide the lower realm in groups of three. Hippolytus mentions other variations in this group's number symbolism. Just as astronomers divide the world into divisions of twelve, thirty, and sixty parts, so, he says, they carve up the aeonic realm.136 Hippolytus also notes that they associate Wisdom (and not Achamoth) with the Ogdoad, and that they specify there to be seventy angels who accompany Fruit-Jesus. These Valentinians' insistence upon a Father that is utterly Monad brings up the most fundamental difference with Irenaeus's Valentinians. To make the importance of the issue clear, it is worth rehearsing what Irenaeus says about the differences in the Valentinian

1 34

Hippolytus, Refutation of All Heresies 6.32.6.

Bs Ibid. 6.33.1, 6.34.1 .

136 Ibid. 6.34.3.

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53 school regarding the status of the perfect aeon (Foresource, Forefather, Depth, or-in Hippolytus - Father). He outlines three differences of opinion in Valentinianism. (1) Depth is without consort since he is neither male nor female, nor even altogether subject to existence; (2) Depth is androgynous, encompassing in himself the hermaphroditic nature; (3) Silence is Depth's bedmate and the two constitute the first syzygy.137 The systems Irenaeus outlines clearly fall in the third group, the one that emphasizes the paratactic relationship between Depth and Silence. The first group, which claims for the Monad utter solitude, resembles the system Hippolytus presents. The second group, however, posits a first principle that encompasses multiplicity. This position falls between the two extremes. In it Depth is neither utterly solitary nor eternally yoked. Hippolytus, however, does not present as many schools of thought in Valentinianism. He reduces the options to two, Irenaeus's first and third groups. For the group that holds to the position of an asexual first principle Hippolytus assigns an origin in Pythagoreanism (Irenaeus's first group). He does not explain the origin of the group that holds to Silence as his consort (Irenaeus' s third group), aside from noting that they were trying to answer a problem faced by the first, of how generation can come from only a Father.138 The distinction between the two groups emerges again when Hippolytus explains how the number thirty is reached in the Pleroma. The first group includes Christ and the Holy Spirit in the total number, and excludes the Father. In contrast, the other group includes the Father and his consort Silence, thus arriving at the quorum thirty before Christ

m

Irenaeus, Against Heresies 1 .1 1 .5.

1 38 Hippolytus, Refutation of All Heresies 6.29.3, repeated at 6.38.5.

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54 and the Holy Spirit are projected.139 But Hippolytus is disinterested in treating at any length the teachings of the second, more dyadic system. Thus, by omitting Irenaeus' s second, middle option, and by discounting the third, the dyadic group of Valentinians, Hippolytus reshapes the Valentinian school to serve his overall purpose, to show how each heretic resembles and depends upon a prior philosopher. In this case, he accuses the Valentinians of following Pythagoras.140 He presents the Valentinians as belonging to one of two groups, either monadic or dyadic, and so Hippolytus mirrors the perception his contemporaries had about the Pythagorean tradition, that it had monistic versus dualistic- or monadic versus dyadic-branches.141 One might think that Hippolytus should have preferred to emphasize the dyadic school of Valentinians, given the early Pythagoreans' preference for polarities.142 Hippolytus, however, is not as interested in writing historically accurate analogies as he is in establishing parallels between the heretics' and the pagan philosophers' lines of succession.1 43 Had Hippolytus chosen to emphasize the dyadic strain of Valentinianism, this

1 39 Ibid. 6.31.3. 1 40 On such polemics by Hippolytus, see Marcovich, Refutatio omnium haeresium, 35-38, and Mansfeld,

Heresiography in Context, passim. 14 1 The older Pythagoreans were supposed to be dyadic; the more recent, monadic. See Dillon, Middle Platonists, 344, 373, 379; Armstrong, "Dualism," 34-41; and Thomassen, "Derivation of Matter," 3-4 . The distinction is made by Sextus Empiricus, whose writings Hippolytus plagiarizes often. See Marcovich, Refutatio omnium haeresium, 36. To refer to the systems, I prefer the terms monadic and dyadic to monistic and dualistic, since the latter pair are subject to so many vagaries and definitions today. E .g., there is ethical dualism, metaphysical dualism, anthropological dualism, and theological dualism. Monadic and dyadic are not used so broadly, and they are built upon the ever-important terms monad and dyad, key to ancient philosophy and Valentinian thought. See excursus B l . 1 42 See excursus 82. Note especially Philolaus's dependence upon limiters and unlimiteds as the basis of his metaphysics, and the table of opposites embraced by early Pythagoreans. 1 43 See above, n. 140.

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55 would have left other systems he discusses elsewhere outside this parallelism. The

Paraphrase of the Apophasis Megale, for instance, has an upper structure similar to that of the .

monadic Valentinians in the Refutation of All Heresies (see below, chapter 4). Thus, Hippolytus accuses the Valentinians of mirroring Pythagoras, and he emphasizes the version of Valentinianism that incriminates as Pythagorean other groups he discusses. Hippolytus's oversimplification of the differences in Valentinianism is intentional. Unfortunately, many modem presentations of Valentinianism follow Hippolytus' s oversimplification, dividing the school into monadic versus dyadic camps. Sometimes this dichotomy is used by editors, translators, and commentators of Valentinian texts to classify them into one of the two groups.144 Although it is not an original observation that monadic versus dyadic classifications oversimplify Valentinianism, the point bears repeating, particularly in this study, where the contrasting symbolism of the numbers one and two affect our interpretation and classification of various authors' number symbolism.145 There are several marks that can be set upon a monadic-dyadic scale. There is, first of all, Irenaeus' s second of three categories of Valentinians, a category that envisions the highest principle as being simultaneously male and female, an association made in ancient 144 Turner uses this monadic-dyadic dichotomy to edit A Valentinian Exposition (91, 97-99). See pp. 6774, below, for my critique. Attridge and Pagels depend on the antithesis for their commentary on The Tripartite Tractate (22:179-80; 23:218-1 9). For scholars' earlier use of the dichotomy, see Stead, "Valentinian Myth," 77 and nn. 2-3. 145 Attridge and MacRae, commenting on their edition of The Gospel of Truth (NHS 22:77), note that in Valentinian systems a primordial principle may also be thought of as dyadic: "It is, in fact, likely that the divergences within the Valentinian tradition on this subject are more matters of emphasis in articulating a complex fundamental theology than they are radically distinct theological positions." What I offer here is not to be confused with the kinds of cosmic dualism Armstrong ("Dualism") treats. Determining the relationship between monad and dyad in a particular author has little bearing on whether that same author is a cosmic dualist or a two-world dualist (Armstrong's terminology).

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56 mathematics with the number one.146 In this model the first aeons are simultaneously monadic and dyadic, in that the dyad resides potentially in the monad, just as the female aspect resides potentially in an androgynous being. To Irenaeus' s second option can be added yet another way of representing the relationship of the first principle to the second. This system envisions the first principle as a self-sufficient monad, but in eternal subordination to it is the second principle, presented and emphasized as an entity distinct from the superior. This differs from Irenaeus' s first group, in that the dyadic aeon is thought of as being always present with the Monad. "There never was a time when the Dyad wasn't," to take a page from the later Arian debates. Under this category fall the systems presented in The Tripartite Tractate, the First Apocalypse of ]ames, and The Gospel of Truth, three Nag Hammadi texts that show clear signs of Valentinian theology.147 Thus, there are at least four ways Valentinians could present the highest principle. The purely monadic system can be depicted as a single entity, completely alone. The next most monadic system is what I call spermatic monadic, since it presents the second principle as an inherent aspect of the first principle, embedded and never separated, like a seed of the Father. The system typically presents the first principle as embedding the second, but sometimes the model can be reversed. In Irenaeus' s Barbelo-Gnostic system, for instance, the second principle, Barbelo, enmeshes the first. The model appears frequently in

1 46 See excursus B2. One is not a number in the ancient world, since ci:QL8 f16� connotes multiplicity. But to write coherent sentences I occasionally call one a number. 1 47 See below. The Tripartite Tractate may be an exception. At fol. 60 it seems the aeons live spermatically within the Father, which suggests spermatic-dyadic Valentinianism, described below.

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57 Pythagorean texts of the period.148 The third system, more explicitly dyadic, is made up of one entity in eternal superiority to a second entity, a relationship often expressed as a Father-Son relationship. I thus call it parental dyadic. It resembles in some ways the Pythagorean relationship between monad and hen, a hierarchical arrangement well known in the second century (see excursus Bl). The fourth system on this scale is more purely dyadic. The first principle is yoked with another entity in a relationship often thought of as a syzygy. In this system, which I call conjugal dyadic, Silence (or occasionally Wisdom) takes on aspects of the role of an accompanying dyad or consort.149 This system too appears in Pythagorean mathematical descriptions.150 Since conjugal-dyadic Valentinianism preserves a sense of hierarchy, it is important to note a fifth possibility, found in the metaphysically dualistic systems of societies further east, where the two principles are absolute peers; one is no greater than the other. I have seen no evidence for this fifth system in Valentinianism - it is avoided in Greco-Roman literature in general -so I omit it from consideration here.151 Whether a writer focuses on the Monad or the Dyad is symbolically important, even if all the various grades describe the same continuum, or merely mark stages along the same process. Hippolytus's Valentinian system presents the Father as the figure one, since one

148 See, e.g., Theology of Arithmetic 1 .1 0-12, 3.1-5 and other examples at Thomassen, Spiritual Seed, 29394. 149 Thomassen, "Derivation of Matter." 1 50 See, e.g., Theology ofArithmetic 13.6-9. 1 51 See Epiphanius, Panarion 4 1 .2 for a complex discussion on the logical problems inherent in a philosophy or religion postulating two equally matched sources. This is not to deny the existence of pure dualists in Greek literature (see above, n. 145, and below, p. 295), but because all ancient theories of causality required one and only one agent, pure cosmic dualism was a rare option.

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58 (technically not a number and therefore above all number) resembles the Father, who utterly transcends the aeons and any consort. This focus on the Monad preserves a theology of monarchy. Irenaeus's Valentinians, however, reflect upon how the Dyad derives from the Monad by using images of gender and numbers to depict the relationship between the one and the many, a perennial problem in philosophy since its invention. Valentinian systems attempt not so much to solve these problems as to enter into them, to depict them, and to theologize on how the present world came from the highest realms. The various metaphors-procreation, marriage, parenthood -used to clarify the relationship between the Monad and the Dyad illustrate contrasting ideas about the constitution of the universe. Arithmetic is a key ingredient in explicating this. The four kinds of monadic or dyadic Valentinianism are depicted in the header to table 1 (see end of chapter), which arranges them from monadic to dyadic. My placement of the various Valentinian systems on this scale reflects my assessment of the texts; others may wish to interpret them in slightly different fashion. Some texts do not permit easy classification, either because they do not discuss the relationship between Monad and Dyad, or because they present ideas that are vague, ambiguous, or self-contradictory. Tertullian accuses the Valentinians of such inconsistency. He snipes at them for introducing to an entity they want to be solitary a second person, both "in him and with him."152 What Tertullian sees as a contradiction we might more benignly consider a paradox or intentional ambiguity. That this is a better way of interpreting Valentinianism will become evident in the course of this study.

1s2 Tertullian, Against the Valentinians 7.5.

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59 By constructing this table I do not wish to replace Hippolytus' s two rigid categories with four. The exercise is meant not to produce incontestable accuracy but to work toward a more flexible but precise presentation of Valentinian theology. The scale is porous, to reflect the emphases (and not necessarily the substantive differences) of various texts.153 One advantage of the scale is that it can be applied to other groups, as I show in later chapters. What emerges from table 1 is the observation that Irenaeus and heresiologists dependent on him report a variety of Valentinian systems, but none that are purely monadic. Hippolytus is different, since he stresses that his Valentinian source is monadic. Also noticeable is the somewhat middle course steered by the Nag Hammadi Valentinian texts. They tend to fall, however, on the dyadic, that is, Irenaean, side of the scale. The

Valentinian Exposition, so close in other respects to Irenaeus's first system, is clearly spermatic monadic, but other Nag Hammadi texts either do not concern themselves with the issue, or lean to a parental-dyadic model. There is no purely monadic, that is, Hippolytean, system presented by any of the Nag Hammadi texts. In sum, the Valentinians use a considerable variety of models to depict the relationship of the Monad to the Dyad. If, as one scholar has suggested, there was a paradigm shift in late antiquity from systems of two and three principles to those of only one, it is not evident here.l54 Also evident from the table is that the descriptions of the relations between the aeons are often indeterminable or contradictory. This throws some doubt on the analysis of Einar Thomassen, who, in Spiritual Seed, sorts all Valentinian texts into two types. The older, type-

153 See above, n. 145 . 1 54 Thomassen, "Derivation of Matter,"17. The difficulty o f dating Valentinian texts makes the hypothesis difficult to test.

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60 A texts do not specify names or arithmetical patterns in their protological systems, whereas the later, type-B texts do. This is a valuable way of organizing Valentinian texts. It makes sense that unnamed, amorphous systems develop into named and highly-structured ones. But Thomassen also claims that type-A texts emphasize the interiorization of the secondary aeons whereas type-B texts "do not stress the idea of a generative exteriorisation of the aeons from within the Father."155 This distinction does not reflect the complexity of the texts. As we shall see in the next chapter, Marcus's protology uses both interiority and exteriority to describe the relationship between the primal aeon and the subsequent ones. Epiphanes' language draws from both spermatic and conjugal-dyadic imagery: the four aeons are treated as distinct, however, monotes and henotes coexist and are said to be one thing. It is uncertain whether his four primal aeons have anything more than a token separate existence. Even in Irenaeus's first Valentinian system, Thought is said to be "projected" ( n:Qof3aAca8m) from the Forefather. This presumes that the projected lies within the projector. And the term projected emphasizes the exteriorization of the dyad. Thomassen's type-B texts show regular interest in the origin and emergence of the secondary aeons.

1ss P. 1 93. Thomassen says (ibid.), "The aeons are described as possessing an initial existence within

the Father, or in his Thought, after which they are brought forth and manifested from him, so as to become independent beings." He intends this to be a definining characteristic of type-A texts, but I fail to see why the description does not apply also to type B. The two texts he takes as typifying type A, the Tripartite Tractate and the Gospel of Tru th, I have marked on my table as being paternal dyadic, since in my opinion these texts emphasize the hierarchical exteriorization of the dyad, not its internalization. Thomassen's final historical analysis is relatively sound, in my opinion, only because of its sounder criterium, that of how well developed the names and numbers in the Pleroma are.

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61 NAG HAMMADI VALENTINIAN TEXTS The Valentinian number symbolism discussed above depends upon several Church Fathers, Irenaeus in particular, who, one might suspect, argue against forms of V alentinianism that may or may not represent the mainstream of that movement. With the publication of the fourth-century library discovered at Nag Hammadi, scholars have hoped to depend upon less tendentious texts so as to understand Valentinianism on its own terms, if possible. Determining what Nag Hammadi texts correspond to what groups is an ongoing, difficult process. The texts generally do not specify either their author or their intended audience, and scholars d o not always agree on their categorization. In the case of Valentinianism, I have deferred to the provisional consensus on what texts are certainly or very probably Valentinian (The Tripartite Tractate [NH 1 .5}, The Gospel of Philip [NH 2.3}, The (First)

Apocalypse of fames [NH 5.3], The Interpretation of Knowledge [NH 1 1 .1}, and A Valentinian Exposition [NH 1 1 .21), and which are only probably Valentinian (The Gospel of Truth [NH 1 .3/12.2} and The Treatise on the Resurrection [NH 1 .4}).156 Other texts were possibly written or redacted by Valentinians, but I do not discuss them. Several of the Valentinian Nag Hammadi texts have little or no number symbolism. The occasional number symbolism of The Gospel of Philip, from the late third century, is peripheral to its theology. The Interpretation of Knowledge might assume its readers know Valentinian number symbolism, but the text is too fragmentary to analyze. The Treatise on

the Resurrection, a Valentinian text dated to the late second century, has absolutely no

1s6 The classification is argued for by Thomassen, "Notes pour Ia delimitation," 244.

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62 number symbolism, although this may be due to the author's assumption that the letter's recipient, Rheginos, already knows the mathematical structure of the Pleroma.157 But several Valentinian Nag Hammadi texts use number symbolism that can be studied. A Valentinian Exposition employs extensive number symbolism that compares well with book one of Against Heresies. Before exploring it, I comment briefly on The First

Apocalypse of James, The Tripartite Tractate, and The Gospel of Truth, all of which use rather divergent types of number symbolism.

The First Apocalypse ofJames, true to its name, reports a series of revelations given by the Lord to James. The Valentinian character of the text, which takes the form of a dialogue, is established by parallels to Irenaeus' s report of unnamed Valentinians, and to Epiphanius's, of the Heracleonites.1 58 It seems to have been written in a Syrian milieu, of unknown date, probably third century .159 Because the text deals centrally with the ascent of the soul after death, its struggle with the archons, and its dealings with other heavenly beings, the Apocalypse cannot be compared too strictly to our other Valentinian texts. Since it does not discuss the structures of the divine emanations, its number symbolism emerges from other concerns. One dominant theme is the archons, twelve of whom stand over seventy-two heavens. Each archon has six beings under its supervision, and thus forms a hebdomad. The

1 57 On the date and Valentinian character of the treatise, see Peel, Epistle to Rheginos, 179-80, and idem,

Gnosis und Auferstehung, 145-46. 158 First Apocalypse ofJames 33.11-35.25 (NH 5.3), compared to Irenaeus, Against Heresies 1 .21.5 and Epiphanius, Panarion 36.3.1-6. See Schoedel and Parrott, "(First) Apocalypse of James," 66-67, 86-87. 1 59 Schoedel and Parrott, "(First) Apocalypse of James," 67.

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63 arrangement takes James off guard.160 Doesn't Scripture allude to only seven hebdomads? James refers here probably to Pentecost. The Lord tells James that the one who told him about this verse had an incomplete understanding, but he will make clear what comes from the one who transcends number. The Lord then proceeds to explain the seventy-two heavens. The implication is that the being beyond number has arranged the world in numbers not evident in the ordinary interpretations of Scripture. What is to be symbolized by the number seventy-two is unclear here. In other texts the seventy-two represent all the nations of the world, but this association is never made explicit in the Apocalypse.161 Later in the text we find that just as there are twelve archons, so there are twelve disciples and twelve pairs.162 This number and association may derive from the Valentinian Dodecad, but a direct connection does not seem likely to me, since twelve pairs suggests a total of twenty-four, a number that features only in Marcus's form of Valentinianism, in his speculations on the alphabet (see chapter 3). Other symbolic numbers in The First Apocalypse

of ]ames, such as the seven women disciples, the three toll collectors the soul meets in the afterlife, and the ten-year wait before Addai writes, show that the author was interested in and used number symbolism.163 But these symbols are not explained enough to allow us to

1 60 The First Apocalypse of James 25.26--2 6.23 (numbers refer to folio and line numbers). The arrangement is illustrated at Layton, Gnostic Scriptures, 12-13, fig. 1 . 1 61 Gospel of Philip 63.26--3 0 (NH 2.3); Origin of the World 1 04.35-105.16 (NH 2.5/13.2); Concept of Our Great Power 41 .6-6 (NH 6.4). 1 62 The First Apocalypse offames 36.1-2. 1 63 Cf. The Sophia o!Jesus Christ 90.17-18 (NH 3.4). Number symbolism often enters descriptions of tollbooths, which are seldom found in Valentinian texts; but there is no exact parallel to the three toll collectors of The First Apocalypse ofJames. The Apocalypse of Paul (NH 5.2), for instance, seems to envision one toll collector at the passage guarding each of ten heavens. The Books of feu 1 .33-41, 2.52, depicts 12 levels, each with its own password or numerical code.

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64 say how much The First Apocalypse of James departs from, or how closely it represents, the V alentinian tradition of number symbolism. The Tripartite Tractate, written probably in the late third century, reflects an earlier strain of Valentinianism that has greatly mitigated the central, highest aspects of its number symbolism.164 In the preface, the Father - the preferred name for the transcendent deity in this treatise - is at first said to be " like a number" (E <JO M"npHTE NNOYHn E), but is then immediately said to be unlike a "one" or "solitary individual" (E
with the Father makes it impossible to speak of the Father only as one.166 Nevertheless, the Father is singular.167 The Father's unity is always shared with the Son, who preexists eternally with the Father.168 The author of The Tripartite Tractate depends upon the terminology of arithmetic to describe the projection of the Son from the Father, "the one who stretches himself out"; such language parallels descriptions of the monad departing from itself to become a dyad.169

164 On the date see Thomassen, Spiritual Seed, 263-66, "L'histoire du valentinisme," 302-3, and Le traite

tripartite, 18-20; Attridge and Pagels, 22:178. I follow the Coptic text in Thomassen's edition. 1 65 Tripartite Tractate 51.9-10, 11-12. Thomassen, Le traite tripartite, 261-62 suggests this means

"multitude" (rrAi']8os), not "number" (aQL8f16s), since one is never a number, but the source of number. But the problem Thomassen purports to solve still remains, since one also is never multitude, which is, anyway, a species of number. See Nicomachus of Gerasa, Introduction to Arithmetic 1 .3.1-2. 166 Tripartite Tractate 5 1 .12-15. 167 Ibid. 51.16, 24. 168 Ibid. 57.33-59.1. 169 Ibid. 56.2-3, 1 6-17; 65.4-5; 66.6-7. See my discussion of the Paraphrase of the Apophasis Megale below, pp. 126-127.

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65 Because the relationship of the two is eternal, like the relationship between the Father and the Son in Nicene Christianity, a parental dyadic model seems to be the main model of presentation. But the Tractate' s observation of how the Father stretches himself out into the Son, of how the Son is "the ineffable one in the ineffable one" suggests that the author was just as happy with metaphors pointing to a spermatic-monadic modeJ.170 The Tripartite Tractate frequently groups the world in sets of three. There are three categories of matter, the aeons give three "glories" and bear three sets of offspring, and there are three elements that go into the formation of the first human being.m All humanity falls into one of three categories: spiritual, psychic, and material, in imitation of the Word, who brought forth these three classes of beings.172 That the created world has so many classes of three is a reminder of the threefold organization of the lower world in other Valentinian systems, discussed above. In this case, however, triplicities begin in the level of the aeons, also called the Church.173 So in the Tripartite Tractate tripartition starts at a level higher than in the other Valentinian systems. The author makes explicit the three levels of the divine economy- Father, Son, and Church -but he never calls them a triad or threesome.174 Instead, patterns of threes begin at the third level of the protology of the godhead. There is little or no suggestion of pairs or syzygies playing a role in the text. If The

Tripartite Tractate is based, as is thought, on a form of Valentinianism that predates 1 70 Tripartite Tractate 56.26-27, Turner's translation. 1 71 Ibid. 103.14; 68-69, 74.19; 106.18-31 . The text is strikingly similar to the account of humanity's

creation in Irenaeus's first Valentinian system. See above, p. 23 and fig. 2. 172 Tripartite Tractate 1 18.14-23. 173 Thomassen, Traite tripartite, 286. 1 74 For other threesomes in The Tripartite Tractate see Attridge and Pagels, in Attridge, Nag Hammadi Codex I, 23:400-401 .

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66 Irenaeus' s first system, then this system reveals a stage that precedes the introduction of complex Pythagorean number symbolism into the core of their theology. Compare to this The Gospel of Truth, which has two types of number symbolism. First, it emphasizes the unity found in the Father, a unity to which all should strive, by purifying themselves of multiplicity.175 Unity is directly correlated with knowledge, just as envy and strife are linked with ignoranceP6 The trope is pervasive in Platonic and Pythagorean texts from this period: unity is, without doubt, the top destination for your average Platonic journeyman. Second, it uses number symbolism to interpret the parable of the finding of the hundredth sheep.177 The savior figure finds the one lost sheep and rejoices, since ninety-nine is a number belonging to the left hand. With the hundredth, the number passes to the right. The Father is symbolized by the righfhand, which draws in the numbers on the left hand, so as to perfect them. The explanation refers to the finger-calculus technique common in the ancient Mediterranean: one through ninety-nine were reckoned completely on the left hand (thereby freeing the right hand in the majority of small transactions to do other tasks, such as pay out coins), and the hundreds and thousands were reckoned on the right.178 Marcus's explanation of the same parable is very similar, although he incorporates the parable in his protology and letter symbolism.179 The idea is not exclusively Valentinian, since it appears often in orthodox writers, too.180 Moreover, The

175 Gospel of Truth 25.5-19 (NH 1 .3). 1 76 Ibid. 24.25-25.3 177 Ibid. 31 .35-32.16, Mt 18.12-14, Lk 15.4-7, Gospel of Thomas 1 07. 1 78 See Williams and Williams, "Finger Numbers," and studies cited there. Despite their attempt to study the subject comprehensively, they omit Marcus's testimonies to the practice. 179 See below, pp. 97, 102, and 159. 180 See Jerome, Letter 48.2 and references in n. 178, above.

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67 Gospel of Tru th shows no sign of a theology of syzygies, arithmetically grouped emanations, or the like. The Gospel of Truth probably preserves an older, more primitive stratum of Valentinianism.181 But the possibility should not be excluded that the text reflects a later development, one either less interested in aeonology or mixed with a system not disposed to number symbolism. From these three texts, certain patterns of number symbolism are evident. There is an emphasis on the unity of the Father (Tripartite Tractate and The Gospel of Truth). In the region below him are certain divine entities arranged in sixes, sevens, and twelves (The First

Apocalypse ofJames). The material world is full of tripartitions (Tripartite Tractate). The patterns, if not the details, correspond to other Valentinian number symbols discussed above.

A VALENTIN/AN EXPOSITION The so-called A Valentinian Exposition, fragmentary as it is, confirms the Valentinian arithmetical arrangement of aeons Irenaeus and Hippolytus discuss. A Valentinian Exposition recounts the Valentinian myth in roughly the same order that Irenaeus and Hippolytus do. First, after explaining the upper realms of the Father, Silence, the Son, Only-Begotten, and other figures (fols. 22-24), the author explains how the aeons were projected (fols. 25-27). The second major section treats the emanation of the first two tetrads (fols. 28-29) and the subsequent projection of the Decad and Dodecad (fols. 30-31). Having explained the origin of the Triacontad, the author then turns to the story of Wisdom, the thirtieth aeon,

1 81 Thomassen, Spiritual Seed, 263-66; Attridge and MacRae, "Gospel of Truth," 23:92.

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68 explaining her error and the way in which she was reconciled (fols. 32-39) . Of these three major divisions in A Valentinian Exposition, the first two are most relevant for our study of the Valentinian theology of arithmetic. It is commonly suggested that the author of A Valentinian Exposition held to a monadic rather than dyadic Valentinianism. There are four reasons why this seems to be the case. The Father is described as being alone, and is called Monad.182 Silence, the usual consort of the Father in Irenaeus's reports, is introduced slowly, through synonyms such as quietness (nK). PID<J) and tranquility (nc 6p).2f), a possible indication that the author wished to downplay any notion that Silence is coeval with or consort to the Father, and that he wished rather to specify that Silence is the nonmythological tranquility of the Father's solitude. This theory of a demythologized Silence is reinforced by A Valentinian Exposition' s epithet for the Father, "root of all," a common Valentinian designation for the primary Tetrad or the ensuing Odgoad, but not applied to the Father alone.183 Further, it seems that in A Valentinian Exposition the "Uncreated One" - understood to be Only Begotten, the third member of the primal Tetrad - generates the second Tetrad on his own, thus imitating the primal solitude of the Father.184 That is, by generating without a consort Only Begotten reveals that the Father is also without consort. These arguments are the main reasons why Turner and Pagels classify the text as monadic Valentinian.185 The arguments are not persuasive. First, although the Father seems to be called

Monad, he is also said to exist in the Monad (2N T MON).C ), and even to exist in the Dyad and 1 82 A Valentinian Exposition 22.19-23.21. 1s3 Ibid. 22.20, 33-34; 23.19. 1 84 Ibid. 29.29-30. 185 Pagels and Turner, "Valentinian Exposition," 96-99, 1 60-61 (s.v. 29.25-30, 29.29-35).

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69 pair ([ZN TA]y�c �ym ZN nc�E 1 (1) ) .186 Later on, an unidentified subject, presumably the Father, is said to exist in the Monad, Dyad, and Tetrad.187 How an entity can be in something, yet be that something as well? How can such a solitary entity dwell in the Dyad or Tetrad? Neither the text nor its editor explains this. I do not think this paradox can be easily solved. Possibly the author of A Valentinian Exposition held that the Father, Silence, and the rest of the primal Tetrad existed beneath, or at least independent from, primal number. As we have already seen, Irenaeus reports that some anonymous Valentinians held to an Ogdoad that preexisted Depth and Silence.188 Thus, Valentinians could, if they wanted, add an upper story to the Pleroma. Perhaps A Valentinian Exposition does this too, placing the Father beneath an archetypal Monad, Dyad, and Tetrad. Even if this is the case, however, the system might still be monadic. To determine this it is critical to understand how the Dyad originates and what kind of relationship it shares with the Monad. Without this explanation, the epithet

Monad for the Father is insufficient to conclude that the system is monadic. The two places that seem to state clearly that the Father is the Monad are suspect as well. The first, based upon Turner's reconstruction, [NE <J(l)OO]� MMON�C, more likely means "[he existed] monadically," than "[he was] the Monad."189 The verb Turner supplies depends, not on the manuscript- the fragmentary blip taken to be � leaves much to be desired- but on analogy with the second passage, where some unspecified subject is said to

1 86 A Valentinian Exposition 22.21, 26. 1 87 Ibid. 25.19-20. 1 88 Irenaeus, Against Heresies 1 .1 1 .5. See above, p. 41 and fig. 3. 189 Crum, Coptic Dictionary, 578-79; A Valen tinian Exposition 22.24. I thank Janet Timbie for her suggestion, here and throughout this section.

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70 be " [the] Root [of the All] and Monad (.Will MONA<;: [ nE ] ) without any[ one] before him."190 But here the lack of the definite article before MONAC suggests that the subject is not the Monad but a monad, i.e., a unit. In A Valentinian Exposition important reified entities such as the Monad are always identified with the definite article. Further, although the Father has no one who exists before him, this is not the same as saying " [He dwells alone]."191+ Thus, A

Valentinian Exposition does not clearly state that the Father is the Monad. It is true that Silence (cnyt1) appears to take the stage slowly on page 22 (Turner's second argument for classifying A Valentin ian Exposition as monadic). But nearly the entire upper half of the page is missing. This lacuna is the beginning of A Valentinian Exposition. This missing text is the proper basis for determining the status of Silence and how quickly she is introduced. On page 22 there is no relationship explicitly established among Silence, quietness (line 22), and tranquility (line 23), so it is impossible to say whether or not the author means the latter two terms to delay the introduction of the former, as Turner suggests. 1 92 If TC 1 rH was introduced in the upper part of the folio, the later occurrence of n K A Pill 'l and n c G p �z=r would only amplify, not soften, Silence's role as consort of the Father.

Even if Silence was not introduced at the top of the folio, the order of the extant text mirrors the presentation of the Valentinian dyadic system at the beginning of Against Heresies. There, Foresource-Forefather-Depth, the first entity to be discussed, "abides in great rest 1 90 A Valentinian Exposition 23.19-21 . Translations of this text are Turner's. For the broken letter see Facsimile Edition, 28. 1 91 Ibid . 22.24-25, 38; 23.20-21; 22.22. See Turner and Pagels, "Valentinian Exposition," 97. In the Facsimile Edition, 28, there is no apparent survival of what Turner indicates to be� so the entire ' conjecture, [E'lU}OOn OY.\EET]'l, depends upon the editor's conjecture that a monadic system is at work. 1 92 "Valentinian Exposition," 97.

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71 and peace" (E:v i]auxL0 Kai. fJQE!1L0 noMl] yEyovtvm). Silence is then introduced in the next sentence. In Irenaeus's report the delay in introducing Silence does not diminish the system's dyadic character. Indeed, the order i]avx(a, TJQE !l La, I:Lyi} mirrors exactly nK�PU>
There is evidence that Silence plays the same important role in A Valentin ian

Exposition that she does in Irenaeus's first Valentinian system. She forms with the Ineffable the primal dyad, and is second to him.193 This language suggests the conjugal-dyadic model, not monadic. Also, the will of the Father, according to A Valentinian Exposition, is to allow nothing to happen in the Pleroma without a syzygy. This would be strange counsel if the Father himself were not the archetype.194 According to Turner's edition, "[the Uncreated One] projected Word and Life," thus crediting Only Begotten - the third member of the primal Tetrad - with generation of the first syzygy of the second Tetrad.195 His reconstruction seems to suggest that Only Begotten creates the syzygy on his own, just as the Father dwells in monadic solitude, although neither Turner nor Pagels are completely clear on this matter.196 This reconstruction, 1 93 A Valentinian Exposition 22.26; 29.31-33; 23.21-22. 1 94 Ibid. 36.28-31 . 1 9s Ibid. 29.29-30. 1 96 Turner and Pagels, "Valentinian Exposition," 161, suggests that the "non-creature" could be the

syzygy Only Begotten and Truth, but this seems to render pointless his distinction at p. 1 60, between dyadic and monadic Valentinian accounts of the generation of the second Tetrad. After all, the parallels Turner presents differ only as to whether the entire primal Tetrad, or merely the syzygy Only Begotten-Father-Mind-Truth project the second Tetrad. But this distinction has nothing to do with whether the system is monadic or dyadic. Even if A Valentinian Exposition says Only Begotten has alone begotten the second Tetrad, this conforms more closely to the conjugal dyadic Valentinian account at Irenaeus, Against Heresies 1 .1 .1 (which has two Tetrads) than it d oes with the monadic one at Hippolytus, Refutation of All Heresies 6.29.6-7 (which has, properly speaking, no Tetrads: the upper level of the Pleroma has six entities).

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72 however, contradicts other parts of A Valentinian Exposition, as well as Irenaeus' s first report, which in so many other respects harmonizes well with A Valentinian Exposition. For both Irenaeus' s Valentinians and A Valentin ian Exposition, the first Tetrad, not Only Begotten alone, projects the second Tetrad.197 In contrast, the monadic Valentinianism of Hippolytus does not use Tetrad of the upper emanations, since they are grouped only in pairs, not Tetrads. Turner's reconstruction of 29.29 is debatable; other readings consistent on every level with the text's meaning and grammar can be supplied so as to place A Valentinian

Exposition on the dyadic side of Valentinian thought.198+

1 97 A Valentin ian Exposition 29.25-26, 35-37; Irenaeus, Against Heresies 1 .1 1 .1 . See previous note. 1 98 Turner reads [C ] ! � [nATCID]CJ?NT [N� E !.]�T EYO. In the Facsimile Edition, only the N is clear in the second word. The stroke interpreted as q> appears too far below the baseline to be an omega. Cf. the omegas at lines 32, 33. There may be several ways to restore the middle of the line; I might suggest one, [ZfJ TM!.Z]<;:NT [ E �E !.}YT EYO ("secondarily he projected" or "in the second he projected"). This option originates from the observation that the "Second" has already been reified as an entity on p. 23. There, the unspecified subject (Turner and Pagels, "Valentinian Exposition," 154, postulates the Father or Root of All) does various things on three different levels: coming forth in the realm of the 360th; revealing his will in the Second; and spreading himself in the Fourth (23.26-31). This so-called Second may be Silence herself (cf. 22.26-27), or it may be the second syzygy, which dwells in, and originates from, Silence (23.21-22). In Irenaeus's report, Only Begotten, the male part of the second syzygy, projects the third, Word and Life (Against Heresies 1 .1 .1 ) . In the interests of brevity, Irenaeus may have omitted any mention of Truth's participation; thus the original idea would have been that the entire second syzygy projects the second Tetrad . This notion parallels Hippolytus, Refu tation ofAll Heresies 6.29.6-7. Thus, under my reconstruction, an unspecified subject (the entire primal Tetrad?) projects Word and Life in a second phase of emanations, or by means of the Second- again this could be Silence or the second syzygy. This suggestion presumes that the top half of fol. 29 specifies the context and meaning for "Second." Something should happen "first," such as what is specified at 25.20-21, where something - apparently the Father - "first brings forth" Only Begotten and Limit, probably the second syzygy. This reconstruction provides a meaning quite consonant with conjugal­ dyadic Valentinianism. I mean to suggest not that this is the only way to reconstruct the text but that we need not let our presumption that A Valentinian Exposition comes from monadic Valentinianism ­ a presumption built upon a false dichotomy- d etermine the restoration of the text. On the complexities of the "Second" in A Valentinian Exposition, see Turner and Pagels, "Valentinian Exposition," 155-56.

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73 The fourth argument for the monadic theology of A Valentinian Exposition is based on the observation that the epithet "Root of All" is applied only to the Father. This is unconvincing on its own. Given that Irenaeus's Valentinian (and dyadic) system calls Nous "source of all" and the Forefather "root without source," this may be yet further evidence for a paternal-dyadic or at least a spermatic-monadic system at the heart of A Valentinian

Exposition.1 99 An epithet is meant to summarize, not explain, the status of its subject. In A Valentinian Exposition the title "root of all" is never explained in securely read text, and therefore I believe it unwise to decide, on this basis alone, whether the author was on the monadic or dyadic side of the scale. Other evidence, besides that already presented, suggests that A Valentinian Exposition is conjugal dyadic. It agrees with the dyadic Valentinian systems of Irenaeus against the monadic Valentinians of Hippolytus that there are a total of thirty emanations, not twentyeight, before Wisdom's fall. The original being dwells in the Monad, Dyad, and Tetrad, and this Tetrad generates the subsequent Tetrad to produce the Ogdoad (not explicitly mentioned as such in the extant text).200 The third and fourth syzygies-Word and Life, and Man and Church -generate the Dec ad and Dodecad, respectively .201 Thus, the Triacontad is constructed in the same terms and groups that Irenaeus uses. The bulk of A Valentinian

Exposition is devoted to explaining the story of Wisdom, a narrative that once again parallels the ones found in Irenaeus.

l99 Nous: Irenaeus, Against Heresies 1.1 .1, aQxilv TWV mxvnuv. Forefather: ibid. 1 .2.1, Tilv avaQxov Qi.C,av. 2oo A Valentinian Exposition 25.1 9-20. 201 Ibid . 30.16-19.

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74 Based on all the evidence above, it seems to me that A Valentinian Exposition falls more on the dyadic, probably conjugal-dyadic, side of Valentinianism. Should my argument be persuasive, in future editions of the Coptic text a few critical passages should be revised.

There are a few unique features in the arithmetical patterns and tropes used in A

Valentinian Exposition. First, there is a renewed emphasis on Tetrads. As already stated, the transcendent being dwells in the Monad, Dyad, and Tetrad, and the first uncreated Tetrad begets the second.202 Further, in A Valentinian Exposition, in the story of Wisdom, the "Tetrad of the world" - presumably referring to the four elements, fire, water, earth, and air -is said to "bring forth fruit," in imitation of the Pleroma, or Demiurge.203 Limit, too, has four powers: separator (oy p ecmo px), confirmer (OY P E C T .\X PO), form-provider (oy p e c [t M]OP<j>H), and substance producer (oy p e c x n eoyc 1 .\).204 One possible way to read the text is to take it as arguing against those who assign to Limit only two powers.2°5+ Whether or not this is a fair reading, it is clear A Valentinian Exposition stresses groups of four.

2o2 Ibid. 25.19, 25, 35-37. 203 Ibid. 37.12-15. Here, the earthly Tetrad's generation of fruit is compared to the Hebdomad of the Pleroma of the world. The Hebdomad elsewhere in Valentinianism is a topos for the Demiurge: Irenaeus, Against Heresies 1 .5.2, 1 .14.6; Hippolytus, Refu tation ofAll Heresies 6.32.7. On the earthly Tetrad see Irenaeus, Against Heresies 1 .1 7.1, 1 .18.1 . 204 A Valentinian Exposition 26.31, 27.31-33. 205 See Turner and Pagels, "Valentinian Exposition," 99-101, 158-59. 1t is not necessary to take the "they" of 27.34 (assigning to Limit two powers) as opposing the "others" of 27.33 (assigning to Limit four powers). Indeed, "they" may refer exactly to the "others." Thus, the "for" q:Jr .\P) of 27.34 would stress the explanation to, and not the doubt behind, the "why" ([ET]�E EY) of 27.30. In this case, 27.34-38 explains how the first two powers function in Limit, and the lacuna at the beginning of fol. 28 would explain how the last two powers work. The passive verb also fits and reduces the contrast (Timbie's observation). Other Valentinian systems held Limit to have two or more powers; Irenaeus, Against Heresies 1 .2.4, 1 .3.5.

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75 Second, the origin of the 360 in A Valentinian Exposition resembles the explanation in Irenaeus. The Dodecad projecting from Man and Church also produces the Triacontad (the collection of Ogdoad, Decad, and Dodecad), and their resultant product is the 360, "the Pleroma of the year."206 The association of the 360 with the year of the Lord is standard in Valentinianism, but the 360 play an even more important role in A Valentinian Exposition.207 An unnamed subject-presumably the Father, the "Root of the All" - goes through three stages of revelation and emanation.208 He begins by dwelling in the 360, then reveals his will in the Second and spreads himself out in the Fourth. Exactly how the 360 can be the beginning of this journey is left, unfortunately, unexplained.209 In other texts from Nag Hammadi the 360 are lower beings.21 0 Here, however, they appear to be higher. Third, A Valentinian Exposition stresses an origin for the Hecontad different from what is taught by Marcus. I will comment on this in the next chapter. On the whole, A Valentinian Exposition corroborates the claims the church fathers make of Valentinianism's predilection for divine emanations that are organized and conceptualized arithmetically. Parts of A Valentinian Exposition show how these ideas could be expanded, refined, or simplified. But the theology is always expounded in the language and structures of arithmetic. 206 A Valentinian Exposition 30.34-38. That is, 8 x 1 0 x 1 2 360. 207 See Irenaeus, Against Heresies 2.22.2. 2os A Valentinian Exposition 23.32, 26-31 . 209 Turner and Pagels, "Valentinian Exposition," 1 54-56, suggests that Mind is the subject, working =

his way from the bottom of the zodiac, i.e., Silence. But this interpretation depends upon assigning to the monadic Valentinianism of Hippolytus a primary tetrad of Mind-Truth and Word-Life. But, as discussed above, Hippolytus's Valentinians avoid Tetrads. Turner and Pagels also never justify the claimed association of Silence and the 360th. 21 0 Eugnostos 83.10-20, 84.4-1 1 .

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76 VALENTINIAN NUMBER SYMBOLISM The most complex number symbolism found in any Valentinian system, that of Marcus, is the subject of the next chapter. Without visiting Marcus, what can be said of the basic elements of Valentinian number symbolism? Depending upon the interests of the particular author or community, the highest level of the divinity is presented as being either a transcendent monad, or a monad in some relationship to a second principle. The more monadic the system, the more the Father's transcendence is emphasized; the more dyadic the system, the more the generation of the aeonic realm is emphasized. The upper aeons are organized into male and female couples, who project yet other pairs of aeons. The uppermost pairs are organized into two tetrads, and these, into an Ogdoad. Other aeons may be generated from this Ogdoad, and when this is described, it is often set in arithmetical terms. Oftentimes these aeons are given the names of numbers and numerical groups, making explicit the implicit mathematical relationships. There are numerous variations on this basic structure, but its principle of organizing emanations into arithmetical patterns is always preserved. Not all Valentinian texts have an arithmetically structured Pleroma, an indication that they are an early form of Valentinianism. Nevertheless, even these systems use arithmetic in their protology. The Valentinian systems that go into the story of Wisdom and her fall oftentimes invoke number symbolism to describe the partitions in the lower realm. The numbers seven, eight, three, and four are instrumental in describing the creation and everything that has come about. Because they are often missing in the upper aeonic realm, the numbers three and seven are used either to organize groups that are in transition, or to contrast with the upper realm of order.

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77 Not every Valentinian system indulges in number symbolism. We have noted several Valentinian texts that have very little of it, for one reason or another. There is undoubtedly a history to the Valentinian use of number symbolism, but to go beyond the broad outlines here would require a separate historical analysis of Valentinianism, an exercise that scholars have only recently taken up.zn What did the Valentinians mean to show or prove with these numbers? How did they intend them to function, and what theological end did they serve? These sorts of questions will be meaningful only after we have studies several systems and surveyed the entire Christian debate over the role of numbers.

211 See most recently Thomassen, Spiritual

Seed. See also Markschies, Gnosticism, ix, for the notice of a

forthcoming study .

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•

Paternal DEdic

②


①
Conjugal Dyadic

@) Other/ Unspecified

No relevant discussion

Leans to dyadic?

Leans to monadic? Depth has two, unequal consorts Leans to dyadic?

Leans to dyadic?

•

•

No relevant discussion

No relevant discussion

Valentinian textsfrom Nag Hammadi

?

?

•

No relevant discussion

Probable Valcntinian texts from Nag Hammadi

•

?

•

?

?

•

•

Valentinian systems reported py the heresiologists

Spermatic Monadic

ee

ps.-Tert. � pseudo-Tertullian, Against All Heresies; Filastrius � Filastrius, Book of Various Heresies; ExTh � Clement of Alexandria, Excerpts from Theodotus; HR � Hippolytus, Refu tation of All Heresies; Pan. � Epiphanius, Panarinn; NH � Nag Hammadi. Not listed: Valentinus (various fragments: no relevant discussion), Barbelo-Gnostics (AH 1 .29: monadic), Heracleon (various fragments: no relevant discussion). Excluded also are Nag Hammadi texts classified by E. Thomassen as merely possibly Valentinian.

AH � Irenaeus, Against Heresies;

Gospel of Truth (NH 1 .3/12.2) Treatise on the Resurrection (NH 1 .4)

Tripartite Tractate (NH 1 .5) Gospel of Philip (NH 2.3) First Apocalypse of fames (NH 5.3) Interpretation of Knowledge (NH 1 1 .1 ) Valentinian Exposition ( N H 1 1 .2)

Valentinians (AH 1 . 1-1 .9) [Valentinus] (AH 1 . 1 1 .1 ) Secundus (AH 1 . 1 1 .2) [Epiphanes] (AH 1 . 1 1 .3) Others (AH 1 . 1 1 .5) Knowledgeable Ptolemaeans (AH 1 .12.1-2; ps.-Tert. 4.8?; Filastrius 41 ?) Prudent Ptolemaeans (AH 1 .12.3) Marcus (AH 1 .13.1-1 .16.2) Theodotus (ExTh) Valentinians (HR 6.29-6.36) Anon. Valentinian (Pan. 31 .5.3-31 .6.10) Ptolemy (Pan. 33.3.1-33.7.10)

Monadic

① (i)

Table 1 . The Monadic-to-Dyadic Scale of Valentinian Theology

'-1 CIJ

3 Marcus "Magus"

The theology of Marcus, given the epithet Magus by the heresiologists because of his liturgical alchemy and his interest in ideas commonly associated with magical texts, exhibits the most complex number symbolism of any Christian theology in the second century. Very little is known about him. Forster, the only modern scholar to investigate thoroughly Marcus's teaching, suggests tentatively that Marcus flourished between 160 and 180, in A sia Minor.1 There he developed a cultic following within the churches. His teachings and liturgical practices agitated church leadership, which subsequently expelled him. Irenaeus preserves a specimen of this agitation, a polemical poem of the mid-second century, written by an unnamed orthodox church leader of Asia Minor.2 Irenaeus, our main source for the life and teachings of Marcus, uses such earlier texts, most of which probably came from Asia Minor, as well as eyewitness accounts and personal observation of a branch of Marcus's sect at work near Lyons, where Irenaeus was bishop. He may have had at his disposal a Marcosian liturgical text and an account of a revelation given to Marcus, texts written, if not by Marcus, then by someone from his circle. The revelation and Irenaeus' s assorted

1 Forster, Marcus Magus, 390. This work is without doubt the best study of Marcus's doctrinal system. 2 Irenaeus, Against Heresies 1 .15.6.

79

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80 paraphrases of Marcus's teaching are the most important sources for this study, since they show the inner workings of his arithmology, which bordered on numerology. Arguments to locate Marcus in one branch or another of Valentinians, or to dissociate him with the movement altogether, fail to convince me, as I discuss elsewhere.3 As will be evident as I present his number symbolism, Marcus belongs squarely in the Valentinian tradition, and in no particular branch but his own. He was a contemporary of other Valentinians such as Secundus and Heracleon. There are contradictions as to who preceded whom, so his writings cannot be dated more precisely. Hippolytus's account is the only ancient report to state explicitly that Marcus was a disciple of Valentinus.4 Four early apologists, including Irenaeus, place him in the wake of Valentinus or his immediate followers, but do not specify exactly where or when.5 Eusebius, who depends explicitly upon Irenaeus, says only that Marcus was a contemporary of Valentinus.6 Other apologists make Marcus the disciple of entirely other heretics? The rest of the heresiological reports, including our earliest testimony to Marcus, the polemical poem preserved by Irenaeus, does not mention his teacher.8 Instead the poem portrays Marcus as a son of Satan and a magician. The poet intentionally removes Marcus from a chain of human teachers and 3 See excursus E, contra Forster, 395-96, who tries to locate Marcus in either eastern or western

Valentinianism; and excursus F, contra Tripp, "Original Sequence," 162, arguing for a dissolution of the association between Marcus and Valentinianism. 4 Hippolytus, Refu tation of All Heresies 6.42.2. s Tertullian, Against the Valentinians 4.2; pseudo-Tertullian, Against All Heresies 5.1; Epiphanius, Panarion 34. 1 . 1 . 6 Eusebius, Church History 4.1 1 .4. 7 Jerome, Letter 75.3, makes him the student of Basilides; Filastrius of Brescia, Book of Different Heresies 42, of Heracleon. 8 Irenaeus, Against Heresies 1 .1 5.6; Theodoret, Compendium of Heretical Fables 9; and the four sources in Syriac and Arabic, mentioned by Forster, Marcus Magus, 42-52.

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81 makes him virtually a heresiarch, inspired by Satan alone. Thus, although many orthodox Christian writers associate Marcus with Valentinus and Valentinian circles, there is no consensus, aside from agreement that Marcus was a late contemporary of Valentinus, as to when he flourished and who were his influences. Marcus's number symbolism suggests that he appears late in the Valentinian tradition, since his doctrines allude to and play with the fully fledged forms found earlier in book one of Against Heresies. Based on only the number symbolism, presented below, Marcus flourished in the 1 70s, just prior to Irenaeus's writing of Against Heresies.

THE SYSTEM Irenaeus begins his treatment of Marcus by revealing both the secret liturgical rites the latter used to seduce women into becoming his patrons and consorts, and the methods his followers used to seduce church members.9 After describing the Marcosians' activities polemic mixed with paraphrases of eyewitness accounts and Marcosian texts - Irenaeus introduces a text that purports to be a revelation from the Tetrad to Marcus.10 That this is a paraphrase or word-for-word reconstruction of a carefully written composition is indicated by Irenaeus's regular use of "saying" and "says" (t\[ywv, £¢11) and, as we shall see, by the tight, coherent internal narrative. For the sake of convenience, I refer to Irenaeus' s source as the Revelation to Marcus. Irenaeus says that Marcus boasts that he is the womb and receptacle of Colorbasus' s Silence, that he is the Only Begotten and "most alone" (!-lov
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82 brought forth the seed planted in him.1 1 Thus, according to Irenaeus, Marcus identifies himself closely with Silence (the second Valentinian aeon) and Only Begotten, her offspring. It is unclear if Marcus claims to be either Silence or Only Begotten. By calling himself the "womb of Silence," Marcus may refer by synecdoche to Only Begotten, the fruit of Silence's womb, and therefore to his unique earthly role, mirroring that of Only Begotten in the Pleroma, or he may refer to his solitary role as the receptacle whereby Silence is made known on earth. It is impossible to tell if the "of" in "womb of Silence" is objective or subjective.12 In any case, Marcus identifies himself in the beginning of the Revelation to

Marcus closely with the second and third aeons. As the Revelation progresses this relationship is strengthened as the Tetrad descends to Marcus in the form of a woman, not a man, since its masculine form would overwhelm the world. She tells him who she is, then reveals to him, whom she calls the "most alone," the creation of the universe, a revelation never before delivered to gods or people. Her rendition of creation is couched in obscure, difficult language, so my summary, which now follows, may be somewhat confusing. It may help first to read, then have on hand, the text of Against Heresies 1 .14-16. I omit a number of details that do not materially affect my discussion of Marcus's number symbolism. Such omitted details are few since Marcus's number symbolism is so effusive.

1 .14. 1 . The Father- who is neither male nor female, and is without substance and is unknown -wished to make the unutterable utterable and to give shape to the unseen, and so opened his mouth and sent forth a Word similar to himself. The Word then came beside

11 The epithet seems to allude to ibid. 1 .15.1, where the highest aeon is called !-lOVO'fT]c;. See below, p. 93 n. 40. 12 Forster, Marcus Magus, 1 66-67.

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83 the Father and showed him who he was, becoming manifest as the shape of the unseen. As for utterance, the pronunciation of the name (presumably that of the Father) began with the first spoken word, a collection (literally, "syllable") of four oral letters (a'WLXEia): llQXTJ· He added a second collection, and it too consisted of four oral letters. Next, he uttered a third collection, of ten oral letters, and a fourth, of twelve. Thus, there were four collections of thirty oral letters. Each oral letter had had its own written letters (yQcXflflCX'ra), impression

(XCXQCXK'rTJQ), utterance (ExcpwvYJ mc;), shape (axfJfla), and images (dK6vEC:;).B None of them n I have found no adequate way of distinguishing in translation the two terms <JTOLXELOV and yQlif.lf.llX, which can each be translated "letter." Dionysius Thrax (ca. 170-ca. 90BCE), for instance, in his influential work on grammar, begins a chapter, D EQL mmxdou, by discussing yQiiflfllXTa. He says that yQiiflfJ-GlTa are called <JTOLXEia because they follow a certain sequence. Thus, Dionysius seems to make little distinction between the terms. But Apollonius Dyscolus (fl. 2nd c.CE), commenting on Dionysius Thrax, sharply distinguishes the two terms, stating that the <JTOLXEiov is the term for a letter's utterance (i:Kcf>WVT)<JL�), whereas a yQlif.lf.llX refers to the glyph (XaQaKn'jQ). Thus, the <JTOLXEiov is oral/aural and the YQlXf.lf.llX is written/visual. Apollonius develops his system further, positing the <JTOLXEiov as the foundation for four subsequent aspects or properties for each letter. Other commentators in the grammatical scholia on Dionysius Thrax show linguistic views that diverge from Apollonius, although most use his distinction between <JTOLXEiov and yQlifl fJGl. See, e.g., Scholia in Dionysius Thrax 1 :323.33--35 (author: "Heliodoros"); 1 .3:32.18-20, 1 .3:31 .19 (author: "Melampus/Diomedes"); 1 .3:192.27-28 (author: "Stephen"). (The first two of these references are treated as depending upon a fragment by Apollonius Dyscolos at Scholia in Dionysius Thrax 2.3:3.) In one scheme, the <JTOLXEiov was considered fundamental to four other concomitant aspects of letters. First was the xaQaKn']Q, taken as the shape of the letter when written or carved; second was the name (ovof.la) of the letter (e.g., Mcpa, �fJTa); third, the completion of the utterance (bUvafl L�, e.g., short or long, vowel or consonant); fourth, the order (Tal;t�) or position (8im�) of letters (e.g., what is allowed to proceed certain vowels or consonants, i.e., orthography). Scholia in Dionysius Thrax 1 .3:31 .19-24. Each grammarian had his own scheme, but all seem to make the fundamental distinction between a letter written and a letter uttered, even if the term <JTOLXEiov was also used in a broader sense, to apply to letters' shapes or names (see, e.g., Scholia in Dionysius Thrax 1 .3:31 7.32-37). I translate aTOLXEiov as "oral letter" and yQiiflf.llX as "written letter," since the Revelation to Marcus distinguishes the terms (Forster, Marcus Magus, 201). See OCD, s.v. "Dionysius (15) Thrax" with Grammatici Graeci, 1 .1 :9; OCD, s.v. "Apollonius (13) Dyscolus," with Grammatici Graeci 1 .3:31-32, 323 (assigned to Apollonius Dyscolus at Grammatici Graeci 2.3:3). See also Forster, Marcus Magus, 1 98-99, 204, and below, p. 213. Marcus's arrangement of the parts of oral letters differs somewhat from that of Apollonius Dyscolus. There is probably no core number symbolism at work in this scheme since the elements of the list changes from one scholiast to the next. Cf. Scholia in Dionysius Thrax 1 .3:197.24-30

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84 see or know the form of the one of whom they are elements. In their individuality, the oral letters know only their own utterance, and not their neighbors', and when they utter everything ('ro n:av), the individual oral letters think they are naming the whole ('ro oAov). These oral letters - parts of the whole-never stop echoing until there subsists only the last written letter of the last oral letter, speaking alone. That is the recapitulation, when everything, descending into one written letter will resound with a single utterance. The image of this recapitulation is the word amen, when spoken by all of us, in unison. The sounds provide shape to the uppermost aeon, which is without substance and is unbegotten. My paraphrase of 1 .14.1 is only slightly less confusing than the original. The key idea here is that the Father utters a series of letters in a pattern of four-four-ten-twelve, the same pattern used in Irenaeus' s first Valentinian system. Each oral letter has written letters subject to it. The oral letters are isolated from each other, and to reach their original unity converge on a single oral letter that has a single written letter.

1. 14.2. The regular, verbal names of the oral letters the Tetrad terms aeons, words, roots, seed, pleromas, and fruit (that there are six terms is no coincidence). Of these various oral letters, the last written letter of the last oral letter sends forth its own voice, the echo of which begets yet other oral letters that adorn the present world, just as the archetypal oral letters constitute the earlier, higher realms. This last written letter is taken by its collection (literally, "syllable") into the fulfillment of the All, but its echo, following alongside the

(oVOfla, axfJfla, xa.QaKTTJQ, MvaflLc;), 1 .3:317.7-15 (OVOfla, xaQaKTTJQ!axfJfla, 8imc;, bUVlXflLc;), 1 .3:31 7.37-31 8.8 (ovofla, axfJfla, 8imc;, xaQaKTTJQ, iK¢wv11mc;, MvaflLc;).

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85 lower echo, remains exiled in the lower realms. The same oral letter (it is unclear what the referent is) derives its origin from the thirty written letters, and each of these possess other written letters, by virtue of their names.14 For example the oral letter delta has five written letters: delta, epsilon, lambda, tau, and alpha. And these written letters have other written letters, brought about through the same process of begetting and succeeding, a process that can be extended infinitely. Marcus's Silence teaches that the Forefather consists of the depth of written letters of the whole name, and he assigned to each oral letter, unable on its own to utter the All, their own utterance. Note that the interplay of oral and written letters is superinscribed on the Valentinian myth of Wisdom. Wisdom is the last letter. Although she is taken back into the Pleroma, she leaves behind an echo- T]xoc; here probably a pun on Axaf.1w8, the Resolution of the first Valentinian system -and a lower echo, that is, Achamoth and the shadowy figure Passion. The oral letter that derives from thirty written letters refers either to the Forefather, Wisdom, or the Savior (who derives his existence from the thirty aeons of the Pleroma in the first Valentinian system). Whichever of these is meant, the cascade of written letters that ensues describes the progression of the world into multiplicity. Note also that the six verbal names of the oral letters parallels the six names of the hexagon Limit, deployed in the first Valentinian system. 1 4 The Greek is ambiguous: To bi: GTOLXELOV a-Lno ci:cp' ov 1:0 YQlXflfllX avv 1:lJ EKcpwvr'] a n 1:lJ i: amov avyKaTfjt\8£ KlX1:W, o YQ1Xfl fllX1:WV dva[ cpT)m 1:QLlXKOV1:a, which can mean the letter (a1:0LXEiov)

either consists of (LSJ, s.v. ELflL, C.III.b) or derives its origin from 30 written letters (LSJ, s.v. E Lfl L, C.III.a). I opt for the latter, since there is a parallel use of dvm at Irenaeus, Against Heresies 1 .14.5, of the origin of the consonants, semivowels, and vowels. If the former meaning of dvm is intended (see, e.g., Williams's trans., NHS 35:216) it is difficult to see what is intended. The text at hand certainly does not explain how a single oral letter can be composed of 30 written letters.

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86 1 .14.3. After explaining all this to Marcus, the Tetrad discusses Truth, which she depicts as a naked woman. Each of her twelve body parts are marked by two Greek letters, alpha and omega assigned to the head, beta and psi to her neck, and so on, down to her feet, mu and nu. This is the body of Truth, the shape of the oral letter and the impression of the written letter. The oral letter is called Man, who is the fount of every word, the source of every voice, the utterance of everything unspoken, and the mouth of silent Silence.

1.14.4. Truth then follows the Tetrad's report by uttering a word (or Word), which becomes a name, the name, the Tetrad says, "we know and speak: 'Jesus Christ' ." This is all Truth says throughout the entire revelation. The Tetrad explains that this name, which she thinks Marcus might disparage, he does not adequately possess in its ancient form. She says that Marcus has only the sound and not the power, a power evident in that Jesus is a noteworthy ( i:n:LGTlf.lOV) name, since it consists of six written letters, a fact understood by the elect. There is obscure wordplay here. Both Marcus and Clement of Alexandria (see chapter 8) make a big deal of the episemon, using it to make very obscure but important theological point. It is worth discussing the term episemon at some length, to highlight its importance and to correct confusion regarding the terminology of Greek numerals. Jesus's six-lettered name is called i: n:[aruwv because this was the late-antique term for c;, the Greek numeral six.15 The late-antique treatise On the Mysteries of the Greek Letters calls Jesus the episemon because the numeral six represents a hole in the Greek alphabet, symbolic of the philosophers' rejection of Christ.16 In an anonymous, undated treatise found in a late 1 5 For the Greek system of alphabetic numeration, see excursus B . 16 Hebbelynck ed., p p . 27, 1 61-64. For more o n this unusual text, see below, p. 2 1 5 .

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87 sixteenth-century manuscript, each of the three non-alphabetic characters used to designate numbers are named: 1 is called xaQCXK'[TJQ; 9, aK61111'[a; and c;, [ n (all!.loc;P A similar list appears in a ninth-century codex, the Psalterium cusanum, in a Latin text intended to acquaint readers with Greek conventions: S (VI) is Episimon, q (XC) is Enacose, and 71 (DCCCC) Cophe.18 In various scholia on Dionysius Thrax, probably written in late antiquity, the three signs are collectively called naQaall!.la, but are not individually named.19 Numerals lay on the periphery of grammarians' interest.20 But these various references show that the preferred term for the an alphabetic numeral six was episemon (not stigma or

digamma), and that as a class the non-alphabetic numerals were called parasema.21+ The term episemon suggests at its root figures that were written or etched, but not uttered. Indeed, [ n(all!.la, naQaall !.lOV, and their cognates were widely used to describe

1 7 Vienna, theol. gr. 289, f. 44r. See Hunger and Lackner, Katalog, s.v. 18 Cod. 9, fol. 64v in Marx, Verzeichnis der Handschriften-Sammlung, 6-7. The terms for the last two

symbols suggests they were inverted, since Enacose should correspond to the Greek word for 900, not 90. The term Cophe looks like it is derived from qoppa, the name of the symbol. The manuscript is discussed in Gardthausen, Griechische Palaeographie, 2:260 and Hamann, De Psalteria triplici Cusano. 1 9 This appears in two very similar passages, attributed to different authors (a certain Heliodorus, and anonymous): Grammatici Graeci, 1 :318.29-37 and 319.21-31 . The idea of the three numerals as "signs" is continued in the Latin and Greek manuscript Laon, cod. 444, f. 311 v, column a: " � et i et c; et 4 et 1' non sunt literae apud Graecos, sed notae et signa" (Catalogue general, 1 :234-36). See Miller, "Glossaire grec-latin," 213. 20 One exception is noted, (pseudo?) Aelius Herodian, nEpi apL8f1WV (TLG no. 0087.042), probably from ca. 2nd c. CE. This text explains the then-obsolete Attic system of numeration. 21 There are references in the grammatical texts to the digamma, but, as I argue below, p. 213, these refer to an obsolete letter, not a numeral. Scholars frequently refer to c; as thestigma, based on its resemblance of the ligature formed by sigma and tau, but I have been unable to find the term used in any ancient text. The same applies to the term sampi for � - Surely, this derives from the Byzantine expression [w]c;; av ni, but the only attempt to date the term is that of Keil, "Eine Halikarnassische Inschrift," 265 n. 2: "Dieser Name [Sampi] stammt iibrigens in dieser Form aus der 2. Halfte des 17. Jahrh. n. Chr." But Keil gives no explanation.

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88 imprints or other distinguishing marks on coins or shieldsP Thus, by calling Christ the episemon, Marcus, and later Clement, highlight not so much his "excellence" as the way he has imprinted himself into the coin of humanity.

1 . 1 4.5. According to the Revelation to Marcus these twenty-four written letters of the alphabet are "reflective effluences" (anOQQOLac; . . . E LKOVLKcic;) of the three powers that encompass the entire number of the upper oral letters. There are nine consonants, which correspond to the Father and Truth because they too lack sound (literally, voices, a cognate of vowels). The eight semivowels derive from Word and Life since they dwell between the other two groups and are intermediaries. The seven vowels belong to Man and Church, since the echo "of his voice" (again, a cognate of vowel) gave shape to the All.23 Out of the bounty residing in the set of nine, that of the Father, one of them moves into the smaller group, thus equalizing all three groups at eight members apiece. All three are then Ogdoads, and the three groups of eight furnish evidence for the number twenty-four. This explains the size of the alphabet. The Revelation to Marcus then provides another story, about the generation of the three double letters. Unfortunately, the two sentences explaining this are unclear.24 The various translations are generally accurate, but unintelligible.25 What is

22 LSJ, 655b-656a, 1323b-1324a. Note, however, that LSJ does not include the technical definition of naQlXOTJI.llX discussed here.

23 The 9 consonants: n, K, T, (3, y, b, <j:>, x, 8; 8 semivowels: A, 1-1, v, Q, c;, [,, E,, tjJ; 7 vowels: a, E, 11, t, o, u, w. The threefold division is typical in this period. See Forster, Marcus Magus, 238-42 for sources and discussion. 24 Irenaeus, Against Heresies 1 .14.5: Ta l.l EVTOL TQL£X 11mv atnoc; TWV TQLWV i:v aui:,uy(q bUVlXflEWV VTrlXQXE LV, & EGTLV [E,, a<j:>' wv anEQ(HJll TG E LKOat TEGG£XQ£X GTOLXEia, T ETQani\a ata a 8i: v m TcfJ Tfjc; tXQQijTOu TETQlXboc; Aoy<;V, TOV atJTOV atJToic; tXQL81.lOV TrOLEL, lXnEQ <J:>llaL

TOU aVOVOI.llXGTOU VTrlXQXELV. OQELG8m bi: atna vno TWV TQLWV bVVlXflEWV, E ic; OflOLOTllTa TOU aoQiXTou, wv aTmxdwv c iK6vcc; E iKovwv Ta naQ' iwiv bmAa yQiXI.ll.laTa vniXQxnv, &

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89 clear is this: (1) There are three oral letters; (2) these oral letters owe their existence to the three powers that are in syzygies;26+ (3) the three oral letters are actually six;27 (4) the twentyfour oral letters flow out of the three oral letters; (5) when the three oral letters are quadrupled by the word of the ineffable Tetrad, they create a number identical to the aforementioned twenty-four oral letters;28 (6) "these" (probably the three oral letters, the subject of [7]) exist thanks to the unnamed one;29 (7) the three oral letters are worn or carried

0UVC
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90 by the three powers, as a likeness of the invisible one; (8) the double written letters are an image of these three letters, which are themselves images; (9) when the three double oral letters are added to the twenty-four oral letters, it makes the number thirty, according to its proportionate potential.30 No wonder the translations are unintelligible. Two types of linguistic generation are depicted here. The first, that of the twentyfour written letters, depends upon the three powers. So does the second type, the thirty uttered letters, which emerge from the three powers in two groups: the first three doubled oral letters and the rest of the twenty-four oral letters. Ultimately, the goal of the Revelation

to Marcus is to show how the letters of the alphabet were generated in a fashion that resembles the projection of the aeons in the classical Valentinian Pleroma. That there is no easy way to link the two comes from the obscurity of this chapter.

1.14.6. The Revelation to Marcus now turns to Scripture to illustrate how Jesus came to be "the fruit of the likeness of the image" of language.31 His Transfiguration took place after a six-day wait. He ascended the mountain as the fourth person, and then, after the appearance of Moses and Elijah, became the sixth.32 He descended and was held in the Hebdomad, even though he was the "episemon ogdoad" - the noteworthy octet. He also possessed in himself the entire number of oral letters, evident in that, when he came for his baptism, the descent of the dove revealed this number. The sum of the letters in 7TEQLCY1:EQ£i

30 The phrase buva!-!EL n] KaTa avaAoyiav is peculiar. The closest parallel I have found is Alexander,

Commentary on Aristotle's Metaphysics, p. 682.19-20 (ed. Hayduck), but there commensurability is qualified as being either potential or actual. 31 Cf. Rom 1 .23. 32 Mt 17.1, Mk 9.2.

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91 ("dove") is 801, written as w a ' - the alpha and the omega.33 The number six is important: Moses placed m an's creation on the sixth day;34 the divine dispensation (olKovo!-lla) and redemption of Adam happened on the Day of Preparation, the sixth day; the beginning and end of this dispensation occurred at the sixth hour, when he was nailed to the wood.35 Why? Because the perfect Mind, knowing that the numeral for six possesses the power of creation and rebirth, revealed to the sons of light the rebirth that came about through the appearance in him of the episemon - the name of the numeral. This is why the double letters (<':, l;, l/J) carry the episemon.36 When this episemon was mixed in with the twenty-four oral letters, it produced the name written with thirty letters. Marcus's numerical meditation on the Transfiguration is dense. I reserve extended comment until chapter 8, where I discuss Clement of Alexandria's adaptation of it. Most important in this chapter is Marcus's return to the episemon and the number six as a theological symbol. He uses it in the phrase episemon Ogdoad. The phrase, which could also be translated "sixly octet," is a paradox because it implies the presence of two numbers. Remember, in section four, Truth utters only two words to Marcus: XQELCJTov l11aouv.J? The 33 Mt 3.13-1 7, Mk 1 .9-1 1, Lk 3.21-22. On this technique of calculating numbers from words, see excursus C. 34 Gen 1 .31. 3s Mt 27.34, Mk 15.33, Lk 23.44. 36 That is, ' is the sixth letter (although it has a numerical value of 7), E, 60, and tjJ 600 (the root of both of which is 6). 37 Although the editions of Hippolytus (Refutatio 6.45.1 .3) and Epiphanius (Panarion 2.12.20), upon which Irenaeus's Greek (Against Heresies 1 .14.4.6) is largely reconstructed, render the name XQLan)v, it seems more likely to me that the original was Xgnan)v since, later in the text, Marcus makes the theological point that "Son, Christ" (Yi6c;; XQELG'r6c;;) is composed of twelve letters, and "Christ" (Xgnm6c;;), of eight (Irenaeus, Against Heresies 1 .15.1 .39, 2.41-50; cited in Hippolytus, Refutatio 6.49.4.4, 5.1; Epiphanius, Panarion 2.18.11, 19.16-20.1). What is otherwise a rather innocuous variant in spelling here takes on theological importance. =

=

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92 Tetraktys comes alongside Marcus and explains to him that one must go beyond the mere sound of the name and penetrate its power. The power of the name is this: "Jesus" is the "noteworthy name" ( br(GYJ flOV OVOfllX) because it has six letters. "Christ" is theologically significant too, since it consists of eight letters. Thus, for Marcus, the power of the name

Jesus Christ is centered in the number of letters used to spell it. He captures this power in the epithet episemon Ogdoad. Marcus also interprets the Baptism so as to link Jesus to the entire alphabet. The value of the letters in dove is 801 . This number is written wa , and therefore '

points to Christ as the alpha and the omega, the beginning and end of the Greek alphabet.

1 .14.7. Silence goes on and says that six uses the magnitude of seven for its deacon, so that fruit might be voluntarily produced. She charges Marcus to think of the episemon of the present as the one who was shaped into the episemon, the one who was, as it were, divided in half and remained outside.38 This is the one who, through his projection, endowed with a soul this world (the world of the seven powers; seven to imitate the power of the Hebdomad) and everything visible. Each of the seven powers, or heavens, that constitute this world utter a vowel, from alpha to omega, and their intermingled sound (literally, echo) glorifies the one who projected them, and the glory of that echo is sent to the Forefather. The echo descends to earth and thereupon molds and creates the things of earth. Thus, using arithmetical terms, the Revelation to Marcus alludes to the Valentinian myth of the exiled aeon Achamoth, representing him (not her!) by the number six, and her projection, the demiurge, by the number seven, the number used for the creation of this

38 "Shaped" : f10Q<j>w8t'vTa, language recalling the shaping of Achamoth in Valentinianism. See fig. 2.

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93 world. Once again, Achamoth - divided in half from her Wisdom -is responsible for the formation of things on earth.

1 .14.8. The proof of this is the soul of a newborn baby, who cries out the echo of each of these seven oral letters (that is, the vowels). Just as the seven powers glorify the Word, so wailing infants glorify Marcus himsel£.39 So too, the distressed soul often resorts to uttering the last vowel in times of distress.

1 .14.9 merely recapitulates 1 .14.1-8, so I omit it here. 1 .15. 1 . The narrative now returns to the creation of the twenty-four oral letters and draws from the distinguished Valentinian teacher whose system Irenaeus discusses earlier.40 Henotes coexists with Monotes, and from them come two projections, Monad and Hen. Two plus two makes four, and when the operation is repeated - four is added to two - the number six is made evident, and these six quadrupled bring forth the twenty-four forms. Silence then turns to the names of the first Tetrad, to show how they couch within themselves the mysteries of the letters. The names AQQll'Wc;, I:nyij (sic), T1a'ri]Q, and

39 This is probably, but not certainly, Irenaeus's sarcastic interjection. 40 Ibid. 1 .1 1 .3. Forster, Marcus Magus, 15, 296, suggests this is a literary fragment of Marcus. Besides

the obvious parallels in substance, Ka8ix nqodQTJTaL in Irenaeus, Against Heresies 1 .16.1 seem to refer clearly to 1 . 1 1 .3. I accept the parallelism, but I doubt that the two passages are by the same author. Yes, both use the same names for the elements of the Tetrad: f.lOVOTTJc;, tv6TTjc;, 1-1ovac;, £v. But at 1 . 1 1 .3, the male members of the tetrad are also called aqxa( (or nqoaqxa l), whereas female members are called buva1-1nc;. Such a terminological distinction is important for the author of 1 .1 1 .3, but Marcus's divergent use of source and power suggest that he has not embraced this distinction. Further, the source for 1 .1 1 .3 uses nQOLTJf.lL for "project," suggesting it was his preferred term (cf. Irenaeus's corresponding mockery, which thrice reuses the term, 1 . 1 1 .4, lines 74 [bis] and 79 in Doutreleau and Rousseau's ed.). Marcus also uses the same verb, but without the same regularity, and only twice (1 .14.1 [line 143 Greek], 1 . 14.2 [line 176 Greek]). Thus, I treat the two passages as coming from separate authors, although I recognize that Marcus probably borrowed from the "distinguished teacher." The reverse is also possible.

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94 AAT]8na consist of a total of twenty-four oral letters, since the first and last each have seven written letters and the middle two, five.41 The same can be shown in the second Tetrad,

A6yoc; and Zwr'], AV8Qwnoc; and 'EKKA11ala., the written letters in whose names add to the same number. Further, YLoc; XQE LaT6c; (sic; "Son Christ") has twelve written letters, and the ineffable name in Christ has thirty written letters. This, says Silence, explains why he is alpha and omega, in order to disclose the dove, the numerical value of whose name is this number (as explained above).

1.15.2. The Revelation to Marcus goes on to illustrate Jesus's ineffable generation by recounting the generation of the Pleroma in terms derived almost purely from arithmetic. The second Tetrad comes forth from the first Tetrad as if a daughter from a mother, and they become an Ogdoad. From this emerges the Decad. The Decad comes alongside the Ogdoad, multiplies it by ten, and makes it eighty. Multiplying by ten once more, the eighty becomes eight hundred. Thus, the entire number of written letters is demonstrated by the progression from Ogdoad to Decad, from eight to eighty, to eight hundred, for a total of 888, the value of the sum of the letters in 'I11aouc;. This indicates that Jesus's birth is supercelestial. It also explains why the Greek alphabet consists of eight units, eight tens, and eight hundreds (see excursus C). And it explains yet again why Jesus is named the alpha and omega. The Revelation to Marcus then offers another approach, with a similar conclusion. When the first Tetrad was added incrementally to itself (1

+

2 + 3 + 4) the

number ten appeared, and this is represented by iota, Jesus's initial.42 Further, XQE LGT6c; has eight written letters and thus indicates the first Ogdoad, which, in combination with ten, 41 Marcus's language suggests the distinction between aTOLXciov and YQCtf.lf.llX is now blurred. 42 See above, p. 34, and below, pp. 169, 1 92, 340.

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95 produces Jesus (as explained above). Further, Yio� XQncn6� has twelve letters, thus indicating the Dodecad. Before the episemon of his name, Jesus, appeared, people were astray and ignorant. But at the appearance the six-letter name, which possesses both the six and the twenty-four, those who knew this were freed from ignorance and went from death to life.

1 .15.3. The aeons, or powers, are said to come out of the Tetrad formed by Man and Church, and Word and Life. These powers generate Jesus, who consists of four places, reserved for Word, Life, Man, and Church, supplied by the angel Gabriel, the Holy Spirit, the power of the Most High, and the Virgin, respectively. This Jesus was chosen by the Father after his birth, and when Jesus entered the water there descended upon him as a dove the very power who ascended and fulfilled the twelfth number. This power is the Father's seed, which possesses within itself Father, Son, the unnamed power of Silence, and all the aeons. The Revelation to Marcus then discusses a number of aspects of Jesus not central to this study, and concludes the section by observing that Jesus, by possessing Man, thereby possessed all eight members of the Ogdoad.

1 .16.1. Irenaeus interrupts his report with a lengthy criticism (1.15.4-6), and when he returns to Marcus's teaching, it is no longer obvious that he is depending upon the

Revelation to Marcus as his source. Irenaeus moves from the singular to the plural, suggesting that the remainder of his report (1 .16.1) includes persons besides Marcus. These people claim that all things come from Monad and Dyad, and that the series from Monad to four engenders the Decad. The Dyad, too, begins a progression up to the episemon (2 + 4 +

6), which results in the Dodecad. Yet a further progression of even numbers from the Dyad to the number ten shows the Triacontad, wherein reside the Ogdoad, Decad, and Dodecad.

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96 This Dodecad they also name Passion, since it has the episemon following it.43+ This is expressly related to the slip of the twelfth member of the Dodecad, and this event is related to the parables of the lost sheep and the lost drachrna.44 In the former parable there were eleven members left over, and in the latter, nine.45 Their product is the number ninety-nine, the very reason Amen has this same number.46

1 .1 6.2. The same people go on to explain that the oral letter eta, along with the episemon, is an ogdoad, since it is in eighth place. Furthermore, reckoning the oral letters up to eta, without the episemon (1 + 2 + 3 + 4 + 5 + 7 + 8), add to the number thirty, thereby revealing the Triacontad. To prove that the Ogdoad is the "mother of the thirty aeons," they explain that, since the number thirty is compiled from three powers, so when it is tripled it & Doutreleau, Marcovich, and Holl, of Irenaeus, Hippolytus, and Epiphanius, respectively, make little sense. The three Greek manuscripts (P = Paris. supp. gr. 464 [14th c.], V = Vat. gr. 503 [9th c.], M = Marcianus 125 [1 1th c.]), compared with Rousseau & Doutreleau' s edited Latin text: Duodecadem igitur, eo quod episemon habuerit consequentem sibi propter episemum, passionem vocant. Tilv ovv bwb�:xabcx, bta n) inioTJ!--l (ov) iaXYJKivm ouvmT)KoAou8rJGEV a-lm':), TO i n iOTJ!--LOV P rra8oc;. Tilv ovv bwbEKabcx, b ta Tov i n iOTJ!-lOv bta TO ouvEOXTJKivm avvEncxKoAov8Tjacxacxv cxvn':), V TO f71LOTJ!--LOV na8oc; Myoum. Tilv ovv bwbEKabcx, bta Tov i n LOTJ!--LOV bta TO auvwxT)Kivm avvEncxKoAov8i]acxv cxvn'i, TO M E71LOTJ!--L OV na8oc; Myoum . It seems to me, based on its affinity with the Latin, that M is the superior reading, although we may wish to edit it [ouv]WXT)KEvm. M follows the Latin nearly precisely, with the notable exception that propter episemum is placed not before but after the eo-quod clause, to avoid the appearance of a relative clause. The thrust of the passage is that the Dodecad is being given the epithet Passion, and this because of the action of the episemon. In defense of the editors of the various Greek versions, it would make much more sense for Marcus to call the episemonPassion, since it tags along with the Dodecad, signifying Wisdom. 44 Lk 15.1-7, 8-10. 45 Note the substitution of 12 for 99 in the parable of the lost sheep, discussed below. 46 Al--lijv = 1 + 40 + 8 + 50. Its numeral, CjB ', is used frequently in MSS and papyri as an abbreviation for Amen. Robert, "Pas de date 1 09"; Vidman, "Koppa Theta."

43 The various Greek editions by Rousseau

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97 makes ninety. So the Trinity, multiplied by itself, makes nine.47 In this way the Ogdoad gives birth to the number ninety-nine. So they say that, when the twelfth aeon abandoned the other eleven aeons, this is a type of the written letters that are positioned in the arrangement of the Word. That is, the eleventh written letter is lambda, whose numerical value, thirty, is set as an image of the upper, divine dispensation, since the sum of the written letters that precede it (again, omitting the episemon) is ninety-nine.4 8 That lambda stands for the remaining aeons, and that mu represents the lost one after which the lambda seeks, is shown by their shapes. M (thought as being written M) is a duplication of A Therefore, according to Irenaeus, they use knowledge to flee the land of the ninety-nine to pursue to the one, which, when added to the ninety-nine, results in a transfer from the left hand to the right.49

MARCUS AND VALENTINIAN NUMBER SYMBOLISM The preceding paraphrase, with select comments, of Irenaeus' s report of Marcus and his circle should make it evident that Marcus owed much of his number symbolism to V alentinianism. Similar to the Valentinians, Marcus depends upon pairs, quartets, octets, tens, twelves, and the entire Pleroma of thirty. The dependence is so strong that the

Revelation to Marcus adopts variant spellings of Christ and Silence so they contain a suitable

47 This Trinity may refer either to the three powers, or the the three oral letters discussed at Irenaeus,

Against Heresies 1 .14.5. It does not refer to Father, Son, and Holy Spirit. 48 a + � + y + b + E + C, + fJ + 8 + L + K + i\ 1 + 2 + 3 + 4 + 5 + 7 + 8 + 9 + 10 + 20 + 30 99. Note, also, =

=

lambda is the first letter of i\6yo�, the "Word" referred to in the previous sentence. 49 See pp. 66, 97, and 159.

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98 number of letters.50 In Valentinianism, these entities are termed aeons, but Marcus synthesizes the Valentinian tradition with principles of ancient grammar. The aeons become letters, both oral and written. The letters unfold as if they were the aeons of the upper realms. In the lower regions the Greek alphabet is an image of the fall and rescue of Wisdom. The extended linguistic metaphor includes the entry into our world of an unspoken letter, the episemon. Overall, Marcus both corroborates and reinvents Valentinian protology by weaving into its number symbolism principles of grammar. Is Marcus a monadic or dyadic Valentinian? At first glance it would seem that he is extremely monadic. He specifies that the Father has no gender and exists alone, even before the emanation of his Word.51 The identification of the upper Tetrad as consisting of four different kinds of unity reinforces this monadic ideal.52 This unity of the Father is reflected in the Marcosian ideal of the human search of unity, a unity epitomized in the mathematical and linguistic return to a single letter and sound.53 Irenaeus accuses Marcus of telling his women adherents, "we must become as one" ('ro f.v), a formula repeated three times; collectively, these references suggest that Marcus envisioned a metaphysical unity as the beginning and the ultimate goal of life. The prayer uttered by his followers, addressed to the

5o Irenaeus, Against Heresies 1 .15.1. Other texts take advantage of unconventional spellings of XQLG'l:Oc;

to make these kinds of points. See Forster, Marcus Magus, 318-19; Hippolytus, Refutation of All Heresies 6.49.4-5; and an inscription at Shnan (IGLS 1403, with commentary by Kalvesmaki, "Isopsephic Inscriptions"). 51 Irenaeus, Against Heresies 1 .14.1 . 52 Ibid. 1 .15.1. See also Forster, Marcus Magus, 306-10, on possible metaphysical parallels with late antique philosophy. 53 Irenaeus, Against Heresies 1 .14.1 .

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99 counselor of God and Silence, presumes that the supplicant has achieved unity with this intermediary being. But this same prayer illustrates that the primal being and his pre-eternal consort, Silence, are a pair, thus undermining a categorical declaration that Marcus was a monadic Valentinian. He reinforces the importance of the uppermost conjugal bond when he claims that Truth, the fourth aeon, the "source of every word and every voice" - probably an allusion to the fifth and sixth aeons - is the projection of Ineffable and Silence.54 That is, Ineffable is not alone. Marcus's emphasis on the traditional Valentinian syzygies and Tetrads also suggests that he was not absolutely monadic. Note, for instance, his dependence upon the second, third, and fourth syzygies to explain the emanation of subsequent aeons or letters. The conspicuous absence of the Father and Silence implies that both are transcendent beings and that they are a pair. How he relates the Monad to Dyad is not specified, although he ascribes not to one but to both the engendering of all things.55 I have thus indicated in table 1 that Marcus is probably monadic, but I think he also had spermatic-dyadic or conjugal-dyadic ideals. Multiple models would not have been inconsistent for him.56 In other Valentinian systems the upper and lower Tetrads remain distant from the material realm. In the Revelation to Marcus, however, the personal agent of revelation is the Tetrad, in the guise of a woman. To be visited by a woman who reveals secrets evokes other revelatory texts, especially those in Jewish wisdom literature, beginning with the book of

54 Ibid. 1 .14.3. 55 Ibid. 1 .1 6 . 1 .

56 On this question see also Forster, Marcus Magus, 301-2.

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1 00 Proverbs. Lady Wisdom promises herself to those who seek after her and walk in the ways of God. Proverbs is neither apocalyptic nor occultish. But it does have Wisdom paint a strongly polarized picture: one is either with the foolish or with the wise. This polarity is recast in the Revelation to Marcus to lay out the metaphysical structures of the universe. The narrative resembles the Shepherd of Hermas, in which a woman (or women, depending upon how you count and interpret the apparitions) appears to Hermas and grants him special, apocalyptic revelations related to the history or future of the salvation of the world. As in the Revelation to Marcus, the Shepherd of Hermas is full of symbolic numbers that are central to the revelation.57 But the Revelation to Marcus goes further in its number symbolism, and is much more explicit. Wisdom is called the Tetrad, thus invoking the tetraktys and its Pythagorean overtones and fusing them with Jewish and Christian themes.58 Just as the number and letter symbolism running throughout the Revelation to Marcus reveals the hidden structures of the universe, so lady Tetrad reveals the Ineffable to the world.59 As in other Valentinian systems, Jesus the Savior consists of four elements provided by four different agents. In Marcus's system, however, all four elements of Jesus are put together by the second Tetrad.60 Jesus therefore begins his ascent to the mountain as the fourth person, representative of the four elements with which he was created. In the Transfiguration, however, his arithmetical constitution is, well, transfigured. He progresses

57 Number symbolism in the Shepherd of Hermas awaits study. 58 Compare Marcus's lady Tetrad to lady Arithmetic, who makes her splendid entry in Martianus Capella's (5th c.) On the Marriage ofPhilologia and Mercury, book 7. See below, pp. 308-309, on Marcus's dependence on Pythagoreanism. 59 Forster, Marcus Magus, 1 8 1 . 6o Irenaeus, Against Heresies 1 .1 5 .3.

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101 along even numbers, going from four to six to eight. Jesus is thus called the episemos ogdoad.61 I noted in the previous chapter how the number three seems to have been reserved in many forms of Valentinianism to describe and organize the lower, fallen world . In Marcus that trope is not as evident. There are the three powers and the three double letters, all part of the upper Pleroma. That the Greek word for the three letters, cnOLXELa, refers equally to three elements contrasts with other Valentinian systems, which place their three elements (water, air, earth) in the material world. One of the most important numbers in Marcus's system is six, which provides the bridge between the Ogdoad and the alphabet, which consists of twenty-four letters. Marcus notes six intrinsic components to each letter, and draws attention to the length of the name '111aouc;.62 The Transfiguration is described with many references to six, and special attention is paid to the numeral six, the episemon. Achamoth is surprisingly described as the number six, not eight as might be expected from other Valentinian systems that make her an image of the Ogdoad. She is thought of as engendering the number seven, which is, true to other Valentinian systems, assigned to the Demiurge.63 The number six is key, both to the creation of the twenty-four letters of the alphabet (in conjunction with the Tetrad), and to accounting for the gap between the number of letters and the number of aeons. The number six also serves to introduce astrological symbolism. The most noteworthy example is the body of Truth, whose twelve body parts each assigned to two letters parallels exactly ancient

61 Ibid. 1 .14.6. 62 Ibid. 1 .14.1, 4. 63 Ibid. 1 .14.7.

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1 02 astrological texts. In ancient astrology the twelve houses of the zodiac were assigned pairs of letters in an order similar to that found in Marcus's body of Truth.64 There is in Marcus a new symbolic number, ninety-nine, taken together with its successor, one hundred. This number is used to combine four different texts or ideas. There is the parable of the lost sheep, the practice of counting from ninety-nine to one hundred on the fingers, the sum of the numerical value of the first eleven Greek letters, and the psephic value of a!-li]v. What holds together all four strands of number symbolism is the ideal of the search for lost unity. This unity is recovered in the number one hundred, the Valentinian sign of the Father's perfective unity in The Gospel of Truth.65 A Valentinian Exposition, too, mentions hundred, once without any context, and once in discussing emanations from the syzygy Word and Life.66 In this second passage, the Hecontad is the result of Word and Life's projection of the Decad, presumably because the Decad multiplies itself. Marcus, however, derives the Hecontad from the product of the Triacontad and the three powers. Implicit in A Valentinian Exposition is the suggestion that the aeons are endlessly multiplicative, since the process that led from Decad to Hecontad could be applied again to get the Chiliad, and applied again to get the Myriad. This principle of self-multiplication is found in other texts.67 For Marcus, however, the Hecontad signifies not extension but return to a primal unity. He illustrates this principle with the parable of the lost sheep. Like other

64

See Forster, Marcus Magus, 222-25, which lists the many primary sources and scholarly studies.

65 31 .35-32.16. See above, p. 66. 66 25.25, 30.33 (NH 1 1 .2). 67 Eugnostos 78.17-22 (NH 3.3), where the progression is Monad, Dyad, Triad, . . . tenths, hundredths, thousandths, and myriads, an arrangement further explained at ibid ., 5.7.23-5.8.25 (Robinson trans., 230a). Note also Marcus's teaching on the endless generation of the letters; Irenaeus,Against Heresies 1 .14.2.

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1 03 Valentinians, Marcus has not used the Scriptures to prove the mysteries of the number. He knows about the symbol before he approaches Scripture. He reads the Bible so as to discover the hidden references to the number symbol. The last new element to note is Marcus's interest in isopsephy. The word n:EQLCJHQa, because it adds to 801, symbolizes Jesus.68 The letter iota represents the number ten and the name Jesus, a theme recurrent in this study.69 And the word cXflrlV has the auspicious psephic value 99. That no other Valentinians use isopsephy suggests that Marcus represents a later development of the movement, probably contemporary with Irenaeus. Psephy first became popular in the first and second centuries (see excursus C), and the Revelation to

Marcus shows a very early attempt to take the practice seriously as a tool for theology. Marcus uses psephy for a very different purpose than does Colarbasus, the subject of chapter 6. But they both take it seriously, without relegating it to a parlor game or literary adornment. This shows that they have a similar belief that psephy can reveal the hidden knowledge of the world. Marcus's thesis, that the Greek alphabet shares the same theology of arithmetic as that found in the Pleroma, makes reliance on psephy a viable option. His theology lays the conceptual foundation necessary to justify isopsephic prognostication (see excursus D). Overall, then, Marcus is through and through a Valentinian. He creatively revises the Valentinianism that the heresiologists criticized. He adopts late Valentinian protology, along with Pythagorean and Platonic overtones implied by its structures, and adds to it

68 Irenaeus, Against Heresies 1 .14.6, 1 .15.1 . 69 See chapter 4, and pp. 34, 94, 1 69, 192, 340.

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1 04 numerical and numerological theories of language. Marcus intensely uses Valentinian number symbols, attempting to enlarge the explanatory power of the V alentinian myth.

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4 Monolmus

All record of Monoi"mus' s existence would be lost, were it not for Hippolytus' s discussion, and a fleeting mention by Theodoret of Cyrus, who says, "They say Monoi"mus the Arab, getting his start from arithmetical knowledge, put together his own heresy," by far the shortest entry in the Compendium of Heretical Fables.1 Hippolytus confirms that Monoimus was an Arab (possibly this means Syrian) but offers no other biographical information. The name Monoi"mus is unattested in Greek literature, papyri, or inscriptions. The common Arabic name Mun 'im, or its diminutive, Munay ' im, is probably the basis for the Greek version.2 The terminology he uses in his letter to Theophrastus suggests he had a standard Greek education. Therefore Monoi"mus probably lived in Syria or Palestine. He flourished probably in the early third century. Aside from the pinax and a recapitulation in book ten, Hippolytus discusses Monoi"mus's system in ninety-one lines of book eight of the Refutation, just after his treatment of the Doketai and prior to that of Tatian.3 Hippolytus's sources are one or more

, 1 .18 (PG 83.369B). 2 I thank Irfan Shahid for this suggestion. The earliest attestations of Mun'im are most frequently Safaitic. See Harding, Index and Concordance of Pre-Islamic Arabian Names, 569, s.v. "MN 'M." 3 Hippolytus, Refutation of All Heresies 8.3, 1 0.17.

1 05

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1 06 unidentified texts. One of these texts, quoted at the conclusion of Hippolytus' s expose, purports to be a letter from Monolmus to Theophrastus.4 Since this text is clearly distinct in form and content from his earlier discussion, Hippolytus had in addition to the letter a treatise from which Hippolytus drew his earlier material.5 Possibly the letter was merely the preface or cover letter to the treatise. The sketchy character of Hippolytus' s paraphrase does not allow a more precise assessment. Monolmus posits two principles, which he calls primarily av8Qumoc; and uioc;

av8Qc�mou (referred to in this chapter as Man and Son of Man for convenience; see figure 7).6 Man is unbegotten, incorruptible, and eternal, whereas Son of Man is begotten, subject to passion, and generated without time, will, or prior determination. Man is to Son of Man as being is to becoming, a Platonic analogy that explains why - so Monolmus argues - some passages of Scripture use f)v rather than £yivE'To, presumably because Scripture has in mind these two principles as well? Mono·imus extends the analogy further. Man is to Son of Man as fire is to light, since light is generated concurrent to the fire's existence, without time, will, or prior determination.8 Monolmus calls Man the one Monad (flLCX flOvac;), which he describes with a series of paradoxes: he is incompositely composite, indivisibly divisible, friendly and combative to all, peaceful and belligerent to all, dissimilarly similar, and like a

4 Ibid. 8.15. s Ibid. 8.12-14. 6 On Man as a title for deity, see Dillon,

"Pleroma and Noetic Cosmos," 1 06-7 and Schenke, Der Gott

"Mensch " in der Gnosis. 7 Gen 1 .2-3; Jn 1 .1-4, 6, 9-10. See below for further discussion of Monolrnus's appropriation of the Timaeus. 8 Hippolytus, Refutation ofAll Heresies 8.12.4.

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1 07 kind of musical harmony.9 In the ancient world harmony was considered a kind of paradox, or even contradiction, since it was the unity of dissimilar tones. Monolmus says that Man subsumes in himself all things, including contradictions and opposites. Three times he uses of Man the phrase 1-1 !a 1-1ovac:, to describe Man's ability to transcend contradiction.1 0 The very words that make up the epithet are a kind of contradiction. In philosophical literature of late antiquity the formal distinction between 1-1ovac; and £v (!-l(a is the feminine form of £v) frequently appears (see excursus Bl). Normally the 1-1ovac; resides in a metaphysically higher plane than the £v, and the former generates the latter. The 1-1ovac: is an ideal object whereas the £v is instantiated in our world in physical, countable objects. The existence of the £v, of course, depends upon that of the 1-1ovac;. The term I-X La 1-1ovac;, then, would be as contradictory as thought thinker or created

creator, since it suggests the confluence of two otherwise irreconcilable realms. The epithet alludes to and plays on the philosophy and symbolism of numbers, illustrating how the two incommensurate realms are united and reconciled in Man. Monolmus uses other paradoxes drawn from number symbolism and philosophical number theory. For instance, Man is both mother and father, related to the widespread notion that the monad is androgynous (see excursus B2). As the source of numbers, and not a number proper, the monad contains in itself potentially both odd 9 Ibid. 8.12.5. w

Ibid. 8.12.5.15, 8.12.7.24-25, 8.13. 1 . 1 .

Figure 7 . Depiction of the iota of Monoi·mus (illustration by author)

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1 08 and even, and therefore, by extension, female and male. Also, Mono"imus states that the best image of Man, whom he regards as perfect, is the one iota ( i�na. £v) or the one apex (f-Ila KEQa(a).11 The language comes from the Sermon on the MountP For Mono"imus Jesus's distinction between iota and apex is a veiled reference to a metaphysical structure. The shape of the letter iota reveals the relationship of Man to Son of Man (see figure 7). The iota and the apex are two separate but intertwined entities. The iota "is incomposite and simple" and yet is also composite and consists of many forms, shapes, and parts.B "That single undivided object is the many-faced, myriad-eyed, and myriad-named single apex of the iota."14 And that apex "is the image ( E iKwv) of the perfect Man." For the analogy Mono"imus draws from the language of Paul. The apex as "the image of the perfect Man" -ilnc; EG'rLV E LKWV '[OU uAdou av8QWnou EKE LVOU, '[OU lXOQinou - alludes to Colossians 1 .15: oc; [= ui6c;, 1 .13] E:anv dKwv 'rOU 8wu 'rOU d:oQthou, Paul's description of the relationship between the Son and the unseen God. Thus, the iota and the apex are separate but interlocked. The former encompasses the latter, and the latter is the image of the former.15 Man is to Son of Man as the iota is to its apex. Up to this point Mono"imus has not declared whether he is interested in the iota qua letter, or qua numeral. It soon becomes clear that he regards its number symbolism foremost. He says that there is the one Monad, then the one apex, then the Decad of the one apex.1 6 He

11 Ibid. 8.13.1 . 12 Mt 5.18. See also Lk 16.17.

13 Hippolytus, Refutation ofAll Heresies 8.12.6. 14 Ibid. 8.12.7. 1s Cf. Tripartite 1 6 Ibid. 8.13.1.

Tractate 1 16.28.

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1 09 explains this new entity, the Decad, by saying, "ten is the power in it," i.e., in the apex.17+ Then come the rest of the numbers, extending from the Monad: Dyad, Triad, Tetrad, and so on, up to the Ennead and ten.18+ These are the complex ( Tioi\uaxLbc"is) numbers, which reside in the simple and incomposite "one apex" of the iota. This explains Colossians 1.19 and 2.9, that "all the Pleroma was pleased to dwell bodily" in the Son of Man. For Mono"imus, these "sorts of combinations of numbers" become the bodily instantiations generated from the simple and incomposite "one apex" of the iota.l9+ Here is combined into one metaphor numerical and allographical symbolism. The prime image is that of the iota, which is drawn with a serif at the top. It is a single letter, created by a single stroke, yet its uppermost part represents and mediates the whole. Monoi:mus reinforces this analogy with the prevailing theories on the generation of

1 7 I accept the buvcq.uc; yaQ ai n� n) "i of the manuscript at ibid. 8.13.1 .2 against Marcovich's reading: buvaf-Hc; yaQ aih:T] TO iwTa. The term iwTa suggests the letter not the numeral. Marcovich's reading is hard to reconcile with the normal senses of buvaf- Hc; and the new arithmological

discussion. [ refers to the numeral, more suitable to the context. Not that this altogether clarifies a convoluted passage of Greek. See also next note. 18 Ibid. 8.13.1, Marcovich's ed.: "Eanv ouv, cpT]atv, i] < f-l La> f-lOvac;, i] f-l La K£Qata, Kat b£Kac;· Mvaf-l L c; yaQ aUTT] TO iwTa, Tfjc; f-l HXc; K£Qa tac;, Kat bvac; Kat TQLac; Kat TnQac; Kat rrcvTac; Kat n;ac; Kai f:rrTac; (Kat) oyboac; Kat ivac; 11txQL Twv

biKa.·Marcovich's third emendation, , is excessive for three reasons. It breaks up the chain of entities (one Monad, one apex, Decad, Dyad, Triad, Tetrad, etc.), it suggests the Monad begets the Monad, and the Monad is not complex (rroAuaxLbijc;, line 5). According to my reconstruction of Monolmus' s system, the text of Refutation of All Heresies 8.13.1 .1-4 should read: "Eanv OUV, cpT] U LV, TJ < f-l La> f-lOVac;, TJ f-l La K£Qata, Kat b£Kac; (bUVaf-lLc; yaQ al!TlJ TO-� Tfjc; f1 Llic; K£Qatac;, Kat buac; Kat TQLac; Kai TETQac; Kat mvTac; Ka t f:E,ac; Kat ETrTac; (Kat) oyboac; KaL ivac; 11txQL 1:wv biKa. 1 9 "Sorts of": reading TOLafnm of the manuscript for Wendland's ToaavTm.

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110 numbers, wherein the first nine numbers, building blocks for all subsequent numbers, reside potentially in the monad.zo Monolmus argues against thinking of creation as a feminine product, and claims that the "very murky rays" of the Son regulate generation and change in the cosmos.2 1 Man, in fact, has nothing to do with the creation of the world. The world is influenced only by Man's proper part, the Son of Man, who fills all things and possesses in himself whatever Man has. There is a parallel here with Nicomachus, who describes the cosmos as "rooted" in the monad, but made and revealed in the Decad.22 So too in Monolmus's view, the Son of Man, as the i.w'ra E.v, a being that synthesizes ten and one, is responsible for being the source, completion, and regulator of creationP Monolmus interprets the Pentateuch in light of his decadology. The six days of Creation are six of the powers trapped in the one apex of the iota. The Sabbath comes into existence from the Hebdomad of the world beyond (arro n)c; 'E�bo1-uxboc; y£yov E 'rl)c; EKEt), probably referring by Hebdomad to the iota itself, combined with the six powers. That is, the iota-Man sends forth a seventh power, which is represented by the Sabbath. The emanation of six or seven powers from a single power has parallels elsewhere. Philo holds to a model of Monad plus six latent powers, which resembles somewhat Hippolytus's Valentinians, with the exception that the six powers are not organized into syzygies.Z4 For seven powers

20 Remember, one was not a number: Nicomachus of Gerasa, Introduction

to Arithmetic 1 .7. See also

excursus Bl-2. 2 1 Hippolytus, Refutation ofAll Heresies 8.13.3--4. 22 Theology ofArithmetic in Photius, Bibliotheque §187, 1 44A25-27. 23 Hippolytus, Refutation of All Heresies 8.13.4.21. 24 Stead, "Valentinian Myth of Sophia," 80.

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111 there is the more remote parallel a t a temple a t Esna, Egypt, where seven gods come out from the mouth of a single goddess.25 None of these earlier systems completely explains Monoi:mus' s protology. Rather, they show that his system, and therefore the Biblical exegesis upon which it depended, was not a novelty. According to Monoi:mus all four elements of the world -earth, water, air, and fire derive their existence from the isometrical shapes of Plato's Timaeus, which themselves come from the numbers retained by the apex of the iota.26 This is an appeal, not merely to understand Moses in terms of the Timaeus, but to understand Plato in terms of Mono"imus. The numbers behind the five geometrical figures of the Timaeus must have some source or origin. Mono!mus identifies that source as the apex of the iota, the Son of Man. The symbolism behind the allograph L also comes into play. Mono!mus considers it significant that Moses uses his rod to generate exactly ten plagues. The shape of the rod in its variegated simplicity represents the iota and its apex. Because the iota resembles the fruitfulness of a vine it reflects the creation of the worldP Citing Democritus, Mono·irnus relates the striking action latent in the term Decaplague (bEKanAYJyoc:;) - the ten plagues or blows- to the severing of the umbilical cord at birth. Ultimately, both are conducive to generation.28 Indeed, Mono!mus later claims that the transformation of creation is actualized

( EVEQYEL'rm) by the Decaplague.29

2s Forster, Marcus Magus, 185-86. 26 Plato, Timaeus 55A-56B; Hippolytus, Refutation 27 Ibid. 8.14.3.

of All Heresies 8.14.1-2.

28 Democritus, frag. 32; Hippolytus, Refutation of All Heresies 8.13.4. 29 Ibid. 8.14.8.

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1 12 The Decalogue and the Pentateuch, too, are each derived from the numbers resident in the one apex. The Decalogue, just as the Decaplague, is based on the Decad, a portal for knowing the universe. The Pentateuch derives from the Pentad, also kept in the one apex.'10 In addition, Mono1mus interprets the number symbolism behind the dates of the Jewish Pascha in light of the Decad.31 He claims that the fourteenth day of the month is the source (cXQXTJ) of the Decad. In arithmological texts, most references to one number as the source of another are invested with metaphysical significance, since it implies that one is the sine qua non for the other. It is puzzling to think that fourteen is the source of ten, since the former really depends on the latter. Mono1mus's explanation? The numbers one through four add up to ten, which is the perfect number and the one apex.32 The process of deriving ten from four is symbolized by the number fourteen, both of whose digits, Lb ', represent the first four numbers and their total sum. To describe fourteen as the source of ten is something of an overstatement, and Mono1mus probably means rather that the one is the image of the other.33 In any case, the Hebdomad derived from observing the festival from the fourteenth to the twenty-first days is itself the creation of the world, which also resides in the one apex.34 Thus, by virtue of the numbers embedded in their dates of celebration,

30 Ibid. 8.14.5. 31 See also below, p. 1 92. 32 On ten as a perfect number, see above, 50 n. 125 .

33 Hippolytus, Refutation of All Heresies 8.14.6. 34 Ex 12.15-20.

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1 13 Pascha and the Feast of Unleavened Bread represent the causes of creation;35 and the Decaplague, its transformation and change.36 Hippolytus accuses Mono·imus of, among other things, reading Moses in terms of Greek wisdom, specifically for using Aristotle's ten categories to interpret the Law _37 This echoes another passage in the refutation where he ascribes to Pythagoras ideas that look suspiciously like Mono·imus's.38 In this earlier passage, he claims Pythagoras differentiated between two worlds, the noetic and the sense perceptible. The noetic world has as its source the monad, whereas the source of the sense-perceptible world is the tetraktys, which possesses the iota, the one apex, and a perfect number. This ten (literally, "L) according to the Pythagoreans is the one apex, which is the first and foremost essence (ova(a, Aristotle's first category) of noetic things.39 These references to the iota and the one apex as a source of generation suggest that Hippolytus for his recreation of "Pythagoras's" teaching at 6.24 is

35 Or the elements (aTEia) of creation, based on Marcovich' s emendation of Hippolytus,

Refutation of All Heresies 8.14.8.38. 36 Ibid. 8.14.8. 37 Ibid. 8.14.9. 38 Ibid. 6.24. This chapter is part of a longer expose (6.23-28) of doctrines attributed, by Hippolytus or his source text(s), to Pythagoras. Marcovich (p. 23) suggests for this section ofRefutation ofAll Heresies "a Gnosticizing Pythagorean treatise" as Hippolytus's direct source. But some parts of this section have no recognizably gnosticizing inclination, whereas others do. Some parts of 6.23-28, such as 6.24, are related to second- and third-century religious movements described elsewhere in the Refutation and have no obvious connection to other parts, aside from an affinity to neo-Pythagorean ideas and texts. Throughout 6.23-28 Hippolytus attributes the ideas alternately to Pythagoras, the Pythagoreans, and unnamed individuals. Thus, I regard 6.23-28 as a potpourri of various Hellenistic Pythagorean texts, dressed by Hippolytus or an earlier anthologist to look like a single account. 39 And sense perceptible, if Wendland's emendation at 6.24.1 .5 is correct.

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114 using a text written by Mono·imus or someone in the same circle. (For convenience, I shall refer to the author of this source as Pythago1mus.)4° Similar to Mono!mus, Pythagolmus argues that there are nine accidents that occur in

ova[a, and he proceeds to list the remaining nine (Aristotelian) categories.4 1 The total, he claims, possesses the perfect number, ten. This comment accords with the Pythagorean tendency to claim for their own tradition, usually under the name Archytas, Aristotle's ten categories, and to explore its numerical symbolism.42 There may then be something substantial behind Hippolytus' s complaint that Mono·imus read the Law in terms of the ten categories, which he lists in full, as if Mono·imus had discussed them seriatim.43 Possibly, given Pythago!mus' s interest in the ten categories and their connection to realms of mental and sense perception, Mono!mus too, in a passage not reported by Hippolytus, interpreted the Pentateuch in light of Aristotle's categories. It would be attractive to an author such as Mono!mus to explore one-to-one correspondences between the categories, the Ten Commandments, and the ten plagues.

40 The author of Refutation of All Heresies 6.24 need not be Mono"imus. At Refutation of All Heresies 8.14.9 Hippolytus summarizes the preceding summary of Mono!mus's doctrine by referring to "these men." This suggests that Mono"imus was but one of a circle of authors with these distinct opinions. 41 Ibid. 6.24.2. Commentators in late antiquity took seriously the order of the categories. The list of categories at 6.24.2 is identical to that at 8.14.9 (but see Marcovich's ed., 335 n. at line 49), but different from that at 1 .20.1 in the placement of quality, quantity, position, and state. The first two passages, by Mono!mus and Pythago·imus respectively, further corroborate the closeness of the two authors, and their possible dependence upon Eudorus, who is probably responsible for rearranging the categories in this order. See Dillon, Middle Platonists, 134-35 and 1 78-80, who notes that Philo carefully makes the most of another order of Aristotle's categories. 42 See, e.g., pseudo-Archytas's Ten Universal Categories, ed. Thesleff 1 965: 3-8. 43 Hippolytus, Refutation of All Heresies 8.14.9.

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115 Monolmus' s letter to Theophrastus, with which Hippolytus concludes his entry on Mono!mus, suggests further comparisons with Pythago!mus' s number symbolism. The letter starts off by exhorting Theophrastus that, if he wishes to know God, he should stop looking for him in creation, but rather look for God within himself, "and learn who it is who appropriates for himself absolutely everything in you."44 To this end Monolmus advises him to say, "My God, my mind, my understanding, my soul, and my body."45+ All five elements are listed in descending order, and resonate well with the arithmological interest Mono·imus shows in his comments on the Pentateuch concerning the number five.46 This shows an interest in the "fives of anthropology," a theme found in other authors.47 Monolmus promises that those who follow his advice of introspection and accurately diagnose their emotions and motivation will eventually discover God, who is both "one and many according to that one apex," and find the escape from onesel£.48 Seemingly that "escape" would occur along the five steps already mentioned, from body to soul to understanding to mind to God. The five-stage process is guided by the one apex. The arithmology of Mono!mus is rather distinct from Valentinian. The Pleroma, which dwells in the Son of Man, is made up not of aeons but of numbers, essentially the first Decad. Missing from Monolmus' s arithmology is any dependence upon syzygies or eights,

Ibid. 8.15.1. 45 Marcovich excludes the phrase "My God," but at the expense of Mono"imus' s metaphysical hierarchy, as explained here. 46 Ibid. 8.14.5. 47 Pythago"imus, at ibid. 6.24.3-4, on the five senses; Clement of Alexandria, Stromateis 6.134.2, who presents man as possessing a decalogue of faculties, composed of two quintets. See below, pp. 1 30 and 1 87-200. 48 Hippolytus, Refutation of A ll Heresies 8.15.2. 44

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116 both of which are centrally prominent in Valentinianism. Instead, the seven powers that emanate from the iota are undifferentiated and unnamed.49 Mono·imus' s numbers are combined especially through the cube, icosahedron, octahedron, and pyramid - a mode of creation inspired by the Timaeus - so as to produce the material world . The classical Valentinian cosmological expositions do not depend upon the Timaeus. A further contrast is that Mono·imus's numbers are agents of transformation in the world, a process pleasing to God since it helps restore people from deception. In Valentinianism numbers do not play this active a role in salvation. Finally, the numerical protology of Valentinianism is far more complex than that of Monolmus, who avoids any elaborate mythology, and only presents two "aeons" - Man and Son of Man. The names themselves, one derived from the other, match this metaphysical simplicity.50 It may be argued that Mono·imus' s seven powers correspond to the Valentinian aeons, but the little we have of Mono"imus's system suggests they played a different role, probably a simplified, nonmythological version of the vision outlined in the Paraphrase of the Apophasis Megale (see next chapter). There is a superficial relationship between Mono·imus and Marcus. Both are interested in the connection between numbers and letter symbolism. Marcus's fascination with Christ as the episemon parallels Marcus's identification of the iota and its apex with Man and Son of Man. But Monolmus' s interest lies in an area not discussed by Marcus, the

49 If Mono"imus named the powers and grouped them into syzygies, Hippolytus uncharacteristically omitted such details. so Mono"imus's scheme, or a related one, seems to have crept into Epiphanius's account of Kolorbasos (i.e., Colarbasus; Panarion 35.2.4-12), whom he accuses of giving to the Father the name Man, on the basis of the Savior saying he was the Son of Man. None of the rest of Epiphanius's discussion on Colarbasus can be attributed to Mono·imus (or to Colarbasus, for that matter; see chap. 6) since the system it describes is a variation of classical Valentinianism.

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1 17 physical shape of the allograph

L,

his preferred way to illustrate the nature of God. In this

area, Monolmus has no parallels with the other authors treated in this study. There is a tradition of allograph symbolism in Greek, and it needs to be studied, but this goes beyond the scope of this study.51 To describe the relationship between Man, Son of Man, and creation Monolmus uses primarily mathematical models that, he suggests, illuminate passages in the Bible. We do not have enough information to locate Mono"imus precisely on the map of religious thought in the third century, but based on the typology of his number symbolism, Mono"imus shows the closest affinity to the Paraphrase of the Apophasis Megale, to which we now tum.

s1 For the symbolism of alphabetic characters see Plutarch, On the E at Delphi, the anonymous On the Mysteries of the Greek Alphabet (preserved only in Coptic), and assorted grammatical notes on the

derivation of letters' shapes and names, such as found in the anonymous commentary on Dionysius Thrax (Grammatici Graeci 1 :320.31-323.1 4) and Michael Psellos's Interpretation of the Twenty-Four

Letters.

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5 Paraphrase of the Apophasis Megale

The ancient tradition regarding Simon "Magus," the Samaritan wonderworker featured in Acts 8, is complex and extensive. Who was Simon Magus? Was he a gnostic? Scholars agree, there is no agreement on the answers. Still, they diligently comb the Simonian tradition and offer various hypotheses. Despite their different ways of reconstructing Simon, all scholars agree that the doctrines of the late second-century Simonian tradition are quite different from those of the first.1 The hopes that the Apophasis Megale, a text only Hippolytus quotes, might go back to Simon were quashed when Fricke} demonstrated that Hippolytus was citing not the

Apophasis Megale but a paraphrase of it.2 Since then, studies of the Paraphrase of the Apophasis Megale have generally tried to tease out the elusive fragments of an original

Apophasis Megale.3 The Paraphrase itself is of little interest because of how much it postdates the original Simon. Nevertheless, the Paraphrase, and not the Apophasis Megale, is of central 1 The best recent ful l-length study on Simon Magus is Heintz,

Simon "le magician. " More recent but less helpful, because it does not interact with Heintz's is Haar, Simon Magus. Haar is especially to be corrected by Heintz concerning the Greco-Roman perspective on magic and the polemical overtones of Acts 8.5-25. 2 Fricke!, Apophasis Megale. 3 Exceptions to this tendency are Mansfeld, Heresiography in Con text, 1 66-77 and Edwards, "Simon Magus." 118

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119 importance in this study. No other Simonian texts use number symbolism a s the Paraphrase does. There is no way to determine the authorship and date of the Paraphrase. Hippolytus' s account provides the terminus ad quem. The intricacy of thought suggests a late development of the Simonian tradition, so the early third century would be reasonable. The Paraphrase of the Apophasis Megale purports to be "the book of revelation of

Phone and Onoma from the Epinoia of the great Power, the unbounded."4 This, the opening line, promises the reader an apocalypse or revelatory text. The Paraphrase shows features common to the apocalyptic genre, but it is much more. First it is also a commentary on two texts: the Bible and the Apophasis Megale. This is evident from the number of quotations from the Bible, its many attempts to reconcile the Pentateuch with a doctrine of syzygies, and the frequent explanations and interpretations of the Apophasis Megale, the original impetus for writing. Second, the Paraphrase is a metaphysical treatise, very similar to Mono!mus's. The author of the Paraphrase of the Apophasis Megale has a vision of how the world is structured, and he finds ways to describe that universe based on disparate and seemingly unrelated texts. As reported by Hippolytus, the author of the Paraphrase of the Apophasis Megale (whom I call deutero-Simon for the sake of convenience) considers the root of the universe to be the Infinite Power (imEQavroc; ouvaf.Hc;).5 This title, repeated twenty times in Hippolytus's account, is clearly important to deutero-Simon, who seems to have been the

4 Hippolytus, Refutation of All Heresies 6.9.4, trans. Mansfeld, Heresiography in Context, 173 n 56. 5 Hippolytus, Refutation of All Heresies 6.9.5.

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1 20 first to use it.6 The term may be a subtle polemic against the New Testament. At Acts 8.10 Simon is called the Great Power? Although occasionally deutero-Simon describes the central power as the Great Power, Simon's moniker in Acts, his term of choice is the Infinite

Power.8 Infinite is infinitely greater than Great, and his preference for the former over the latter suggests that the term was carefully chosen, to show that over Simon, the great power, there was a higher power to which he was subordinate, thus answering the charge that Simon thought he was God.9 The Paraphrase also toys with an important part of the ancient Pythagorean tradition.

AnEQlXV'TOs and ix6QLG'TOs (and cognates) were traditionally applied to the Dyad, not to the Monad.10 Rather, the Monad was thought of as a limiting force, an agent that brought stability and shape to an unshaped Dyad . In the Paraphrase of the Apophasis Megale the opposite is true. It is not the dyad that is "without bound," but the one greatest power

(anEQlXV'TOs bvva1-w;). In contrast, Thought, Name, and Consideration, the second, fourth, and sixth powers (to be discussed below), all complete or limit their conjugal counterpart. 6 Compare the undatable H ermetic frag. 28, cited by Cyril of Alexandria, Against Julian 1 .46.10-19: '0 b£ TQLCYf..tEYLGTOs 'EQflTJs oihw cp8iyynm nEQL E>c:ou . . . . "H ouv 7LVQCXfl Ls, cpJlaiv, imoKE LflEVJl T1J cpvan KCXL n.fJ VOEQcfJ KOCYf-1.4-J" i'xn yaQ UQXOVTCX E71LKE LflEVOV TOY bJlfllOVQyov Aoyov TOU mVTWV bwnOTOV, Os flET' EKELVOV 71QWTJl buVCXfl ls, ayEVVJlTOs, lX11EQCXVTOs, a; EKE LVOV 11QOKvtjJaaa KlXL £ n iKE LT£XL KCXL UQXEL -rwv bL' au-rou bJl fl LOVQYJl 8 iv-rwv, i'an b[ -rov nav-rt:Adov

TI

Q6yovos KCXL

-riM LOs Kai yovLflOs yvfJmos Yi6s." But the combination of the two words is almost incidental, far from deutero-Simon's near-technical use. See also Hermetic frag. 26. 7 Ou-r6s i anv fJ bUVCXflls TOU ewv fJ KCXAOV flEVJl Mt:y.iAJl . Literally, "the power of God, so-called Great." 8 But see Hippolytus, Refu tation ofAll Heresies 6.13.1.13 and 6.18.3.10, where the Infinite Power is called the Great Power. 9 The very charge Hippolytus makes at ibid. 6.14.1. 1 0 See, e.g., Aristotle, Metaphysics 1081-83, where the aOQLCJTOs bvas is discussed. In the Pythagorean tradition influenced by Philolaus, it is chiefly "infinites" or "unlimiteds" (anE LQCX) that correspond to the dyad and even numbers.

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121 Thus, in the Paraphrase the dyadic, female powers limit the odd powers, the reverse of what is found in ancient Pythagoreanism. The Infinite Power and its twofold nature form the foundation of the system outlined in the Paraphrase. It dwells in the habitation of man (d:v8QW7Ws) and consists of two aspects, hidden and visible.11 Fire, the most fundamental element in the universe, is an example of this. It does not have, as many think, a single nature. Rather, its nature is twofold; its hidden aspect hides in its visible, and the visible aspect is brought into existence by the hidden one.12 Deutero-Simon links this polarity to the distinction Aristotle makes between potentiality and actuality, and Plato's contrast between mental and senseperceptible objects. The two aspects of a single nature recurs throughout the Paraphrase, in terms drawn, not only from sense perception (visible versus invisible, audible versus the voice itself), but from arithmetic, from the distinction frequently made between numbers and numerable things.13+ The Infinite Power bestows on man this bipartite structure by 11

Hippolytus, Refutation of All Heresies 6.9.5.

1 z Ibid.

6.9.5-6.

Ibid. 6.1 1 .1 . For my interpretation "between numbers and numerable things" I depart from Marcovich's Greek text at 6.11 .1, which describes the two parts of the fire: Tmo{n:ou bi: ovw<;, w<; bL, oA[ywv cl71civ, KaTa n)v Llf-!WVa 'WV 11VQO<;, Kat 71lXVTWV n0v < f-tcQWV ainoV,> OVTWV OQaTWV Kai aOQlXTWV, ivf]xwv Kat < aV>TJXWV, aQL8f-lfJTWV Kai agt8f-1WV, <¢QOVfJaLV EXOVTWV > - WV ain o<; iv n'j Anocpaan TTJ f-lcyaAT;J KaAci TCAc[wv VOcQWV - [oihw<; W<;] EKamov TWV arrnga(KL)<; amLQWV < f-tEQWV imbExnaL> i mvofJ8f]vm <W<;> buvaf-lcvov Kai AaAciv Kai bwvocia8aL Kai ivcgyciv, oihw<; w<;, ¢fJCJLV, 'Ef-lrrcboKAf]<; aQlef-!WV, d oes not create the clear-cut opposites he seems to intend, evident in their translation "countables and innumerables" : presumably one could have countable things that are too numerous to count, such as grains of sand. The manuscript without ernendation -agL8f-lfJTWV Kai agt8f-1wv - makes sense to me. It appears to draw from an idea popularized by Moderatus of Gades (frag. 2) and Theon of Smyrna (Mathematics Useful for Reading Plato 19.18-20.2), and further attested in Plotinus, Ennead 6.6.9: numbers constitute a metaphysical order higher than countable things. For Theon, the monad is to numbers as the hen is to 13

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122 creating him in "the image and in the likeness," a verse that deutero-Simon interprets in light of bipartite nature, assigning to "image" and the upper part of man the spirit who "hovers over the waters."14 The Infinite Power is called the root of the universe.15 Deutero-Simon develops the idea further, by likening the Power to the tree seen by Nebuchadnezzar.16 The trunk, branches, and foliage are the visible halfP The purpose of the tree is to produce perfect, well-shaped fruit that, unlike the other visible elements of the tree, will be put into the storehouse rather than the fire.18 The fire that consumes the tree is the Infinite Power itself, which begets the cosmos and the first six roots of the beginning of creation.19 These roots emerge from the fire as three syzygies: Mind and Thought, Voice and N arne, Reason and Consideration (figure 8) .2o

countables. See Excursus B l . Note, too, that deutero-Simon's first pair is not so much a contrast of opposites as of metaphysical superior and dependent, illustrated in the analogy of fire at 6.9.6. Here at 6.1 1 .1 is a list not of opposites but of correlative pairs. Thus, iviJxwv Kat f1xwv needs no emendation. A voice, after all, can be treated as the metaphysical superior to things heard, and the relationship of voice to sound mirrors that of number to countable object. 1 4 Hippolytus, Refutation of All Heresies 6.14.5-6; Gen 1 .2, 26. Hippolytus does not mention what deutero-Simon assigns to the lower half. Presumably this is the soul. 1 5 Hippolytus, Refutation ofAll Heresies 6 . 9 .5, 6.1 7.3. On root as a theological metaphor in gnosis, see Attridge and Pagels, "Tripartite Tractate," 21 7-18. 16 Hippolytus, Refutation of All Heresies 6.9.8. 1 7 Ibid. 6.9.9. 1s Ibid. 6.9.8-10. It is noteworthy that the LXX version of Daniel, unlike the Theodotian version (which generally replaced the LXX version in antiquity), emphasizes a single root being left on the tree. Dan 4.15 LXX: KCI:l OlJTWt; dm 'P[£::av fllCI:V acpcrE ainov EV TlJ yl], onwc; flETCX TWV 8TJQLWV Tilt; yf)c; EV TOLt; OQWL XOQTOV we; �ouc; VEf111TaL. It seems that this particular Greek translation of Daniel formed the basis of deutero-Simon's interpretation, which starts with Nebuchadnezzar's tree, but grafts into it the teachings found elsewhere- especially the New Testament: Mt 3.10, 7.19; Lk 3.9; Gospel of Philip 123-concerning trees. Hippolytus, Refutation of All Heresies 6.9.9 1 9 Hippolytus, Refutation ofAll Heresies 6.12.1. 20 Voice = wviJ; Name = Ovo11a; Reason = Aoywp6c;; Consideration = 'Ev8Df111GLt;.

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123 According to deuteroSimon the entire Infinite Power resides in these six roots, potentially, not in actuality, and the six roots allow a person to unite with the Infinite Power in essence, power, size, and perfection.21

Figure 8. Partial depiction of the theology of the

Paraphrase of the

Apophasis Megale. Arrows indicate actions; darkened stems, lines of generation (illustration by author).

Should a person not utilize the six powers latent in the soul and be fully formed that person is destroyed and perishes. According to deutero-Simon, some people in a similar manner ignore the grammatical or geometrical knowledge latent in their soul, much to their loss. In addition to the Infinite Power and the six powers there is a seventh power, given a title consisting of three participial forms of i'crrllf--H, "I stand": i:cn:wc; a'rac; G'rf1GUf1Evoc;P Each of the participles corresponds to one of three stages in this seventh power (which I call "Thrice-Standing" for convenience). In "having stood" (i:a'rwc;) it resided above, in the unbegotten power. In "standing" (a'rac;) it is begotten below in the flow of waters, in the image of the Infinite Power. It "will be standing" (G'rf1GUf1EVoc;) above, alongside the Infinite Power.23 This seventh power, then, unlike the other six, begins in the Infinite Power, sojourns in the lower world as an image of the Infinite Power, and then ends at the side of 21 Ibid. 6.12.3. 22 For textual parallels for this phrase in Hippolytus and other works see Marcovich's ed., 214, n. to line 5. See also Williams, Immovable Race, passim. 23 Hippolytus, Refutation of All Heresies 6.1 7.1 .

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124 the Infinite Power. Throughout the Paraphrase the Thrice-Standing and the Infinite Power are so closely identified they are sometimes indistinguishable. Nonetheless, Thrice-Standing is an entity distinct from its source, Infinite Power.24+ The Thrice-Standing acts on behalf of the Infinite Power by descending to creation and waiting to be perfected in beings so as to bring them back to the Infinite Power. All six powers have the Infinite Power latent within them, but the seventh power, the ThriceStanding, perfects their work by raising to the side of the Infinite Power persons who have been perfected.25 Because of its special mission, the Thrice-Standing is the subject of a number of cryptic or paradoxical epithets, and possibly even worship.26 The ThriceStanding, deutero-Simon says, explains the saying, "I and you are one; before me, you; after you, I."27 This single power is "divided up and down, begetting itself, growing itself, seeking itself, finding itself, being its own mother, its own father, its own sister, its own

24 At ibid. 6.12.3.10 the Thrice-Standing seems to be conflated with the Infinite Power: Elvm bi: iv Tat� [E, (>(i:,m� w:tnm� 7Hiaav OflOlJ TrlV an:iQavwv bvvafl LV bvva v E L, ovK EVEQYE L£;x, ilvnva an:iQavwv bvvaflLV < dval> ¢TJat TOV l' an�na < O"TaVTa> UTY]UOflEVov. But this identification depends upon Marcovich's insertion of and < UTavTa>. Note that the text omits the second "standing," ( ) the one stage when the Thrice-Standing is away from the Infinite Power. Possibly the verb to be understood here is not Elvm but EXELV, an emendation that would highlight the Thrice­ Standing's two stages that are in the presence of the Infinite Power. At 6.14.2, however, deutero­ Simon identifies the Infinite Power with the seventh power, which he calls the Thrice-Standing at 6.13.1.9. Possibly 6.14.2 depends upon a passage in theApophasis Megale that calls the Thrice-Standing "infinite" by virtue of its special relationship to the Infinite Power. At any rate, Refu tation of All Heresies 6.17.1 clearly articulates the distinction: "having stood" is in the unbegotten power, "standing" is in its image, and "will be standing" will be alongside the Infinite Power. At 6.14.3 is repeated the idea that the seventh power, another epithet for the Thrice-Standing, exists in the Infinite Power. On balance, then, it seems that the Paraphrase of the Apophasis Megale d oes not conflate the Thrice-Standing with the Infinite Power. 25 Hippolytus, Refutation of All Heresies 6.12.2. 26 Clement of Alexandria, Stromateis 2.25.2. 27 See Marcovich, 222-23, n. to line 10 for numerous close, but inexact, parallels in other ancient texts.

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125 m arriage (crui;;uyoc;), its own daughter, its own son."28 Paradoxes of this type are normally reserved in other systems for the One or the Monad, but here they describe a power that emanates from, and returns to, the Infinite Power!9 Toward the end of Hippolytus's account of the Paraphrase of the Apophasis Megale, deutero-Simon explains more fully - and more cryptically - the internal structure of the three syzygies.30 He says that for all the aeons there are two "shoots" (7TaQa
28 Hippolytus, Refutation of All Heresies 6.16.3. 29 Texts from a number of gnostic traditions refer to a standing god or other entity, but these beings

function somewhat differently from each other and from the Paraphrase. For more on this theme, see Williams, Immovable Race, 37-38, 57. 30 Hippolytus, Refutation of All Heresies 6.18.2-7. 3l I take as objective the genitives in bvo E LOL TWQet¢vabEC; n0v o;\wv aiwvwv. 32 Note now the late introduction of the classic Valentinian name for the first aeon. 33 Ibid. 6.18.3. 34 The Infinite Power has no limit (anEQetVTO�), and the gap has no limit (�iyrE niQa� [xovra). Ibid. 6.18.3.13. 3s Ibid. 6.18.4.

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126 This account of the generation of the powers is confusing. It starts off with three entities- the one root with two shoots is the Father with Mind and Thought. But it then describes Thought as proceeding from the Father, as if Father and Mind were the same and there are only two entities. Further, Silence's role in generating the syzygies is mentioned, but never elaborated . Despite this confusion, it is apparent that deutero-Simon sees the generation of the syzygies as being organic and internal to the Infinite Power. The male half of each syzygy is alone, although he internally possesses the female part.36 He becomes "first" only after he yields the "second" through an act of self-introspection that reveals his Thought. The act is described as the Father "issuing forth himself from himself," whereby he makes manifest his Thought. This second figure now calls the first "Father," and hides him in herself, and the union creates an androgynous being: power and Thought, with the power as the upper half and the Thought as the lower.37 This explains a phrase, presumably from the Apophasis Megale: "Being one, two are found" (£v ov bvo EVQLaKETat). The male and female have a spermadic-monadic relationship (table 1 ) . The male first subsumes the female, then the female surrounds the male. This description of the powers depends upon terms and analogies drawn from Platonism and its mathematics. There is the pervasive idea of emanation from an ineffable One, and return to that unity. There is also a description of the generation of numbers, symbolized by the deutero-Simon' s powers. Moderatus of Cades' definition of number, widely accepted in the ancient world, was that number was either a collection of monads

(auG'rllfJIX fJOVabwv), or the advance of a multitude starting out from the monad and a 36 Ibid. 6.18.5. 37 Ibid . 6.18.6. Here bvvapLc; seems to be equated with Dan')Q or Nove;.

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127 return when abating into the monad. Thomassen has shown that Moderatus' s description of quantity emerging from being underlies this very simple idea, that the dyad emerges from the internal life of the monad.38 The notion informs most philosophical considerations of the generation of number, for example, Plotinus's complex discussion of the ontology of number and multiplicity. Much later, but still in line with the tradition, Proclus compares the monad and dyad to the point and line. He considers the generation of a line from a point an apt illustration of how the dyad can emerge from, yet still be part of, the monad.39 Many other examples could be given. Like Proclus, deutero-Simon brings other metaphors -in this case, fire, trees, and powers - to bear upon the philosophy of number. The numerically inspired doctrine of syzygies is central to the Paraphrase's exegesis of Scripture. Deutero-Simon brings to the creation account of Genesis his doctrine of the six powers and the Thrice-Standing, albeit with uneven results. To begin, he assigns to each of the six powers key parts of creation: Mind and Thought are heaven and earth. Just as Mind oversees and guards his consort, Thought, who, in tum, receives his seed, so the masculine heaven looks down upon earth, which receives that which heaven sends down. Voice and Name are the sun and moon, and Reason and Consideration are the air and water.40 He then mentions the Thrice-Standing, calling it the seventh power and thereby associates it with the seventh day, "the cause of the good things praised by Moses," who said, "very good" (Kcv\a ;\lav).41 The only time "very good" is used in Genesis 1 is at the end of the sixth day, to summarize the entire six days' worth of creation. Days one through 38 Spiritual Seed, 274. 39 Proclus, Commentary on Euclid Defs. 2-3. 40 Hippolytus, Refutation of All Heresies 6.13.

41 Ibid. 1 .13.1 . 1 0; Gen 1 .31 LXX.

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128 five are called merely "good."42 Deutero-Simon's point seems to be that the phrase Ka'l"a

A lav distinguishes the six days of creation from the Sabbath, which perfects the goodness of the prior days. So too the Thrice-Standing is the cause of goodness in the six powers. Deutero-Sirnon continues his extended comparison of creation and the powers, but with uneven results. He says that the three days that occur before the creation of the sun and moon (i.e., Voice and Name), refer to the first syzygy (Mind and Thought) and the seventh d ay of creation.43 It is unclear how the seventh Power, earlier assigned to the Sabbath, can now consistently represent one of the first three days of creation. He applies number symbolism to other Biblical texts. For instance, he differentiates the garden of paradise from Eden, in line with his tendency to identify binary pairs.44 The garden of paradise is a womb, as Isaiah says, "I am the one who fashioned you in the womb of your mother."45 Eden is a membrane, afterbirth, and navel, since "a river proceeding out of Eden waters paradise."46 The four springs that flow out of Eden resemble the four channels that are attached to the embryo. Two of these convey breath (or spirit) and two, blood.47 The four rivers of Genesis further symbolize how the embryo only has four of the

42 Gen 1 .4, 8, 10, 12, 1 8, 2 1 . 4 3 Hippolytus, Refutation of All Heresies 6.14.2. 44 Ibid. 6.14.7-8. 4s Ibid. 6.14.7, citing Is 44.2, 24. 46 Hippolytus, Refutation of All Heresies 6.14.8, citing Gen 2.10. 47 See Pouderon, "Notice d'Hippolyte." Here, deutero-Simon integrates his theology with common beliefs about the fetus. In other parts of the Paraphrase of the Apophasis Megale the breath/spirit is seen as the higher aspect in av8Qwnoc; (Hippolytus, Refutation of All Heresies 6.14.6), and the seventh power itself, as the image of the Infinite Power (ibid. 6.14.4). The blood is fire, the sources of things begotten (ibid. 6.17.4). Just as the root of all bifurcates into shoots (ibid . 6.18.2-7, discussed above), so does the blood, into semen in men and milk in women (ibid . 6.17.6).

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129 five senses- sight, hearing, smell, and taste.48+ These four senses, in this, the standard order of the senses, are alluded to by the titles and content of each of the first four books of the Pentateuch. Genesis is sight, Exodus is hearing, Leviticus is smell, and Numbers is taste.49 The fifth sense, touch, is addressed by the title of the fifth book, Deuteronomy, which is geared for formed children in order to confirm and summarize their other four senses. Thus, deutero-Simon synthesizes into his theory of sense perception two very different Biblical numbers, four (the number of rivers in paradise) and five (the number of books in the Pentateuch). It may seem a bit forced to say that the overall message of Exodus is about hearing. But for deutero-Simon, the preservation of the orders of the five senses and the Torah are the important thing, not the establishment of some kind of natural correspondence between them. 48 At ibid. 6.15.1 .3 the manuscript reads: OQCWLV, aKor'Jv, m¢QTJOLV, YElJOLV Kctl a¢i]v. Marcovich

renders it: OQctOLV, [aKor']v,] yn:Jmv, oo¢QTJOW Ka.L a¢i]v . But his emended text contravenes the order of the senses presented at 6.15.2-6.16.4: sight, hearing, smell, taste, and touch. This latter order follows exactly that of Chrysippus, frags. 827, 836 (SVF 2 :226--27), Aetius, Placita 4.9.10 ( Stobaeus, Eclogae 1 .50.27 [Hense and Wachsmuth 1 :476]), and others (see, e.g., Lampros, KaTaitoyoc:, 2:17, no. 4212.72). The same order is preserved in the independent but parallel accounts at Irenaeus,Against Heresies 1 .18.1 and Hippolytus, Refutation of All Heresies 5 .9.16-18, where the first four are assigned, in that order, to the four rivers. Because these parallel texts omit touch so as to create a list of four senses, it is likely that the Paraphrase of the Apophasis Megale does so as well at 6.15.1 .3. My intuition is justified by an observation made much earlier by Salles-Dabadie, Recherche, 28 n. 1 7, the only modern editor to seclude Ka.L a¢i]v: in deutero-Simon's system the fifth book of the Torah is called Deuteronomy in order to supply to an already formed child - presumably after birth - touch, the capstone of the senses (Hippolytus, Refutation of All Heresies 6.16.3): L'l.cvTEQOVOflLOV bi: T<J 7lE fl7lTOV (3tf3itlov, OnEQ, ¢TJOLV, EOTL 7TQOc; Tilv a¢ilv TOU mni\a.OflEVOV nmb[ov YEYQctflflEVOV. WOnEQ yaQ i] a¢il '[(X vno TWV aAi\wv a.ia8f]aEWV OQct8EVTa. 8tyouoa. ava.KE¢a.i\a.tOUTa.L Ka.L (3Ef3a.toi, OKi\TjQOV i] yi\[OXQOV, i] 8EQf10V i] 1./JVXQOV boK L flaaa.aa, ovTwc; TO 7lE fl7lTOV (3 L(3i\[ov TOU VOflOV ava.KE¢a.i\a.[wo[c; ian TWV 7TQO a.inov yQa.¢ivTWV TEOOlXQWV. Thus, Kctl a¢i]v at 6.15.1 .3 was inadvertently inserted at the list's end, where many such scribal intrusions occur, and the text should read OQa.OLV, aKor']v, oo¢QTJOLV, [Ka.L a¢i]v] . For departures from the canonical order of the senses, see below, p. 191 n. 34. 49 Hippolytus, Refutation of All Heresies 6.15.2-6.16.3. =

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130 Monolmus also attempts to understand patterns of five and ten in the Pentateuch in anthropological terms. Whereas deutero-Simon connects sense perception to the four rivers and the five books of Moses, Monoi:mus connects the tens in Scripture to Aristotle's ten categories and the shape of the iota. Monoi:mus and deutero-Simon are similar in other respects. Monolmus calls the 1-llcx 1-1ovac; "many-faced and ten-thousand-eyed and tenthousand-named" ( noAvnQ6awnoc; KaL !-lVQL0!-11-la'roc; KaL !-lVQLWVV!-loc;); the Apophasis

Megale seemingly says the Son is "many named, ten-thousand eyed, incomprehensible" ( noAvwvvl-loc; 1-lVQL0!-1!-la'Wc; aKa't"aArJ71't"Oc;) .50 Both deutero-Simon and Monolmus attempt to relate the seven days of creation to seven powers latent in a transcendent realm (termed

Infinite Power in deutero-Simon and Man in Monolmus). These powers emerge first as a set of six, and then the seventh follows. Monolmus' s system does not teach the syzygies found in deutero-Simon' s, but their shared arrangement of the seven powers in groups of six and one is striking, resembling the core of the Pleroma taught by Hippolytus's Valentinians. Deutero-Simon's syzygies resemble those of the Valentinians.51 But unlike the syzygies in the models of V alentinianism reported by Irenaeus, all the syzygies in the

Paraphrase emanate from the Infinite Power. In Valentinianism, one syzygy begets another. There is no hint in the Paraphrase of a doctrine of Ogdoads, Decads, Dodecads, or Triacontads. In contrast, the Paraphrase emphasizes the number seven, for instance in the role of the Thrice-Standing, who is ranked seventh. The Valentinian emphasis on pairs, Ogdoads, and Tricontads is so strong that the number seven is not given much significance, 50 Ibid. 8.12.7, 5.9.4. "Seemingly" because this phrase occurs in Hippolytus's discussion of the

"Phrygians," but just prior to an explicit reference to theApophasis Megale. Hippolytus may have introduced the phrase in anticipation of the section to come. 5 1 See Marcovich's ed., 217 n. 7 for extensive comparisons.

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131 except as a symbol of the Demiurge. Further, the deutero-Simon's naming scheme differs from the V alentinians' . The three male powers describe human faculties (Mind, Voice, Reason), and the names of the three female powers are the product or result of their male counterpart (Thought, Name, Consideration). There is no direct connection apparent with the various Valentinian naming schemes, even though Valentinians would probably have found deutero-Simon's names understandable. Overall, the typology of the number symbolism of the Paraphrase of the Apophasis Megale stands somewhere between that of Mono1mus and that of the Valentinians, but closer to the former than the latter. There is nothing to suggest that the Paraphrase depends on either one for its number symbolism. Its independence makes clear at least one trend in late second- and early third-century Christianity: various groups used their own kinds of number symbolism to depict their own widely different ideas about the interpretation of the Bible and about the structure of the divine realm.

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6 Colarbasus

Colarbasus (KoAaQ�aaoc;; alternately, KoA6Q�aaoc;) was a contemporary of Marcus.1 Some ancient sources call Colarbasus a follower of Marcus;2 others, an associate.3 Epiphanius claims Colarbasus followed Ptolemy the Valentinian, which matches the general order given by Irenaeus, whose narrative does not specify where in the line of succession Colarbasus should be placed.4 Epiphanius probably misread Hippolytus, who accuses Colarbasus of pursuing the doctrines of Ptolemy the astronomer. Theodoret's entry for the Colorbasians is separated from his entry on Marcus by three chapters, suggesting that Theodoret saw no direct line of influence. Despite these differences, all these sources, including Tertullian, place Colarbasus in the Valentinian school.5 Marcus says that the Monotes is the womb and receptacle of Colarbasus' s Silence.6 Forster analyzes this puzzling statement and argues that Colarbasus probably influenced

1 Irenaeus,

Against Heresies 1 .14.1. 2 Filastrius, Book of Different Heresies 54 [15]; Epiphanius, Panarion 35.1 .1 . 3 Irenaeus, Against Heresies 1 .14.1; Hippolytus, Refutation of All Heresies 6.5, 6.55.2-3; pseudo­ Tertullian, Against All Heresies 5; Epiphanius, Panarion pinax to 34, 35. 1 .2. 4 Epiphanius, Panarion 35.1.1; Irenaeus, Against Heresies 1 .14.1. 5 Tertullian, Against the Valentinians 4.2. 6 Irenaeus, Against Heresies 1 .14.1.

1 32

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133 Marcus, inspiring especially the psephy in his theology? Although Forster's argument is plausible, I do not think it likely since the rest of the tradition places Colarbasus alongside of or after Marcus. There is little or no biographical information on Colarbasus; and the little of his teaching that can be reconstructed cannot be proved to have influenced, or to have depended upon, Marcus's. It seems to me wisest to consider Colarbasus merely a contemporary of Marcus. Like Marcus, Colarbasus developed his own school, and thereby became prominent enough in the Valentinian movement to draw criticism from the orthodox.8 Since we have no biographical details of his life, Colarbasus' s provenance can best be guessed at through his name. At first it seems Semitic, a combination of ?:J and :n� . This would give his name the meaning "all four," referring to his interest in the Tetraktys. This was suggested first by Heumann in 1743, to dismiss the idea that Colarbasus was more than a literary creation. Although Heumann's skepticism has failed to win support, his etymology of the name has been more influential. Forster, however, has shown that the name and its variations can be traced through inscriptions to Cilicia.9 I agree with Forster, yet to identify Colarbasus as a Cilician does not indicate where he worked and traveled, since the name is attested as far west as Rome, and as far east as Mopsuestia.10 To put

7 Marcus Magus, 1 64-73. 8 In addition to the frequency with which Colarbasus appears in ancient Christian antiheretical literature (see nn. 1-5, above), there is the report of an ancient treatise directed against Colarbasus's school. See Markschies, Valentinus Gnosticus ? 262 n. 20. 9 Forster, Marcus Magus, 1 69-70, with nn. 8-9. To be added to Forster's references to attestation of Kolarbasis is SEG 38:1 486. The name may be derived from the city Ko;\v�Qa.aad)(;;, tentatively identified by Bean and Mitford, Journeys in Rough Cilicia, 69-71 with Ayasofya, in the western part of Rough Cilicia. w Rome: IG 14.1685; IGUR 612. Mopsuestia: Heberdy and Wilhelm, Reisen in Kilikien, 37.

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1 34 Colarbasus in Rome or Asia Minor would probably not be too far off the mark, although Egypt cannot be ruled out, either.11 Irenaeus' s offhand reference to Colarbasus' s Silence remains cryptic. It seems to charge Colarbasus with speculating on the aeons, particularly the second, but Irenaeus does not explain. An Armenian fragment of Irenaeus, said to be a discourse against Colorbasus and his circle, accuses him of dividing Jesus from Christ, of assigning them separate roles and origins, that is, of teaching classical Valentinian doctrinesP Later sources also portray him as a Valentinian, but they are not consistent with each other in their details. Epiphanius ascribes to Colarbasus, apparently arbitrarily, the system found in Irenaeus, Against Heresies 1 .1 2.3-4, fusing it with the Man-Son of Man system taught by Monolmus.13 Theodoret follows Epiphanius' s lead, but restricts the Colorbasians' teaching to the system found at Against Heresies 1 . 12.4.1 4 On the other hand, pseudo-Tertullian and Filastrius state that Colarbasus' s doctrine concerned the letters of the alphabet and numbers. They do not assign to him doctrines concerning the Valentinian Pleroma. Hippolytus concurs and presents Colarbasus as the most prominent of a number of people who "tried to expound religious piety through measures and numbers."15 Hippolytus then outlines in considerable detail a system of

11

See Markschies, Valentinus Gnosticus ? 262 n. 20, and references there to conjectures on an Egyptian provenance. 12 Frag. 7, at Patrologia Orientalis 12 (191 9): 741-44; frag. 1 1 in Jordan's ed., 19, 1 50. 13 Epiphanius, Panarion 35.1-2. 1 4 Compendium of Heretical Fables 1 .12. 1 5 Refutation of All Heresies 4.13.

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135 numerological prognostication.16 Although Colarbasus is not explicitly named as the author and main proponent of this prognostication, it is implied. Our concern here is not with Colarbasus' s Pleroma. Even if he really were a Valentinian, his Pleromatic structure would have resembled the systems already discussed in chapter two. Rather, I treat here Hippolytus' s account of Colarbasus' s technique of numerological prognostication. This is the earliest discussion we have of this system, and it appears frequently in Greek manuscripts, usually in anonymous form (see excursus D). Hippolytus' s discussion amounts to a set of rules used to predict outcomes of combat. One uses the normal conventions of isopsephy (see excursus C) and assigns to letters with values in the tens and hundreds their corresponding value in units. Thus, for example, YJ, n, and w - the numerals 8, 80, and 800- can be reduced mod 10 to a value of eight. The eight is called their root ( nu8!Jr'Jv)F You then take a person's name, find its roots, and add them together. Aya!JEflVWV, for instance, is reduced to a ' + y ' + a ' + b ' + E ' + b ' + E ' +

YJ

'

+ E ' = ,\� ' (1 + 3 + 1 + 4 + 5 + 4 + 5 + 8 + 5 = 36).18 This sum is also reduced to its roots: ;\.� '

= y ' + � , = 8 ' (36 = 3 + 6 = 9). Nine can be reduced no further.19 A second name is then taken - Hippolytus's example is "EK'rWQ, Agamemnon's adversary -and the same ' procedure is followed: E ' + W + y ' + YJ + a ' = L8 ' = a ' + 8 '

= 10

=

=

L' = a ' (5 + 2 + 3 + 8 + 1 = 1 9 = 1 + 9

1), or, more simply and in modem mathematical notation, 19 mod 9 = 1.2° After

providing one more example of how to reduce a name (llcX'rQOKAoc; = 34 mod 9 = 7),

1 6 Ibid. 4.14. 1 7 Ibid. 4.14.1-3. 1s Ibid. 4.14.3-4.

19 Ibid. 4.14.5. zo Ibid. 4.14.6-7.

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1 36 Hippolytus mentions a variation and two exceptions. The variation (var. a) on the system follows similar rules, but reduces the value of the names mod 7.21 One of the exceptions (exc. a) states that a letter used twice (and only twice) should be counted only once, so that e.g.,

Tia'rQOK/\oc; should be reckoned as if it were Tia'rQOKi\c;.Z2 One other exception (ex c. b) appears to be that if two letters share the same root one should be dropped . But Hippolytus's example, I:aQnf]bwv, is confusing. He advocates dropping the w ' since r] ' is of the "same value" (iaobuva!-!Ei:v) and because doublets shouldn't be counted . But the rule seems not to apply to the n ' (also a root of 8) or to the pair a' and Q' (each with root 1).23 With this procedure, it is possible to predict who beats whom. The psephic values of the names of two opponents are calculated and reduced mod 9 . If one is odd and the other even, the higher number wins.24 If both are odd, or both are even, the smaller number wins. Hippolytus furnishes examples. I:aQnf]bwv mod 9 mod 9

=

2) and Tia'rQoK/\oc; mod 9

=

=

2 (2 + 1 + 1 + 8 + 8 + 4 + 0 [ex c. b] + 5

9 (8 + 1 + 3 + 1 + 7 + 2 + 3 + 0 [ex c. a] + 2

so the latter beats the former since 9 beats 2.25 So too, A'lac; mod 9

=

=

27 mod 9

4 and "EK'rWQ mod 9

so Aias beats Hektor.26 In the contest between Ai\[l;avbQoc; and MEv[i\aoc; (mod 9 is dropped [exc. a]), the former is assigned the proper name TiaQLc; (mod 9 beats Paris since 9 beats 4.27 "A!-!uKoc; (mod 9

=

=

=

=

=

29

9), =

1,

9; one E

4), so Menelaos

2) loses to Tioi\vbwKf]c; (mod 9

21

=

7; drop one

Ibid. 4.14.8-10. Ibid. 4.14.12. 23 Ibid. 4.14.14. It is unclear whether the problem rests with Hippolytus, his source, or a later scribe. 24 Ibid. 4.14.13. 2s Ibid. 4.14.13; Homer, Iliad 16.419-683. 26 Hippolytus, Refutation of All Heresies 4.14.15; Homer, Iliad 7.181-305. 27 Hippolytus, Refutation of All Heresies 4.14.16; Homer, Iliad 3.340-82. 22

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1 37 u

[exc. a]).28 Atac;; (mod 9

==

4; drop one a [exc. a]) wrestles and beats Obuacnuc;; (mod 9 == 8;

drop one u but retain all three sigmas since exc. a applies only to doublets). Hippolytus objects to this result and wonders whether Odysseus's proper name has really been used, since according to Homer the opposite happened.29 AxtAAc uc;; (mod 9 a]) beats "EK'fWQ (mod 9

==

1);30+ AxtAA cuc;; (mod 9

==

==

4; drop one i\ [exc.

4) beats Aa'fEQOna'ioc;; (mod 9 3; ==

inexplicably, the doubled a and o are dropped [exc. a] but not the doubled a)f1 and M Ev[i\aoc;; (mod 9

=

9; one E dropped [exc. a]) beats Ev¢oQ�oc;; (mod 9

==

8; one o dropped

[ex c. a ]).32 Along with the use of mod 7, Hippolytus lists four more variations. Some use mod 7 and only on vowels (var. b).33 Others separate the vowels, semivowels, and consonants and decide each contest independently (var. c). Others randomly reassign numerical values to the letters so that, e.g.,

n ==

5 and E, 4 (var. d). In the last variation the user first determines ==

how many times in the past the opponents have met. If this is their second time, you remove the first letter and recalculate; if the third contest, you remove the first two letters, and so forth (var. e).34 These variant systems presumably belong to Colarbasus's successors.35

28 Hippolytus, Refutation of All Heresies 4.14.17; Homer, Iliad 23.778. 29 Hippolytus, Refutation of All Heresies 4.14.17; Homer, Iliad 23.700-37 and 752-79. 30 Hippolytus, Refutation of All Heresies 4.14.18; Homer, Iliad 22. Marcovich needlessly emends to Axu\n)c:;. 31 Hippolytus, Refutation of All Heresies 4.14.18; Homer, Iliad 21 .136-99. 32 Hippolytus, Refutation of All Heresies 4.14.18; Homer, Iliad 1 7.43-60. 33 Hippolytus, Refutation of All Heresies 4.14.19, also probably alluded to at 4.44.3. 34 Ibid. 4.14.20. My interpretation of this convoluted passage depends on taking on)n:QOV (4.14.20.104) as adverbial and not an accusative, a case that cannot be reconciled as the object of ayavii:;wvmL. M{JTEQOV is adverbial at ibid. 1 .2.6 ( 4 .51 .4), 4.28.8, 4.33.3, 4.51 .4, and 5.15.3. 3s The ETEQOL b£ of ibid. 4.13. 1 . =

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1 38 This is the earliest datable specimen of Greek numerology. Of the many types of Greek numerological prognostication, Colarbasus' s system is well attested in dozens of manuscripts, dated as late as the nineteenth century.36 Many times the technique is prefaced by a letter from Pythagoras to Telauges, yet the examples given include those found in Hippolytus' s account. The practice was widespread, and involved a bewildering array of techniques and tables (see excursus D). Prognostication was not the only way to use psephy. Hippolytus reports the common practice of wearing an amulet inscribed by the name God

(8E6s), since its psephic value, reduced mod 9, is 5, an odd (and therefore beneficial) number. Another practice uses the same method to explain why a certain plant, tied around a patient, restores him.37 Therefore, this kind of psephy could be used in magical techniques, not just prognostication. Is Colarbasus the inventor of this tradition? Is he the author of the pseudepigraphal letter from Pythagoras (see excursus D)? Both suggestions are plausible, but cannot be demonstrated. Isopsephy first emerges as a literary phenomenon in the first century (see excursus C). Some time elapsed before isopsephy could be used widely enough to use it for prognostic techniques. The 160s and 1 70s would be as good a time as any for the development of isopsephic prognostication. We cannot trace its origin to Colarbasus specifically, but if his association with Marcus was more than casual, he probably had a role in its propagation. The frequent appearance of astrological and psephic techniques in advanced forms of Valentinianism suggest that this particular Christian movement was fertile ground for numerology like Colarbasus' s. E.g., CCAG 1 0:27, cod. 1 1 (Athen. 1350), f. 2. The technique is still found in modern Greece. 37 Hippolytus, Refutation of All Heresies 4.44.2. 36

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139 Despite Hippolytus' s criticism, that Colarbasus tried to establish "religion"

(8wa£j3nav) yet wound up a heresiarch, there is little in Hippolytus's report to connect Colarbasus to any kind of theological system.38 Marcus depends upon gematria, but it is not used to predict the future. Colarbasus' prognostication, however, is designed for exactly these mundane ends, not for elevating readers' minds to contemplate higher realms of existence. But it would be hasty to conclude that, because no theological system is outlined in Hippolytus' s extract, Colarbasus could not have been the religious figure depicted in the heresiological tradition. The same reasoning could be used to show that, purely on the basis of his Theology of Arithmetic, Anatolius of Laodicea was not a bishop, or that Julius Africanus - the author of the Kestoi, a collection of miscellaneous notes on a variety of topics, including magic- was not a Christian. Both were devout Christians, yet both were also interested in other topics. Their examples show that some religious writers could be expected to compile handbooks somewhat tangential to their chief interests. The 8c6c; amulet, along with the many other examples of religious Greek numerical prognostication listed in excursus D, show that isopsephy could be easily incorporated into a religious system. There might be something to the report that Colarbasus was a Valentinian, but it cannot be demonstrated.

38 Ibid. 4.13.1 .3, 4.15.2.9.

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7 Irenaeus

Born in the early second century, Irenaeus spent his youth in Asia Minor, where he listened to the teaching of Polycarp of Smyrna (d. 156), the famous martyred bishop who, in tum, reportedly learned at the feet of the apostle John.1 Irenaeus's early interaction with Polycarp and other elders from the orthodox churches shaped his career as a priest and bishop in Lyons, where he remained from the 170s until the end of his life, probably around 200. His tenure there was marked by his popularity among Gallic Christians who suffered persecution, and by his attempts to reconcile the Roman church with other Christians who held to a different dating of Easter. Little else is known of his life, aside from what Eusebius reports.2 Only two of Irenaeus's many works are preserved complete, Against Heresies and

Demonstration of the Apostolic Preaching. The latter, a catechetical work that crosses over into apologetics, is of less concern to this study than the former, a five-book refutation of heresies, Valentinianism and Marcionism in particular. Also preserved are various fragments from Irenaeus's letters, sermons, and treatises. A title of one of these treatises, On

1 Irenaeus, Against Heresies 3 .3.4. 2 See DECL, s.v. "Irenaeus"; Eusebius, Church

History 5.4, 7-8, 20, 26.

140

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141

the Ogdoad, now lost, attests to Irenaeus's unflagging opposition to Valentinianism. It was directed against a certain Florinus, who broke away from the church in Rome and later joined Valentinian circles.3 Although we no longer have the treatise, its main arguments may be preserved in Against Heresies, our main source for assembling and assessing Irenaeus's critique of Valentinian number symbolism and his constructive approach to numbers in theology. Most scholarly treatments of Valentinianism attempt to read Irenaeus out of Against

Heresies so as to achieve as uncontaminated a view of the system as possible. The ultimate goal, a bias-free view of Valentinianism, is utopic, but the approach taken is useful since it tries to read a theological movement in its own terms, not that of its opponents. For much the same reason, in earlier chapters of this study I have only briefly discussed Irenaeus' s critique, and have tried to uncover the ideas and terminology native to Valentinianism. But to eliminate Irenaeus from his writings is to leave incomplete the picture of Valentinian number symbolism. He too must be understood on his own terms. To understand both his critique of Valentinian theological arithmetic and his alternative use of numbers in theology is to provide the means for understanding better what, if anything, he tampered with in his representation of Valentinianism. Thus, to understand better Irenaeus' s number symbolism is to understand better the Valentinians' . Setting aside the rhetorical flourishes expected in theological polemic-his sarcasm and his accusation that Valentinianism derives from Pythagoreanism and paganism - there are four general theses Irenaeus advances against the Valentinians' use of numbers: the

3 Eusebius preserves the closing words of the treatise: Church History 5.20.2.

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1 42 aeons in their Pleroma are inconsistently numbered; their doctrine makes claims that depend upon the changing, culture-bound customs of language and numeration; their number symbolism does not correspond to the structures of the created, natural world; and their method of appropriating the rule of faith, Scripture in particular, is faulty. While pursuing these four lines of attack, Irenaeus promotes some basic principles about theology and exegesis, both to discredit Valentinianism and to articulate core principles of the faith held by the churches around the world. These key principles explain Irenaeus' s theology and exegesis, both of which he frequently pursues in Against Heresies with little reference to the heresies tha t first prompted the formulation of the principles. In this meandering, Irenaeus never completely forgets Valentinus, Ptolemy, Marcus, Marcion, and the rest, but in many places, particularly in books three through five, he develops ideas about numbers and theology that go beyond his immediate concern with these specific heresies. Irenaeus' s constructive use of number symbolism provides the examples we need to see how consistent he was in his critique of V alentinian number symbolism. Does Irenaeus fall by the same sword he uses against the Valentinians? Why or why not? I address these questions at the end of this chapter.

IRENAEUS'S CRITIQUE I have already suggested that we should bar Irenaeus's sarcasm against Valentinianism as a criticism of substance. Nevertheless, his colorful insults help explain his substantive points.4 He ridicules the Valentinian Tetrad by constructing his own out of an emptiness, a gourd, a

4 Besides the examples of sarcasm listed here, see below, p. 389 n . 9.

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1 43 cucumber, and a rnelon.5 The emanation of fruits, Irenaeus argues, is just as plausible as that of aeons, and they are equally arbitrary. Irenaeus also associates his opponents with pagans whose teaching and habits contradict Christian doctrines. While reporting Marcus's system, Irenaeus accuses him of trying to preach something more mystical than the other systems do, of achieving new mystical heights by breaking down everything into numbers. According to Irenaeus, they say "everything derives existence from a monad and a dyad," clearly Pythagorean terrninology.6 The Pythagorean slur occurs again in book two, where Irenaeus attributes the Valentinian tendency to translate everything into numbers as corning from the Pythagoreans? His logic: they were the first to make numbers the first principle of everything, the first to make even and odd the first principle of numbers, and the first to make odd and even the basis of sensible and intelligible things. Even numbers are the basis for underlying substance (in Aristotelian terms, a primary substance), whereas odd numbers are the basis for intellection and essence.8 The difference between even and odd resembles the parts of a statue, which has both substance (equivalent to even numbers) and form (odd numbers). This is the sort of model, Irenaeus says, the Valentinians apply to beings outside the Plerorna. They (the Pythagoreans or the Valentinians - the text is vague) claim that by knowing "what was first assumed," a person seeks out the beginnings of intellection and in exhaustion races to that which is one and indivisible. This one - the iiv -

s Irenaeus, Against Heresies 1 .1 1 .4 .

Ibid. 1 .16. 1 . See also excursus B. 7 Irenaeus, Against Heresies 2.14.6, upon which the rest of this paragraph is based. 8 The preserved text is muddled here. My paraphrase follows the conjecture of Rousseau and Doutreleau, 2.1 (SC 293): 260. 6

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1 44 is the principle of everything and the basis of all generation.9 From it come the Dyad, Tetrad, and Pentad, which terms the Valentinians use to describe the Plerorna and Depth. This Pythagorean number symbolism undergirds the doctrine of the syzygies. Marcus, boasting about the great novelty of his invention, speaks about the tetraktys of Pythagoras as if it were the origin and mother of everything.

In this section of book two, Irenaeus portrays the Valentinians not only as a derivative of Pythagoreans. He suggests they are a pastiche of Horner, Hesiod, Dernocritus, Epicurus, Anaxagoras, Ernpedocles, Plato, Aristotle, and the Cynics, as well as the Pythagoreans. This approach differs from that taken by Hippolytus, who establishes one-toone correspondences between various philosophers and heresiarchs, to demonstrate that the heretics and pagans have parallel lines of succession.10 Irenaeus, however, links Valentinianisrn not just to one but to all the various strains of philosophy and Hellenism. To cap the insult, he claims that his opponents draw inspiration from the pagan pantheon of twelve gods, and make them images of the Dodecad.n Because Irenaeus does not quote verbatim from the Valentinians here, it is impossible to tell exactly what kind of relationship, if any, the Valentinians saw between the Dodecad and the gods, and whether it was really as sinister as Irenaeus suggestsP

9 The hen, not monad, is the first principle. This suggests that Irenaeus's Pythagorean ideal here is more Platonic or eclectic and less Pythagorean. See excursus Bl. 1 o See above, p. 54 and n. 140. 1 1 Irenaeus, Against Heresies 2 .14.9. 1 2 Irenaeus may be inferring from Valentinian appeals to the zodiac a more general appeal to the gods of mythology. Or Irenaeus may be depending upon (now lost) Valentinian texts that argue that even the pagans were able to recognize the truth of the Dodecad, albeit imperfectly.

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145 Although ridicule and insult is standard in his polemic, these are rhetorical decorations to his main arguments. Using counterexamples drawn from Scripture, history, and the natural world to demonstrate his opponents' inconsistency or incompleteness, Irenaeus argues directly and forcefully about substantive theological issues. His insistence that the Valentinians have not correctly counted the number of aeons in the Pleroma is the first of his four main arguments against the number symbolism in Valentinian theology. To make this point, he defends two claims. First, by their own reckoning, their Pleroma has less than thirty aeons. Second, the Pleroma ought to have more than thirty aeons. In each case, the Valentinian school is shown incapable of responsibly handling the numbers they so esteem in their theology. In the first of these arguments, that there are really less than thirty aeons, Irenaeus first focuses on the role of the Forefather.13 If he is the source of the various projections, he ought not be counted with them, since you should not group one who emits, who is unbegotten, who is neither circumscribed nor given form, with one who is emitted, begotten, circumscribed, or formed. Likewise, the Forefather should not be grouped with Wisdom, since this is to group together errant and inerrant aeons. And what about Silence (Thought), Depth's consort?14 Can anyone's Silence and Thought be separated from them? Indeed, does not the very notion of conjugal unity forbid any idea of separation? If so, then Thought is in every way similar to Depth; they share a single existence. This applies as well to the other conjugal pairs. Mind and Truth, who always inhere one another, cannot be separated, just as water and moisture, fire and heat, and stone and hardness cannot be 1 3 Ibid. 1 .12.1. 1 4 Ibid. 2.12.2.

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146 separated. Likewise, Word and Life, Man and Church, and all the other pairs of aeons cannot be disentangled. It is necessary, after all, for the feminine aeon to be equal to the masculine, "since the former resembles the latter's disposition.''JS Disposition, a Valentinian term, implies metaphysical unity.16 So you should be able to count only syzygies, not aeons. Irenaeus anticipates a response, that the syzygies are in fact divided, so individual aeons can be enumerated apart from their matesP But, Irenaeus charges, this makes absurd their other claim, that the syzygies are unities and that the male and female are one. If the aeons of a given syzygy are separate, then the female gives birth to offspring apart from her mate. If this is the case then she resembles a hen, which hatches eggs without the help of a rooster. Irenaeus's argument here boils down to whether or not the syzygies are real unions or only symbolic ones, and how they are to be counted. The Valentinians' inability to specify whether the syzygies are true unions or only token unions makes it impossible to tell whether they have counted accurately. Further, to count the Forefather and Wisdom together is to suggest they share the same nature, an implication hard to swallow, given Wisdom's fall from the Pleroma. Irenaeus also argues that the Valentinians have more than thirty aeons in their Pleroma.18 They say that four other entities are projected - Limit, Christ, Holy Spirit, and Savior-but they do not include them in the canonical thirty of the Pleroma (see figure 1 ) . Why not, Irenaeus asks. Are they so weak as t o b e unworthy o f the designation? Are they

15 cum sit velut adfectio eius. Here, adfectio probably represents bLa8Emc;. See next note. 16 See SC 293, index, s.v., bLa8unc; and adfectio. To describe the female aeon as the bLa8Emc; of the

male is characteristic of the "more knowledgeable" Ptolemaeans discussed atAgainst Heresies 1 .12.1. 1 7 Irenaeus, Against Heresies 2.12.4. 1s Ibid. 2.12.7, upon which this paragraph is based.

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1 47 superior to the other aeons? It would be absurd to suggest that they are weaker, since they were projected to stabilize and correct the Pleroma. But it would be equally absurd to suggest they are better than the primal Tetrad. So, if they are neither weaker than the weakest aeons in the Pleroma, nor better than the best, then they should either be numbered with the Pleroma, or the honor associated with such a name (Pleroma means fullness) should be removed from the other aeons since, obviously, the Pleroma does not include the fullness of the aeons. Elsewhere Irenaeus claims that the Valentinians were at odds as to the number of aeons in the Pleroma. Some held to thirty, and others, an innumerable amount.19 Yet others had more simple systems, of less than thirty aeons.20 We have encountered in the Valentinian First Apocalypse of James a world of seventy-two heavens.21 Outside Valentinianism, the variations grew. For instance, Basilides taught 365 aeons_22

Irenaeus' s second line of attack calls Marcus to account for his misuse of human conventions of numeration. He ridicules the notion that the Word the Father uttered consists of thirty letters and four syllablesP If this were so, then the Father, whose image the Word bears, should also consist of thirty letters and four syllables. Indeed, is this really the final arrangement? Marcus bottles up the Creator in various numbers and patterns, at one time thirty, at another, twenty-four, at another, merely six. Even the technique Marcus uses

1 9 Ibid. 1 .1 0.3. 20 Ibid. 1 . 11-12. See also above, chap. 1 . 21 See above, p. 62. 22 lrenaeus, Against Heresies 1 .24.3-7, 2.35.1 . 23 Ibid . 1 .15.5.

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1 48 to calculate alphabetic numbers is inconsistent, since at one time he computes a name's psephic value, at another time, the number of letters in the word.Z4 Jesus, Irenaeus points out, is not a Greek name, yet Marcus nevertheless makes its Greek transliteration the center of his theology. Sometimes he calls it the episemon because it has six letters, and sometimes the fullness of the Ogdoad, since the psephic value of 'IT}aouc; is 888. That Marcus would apply Greek conventions of numeration to a non-Greek name for deeper theological meaning, but ignore the numbers latent in a Greek name like I:w'ri]Q (Savior) is duplicitous. Marcus claims that the Father providentially named the Lord Jesus so as to indicate, whether through psephy or the number of letters, the numbers in the Pleroma. But even if this were true, he doesn't do this with the Lord's other names and titles, such as L:w'ri]Q. And no wonder, since neither the psephic value, 1408, nor the number of letters, five, are related to the numbers or patterns in the Pleroma. So too the psephic value of XQE LCY'r6c; (1485) has no arithmetical connection with the Pleroma Christ allegedly stabilizes and corrects.25 The same applies to Tia'ri]Q, Bu8oc;, MovoyEvi]c;, and other Greek names of aeons in the Pleroma. These inconsistencies, applying Greek linguistic conventions to Hebrew names and not applying the same method to the more important Greek names, Irenaeus argues, proves that their system is false.26 Irenaeus argues that the system does not square with the history of the alphabet. He notes, the Greeks agree that only recently - recently, that is, relative to the creation of the world -Cadmus introduced the first sixteen lettersP Some time after, other Greeks invented 24 Ibid. 2.24.1. 2s Ibid . 2.24.2. 26 Ibid. 2.24.1, repeated at 2.24.2. 27 Ibid. 1 .15.4.

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149 the aspirates and the double letters. Palamedes provided the long vowels, the final step of the alphabet's evolution. Thus, Irenaeus argues, how could Marcus's Truth exist before the Greeks, seeing that her body had to postdate Cadmus and anyone prior to him? Indeed, Truth postdates "even yourself [Marcus}, for you alone have dragged down your so-called

Truth as an idol."28 Irenaeus's version of a universally known history of the alphabet is flawed in its details - the specifics about who invented the Greek alphabet, and when, vary from one ancient author to the next-but his overall point, that the Greek alphabet had an origin at a specific moment in time, is correct, both by his generation's understanding of the history of the alphabet and by modem scholars.29 Irenaeus charges Marcus with failing to abide by the conventions appropriate to a given language.30 Jesus, a Hebrew name, properly consists of two and a half letters, a claim Irenaeus justifies by appealing to Jewish experts, who take each of the letters in :llitr (instead of the Biblical !1\U1;-P) as an acronym for "Lord, heaven, earth." (Here the yod seems to be counted as the half letter.) Thus, just as L:w'fi]Q exposes the inconsistency of their system, so too does Jesus's Hebrew name. Its mere two and a half letters show that Jesus cannot be considered the episemon. The interpretation of Jesus as 888 too cannot be sustained in the context of the name's original language. Hebrew letters don't match Greek letters, and because the former are older and more stable than the latter, any calculation of names

2s Ibid. 29 See Pliny the Elder, Natural History 7.192; Tacitus, Annales 1 1 .14; and many others cited at Forster, Marcus Magus, 238-42 and Teodorsson, Commentary on Plutarch's Table Talks 3:318. Irenaeus's report resembles that of Plutarch, Table Talk 9.3 (738F), discussed below, p. 256. For modern attempts to reconstruct the history of the Greek alphabet, see OCD, s.v., "Alphabet, Greek." 3D

Against Heresies 2.24.2.

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150 should be preserved in the older. But even then, the very structure of the Hebrew alphabet precludes any kind of psephy.31 Baruch, the name Jews give to the most high God, has only two and a half letters, and has no relevance to the Pleroma.

According to the Valentinians, the Demiurge fashioned the natural world as an image of the unseen Pleroma.32 This proposition leads to Irenaeus' s third argument against the Valentinians, that the numbers in their system do not correspond to what we know of the natural world. Irenaeus pursues this attack numerous times, in every case criticizing as illogical the notion that an errant being, the Demiurge, could create an errant world as a true reflection of an inerrant Pleroma.33 He anticipates a possible response, that the natural world is the image of the Pleroma, not in figure or form, but in number and rank.34 Irenaeus responds that not even this is true, since the Valentinians tend to tinker with their numbers and their aeons so as to make them fit certain numbers in creation. But suppose that they have managed to make some associations with the natural world. How can they claim on this basis that a mere thirty aeons are the antitype for the vast number of things in the

31

This is my interpretation of ibid. 2.24.2.40-46, a convoluted passage poorly preserved in the Latin. As we have it the text states that Hebrew has ten letters, each written "through fifteen, the more recent letters joined with the first." The text also seems to appeal to the directions of writing, from right to left. The earlier part of 2.24.2 deals with two numerical practices with names: the number of letters in a word, and its psephic value. Irenaeus dispenses with the first notion by highlighting the peculiar way (he says) letters are counted in Hebrew. This incomprehensible and unparalleled explanation of the structure of the Hebrew alphabet must then refute Marcus's claims based on Greek psephy. 32 Treated passim in Irenaeus, Against Heresies 1 . See above, pp. 22-23 and 31-32. 33 Irenaeus, Against Heresies 2.7.1-6. 34 Ibid. 2.7.7.

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151 m aterial world? The vast numerical complexity of the created world cannot be explained merely by a group of thirty entities. The world is no image of the Pleroma. Further in book two, Irenaeus extends this argument.35 The Valentinians claim the thirty aeons were not made for creation but vice versa. That is, the creation is the image of the thirty aeons, not the other way around . According to their reasoning, the month has thirty days because of the thirty aeons. So too, the day has twelve hours and the year, twelve months, because of the Dodecad. The reasoning is arbitrary and incomplete, Irenaeus says, since they do not explain why Man and Church had to project twelve, no more and no less. They also do not explain why an Ogdoad, and not, say, a Pentad, Trinity, or Heptad, is the core of the Pleroma. If the year is an image of the Dodecad, and the month, of the Pleroma, then what important occurrence of the number eight in nature is an image of the Ogdoad? Irenaeus accuses the Valentinians of using analogies that invert the order of nature.36 Each aeon is supposed to be one thirtieth of the Pleroma, but a month is one twelfth of a year. If the divisions of time really reflected those of the Pleroma, wouldn't it have been more appropriate for the year to be divided into thirty months and each month divided into twelve days? Irenaeus chides, the Savior must have been an idiot to have made the month an image of the Pleroma and the year, the more important division of time, of the Dodecad, a less important subset of the Pleroma. And the analogy does not account for the realities of the calendar. Not every month has precisely thirty days, just as not all days have twelve hours, depending upon the season of the year. Thus, neither can the day be a true image of the Dodecad, nor the month, of the Pleroma. And why do they group the Pleroma into 3s Ibid. 2.15.1.

36 Ibid. 2.24.5.

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1 52 Ogdoad, Decad, and Dodecad and no other arrangement?-'7 Why three divisions, and not four, five, six, or some other number more commonly found in creation? After all, the year is divided into four seasons.38 Were the year truly an image of the Pleroma, it would have had four major divisions, not three. Whenever they are cross-examined about the Pleroma, Irenaeus says, they retreat to explanations about human dispositions and to discourses about creation.39 But this is to focus on secondary rather than primary matters, since the issue at hand is not harmony in creation or human dispositions, but the Pleroma, of which creation is an image. If the Pleroma is trisected into Ogdoad, Decad, and Dodecad, then they must admit the Father arranged the Pleroma in vain and without providence, since its structure did not correctly anticipate the structures of the natural world. If so, then the Father acted irrationally and, like the Demiurge, made a deformity. In other words, given their analogy between the Pleroma and creation, they must admit that the Forefather is just as inept as they say the creator of the natural world is. But if they do not want to go that route, and they want to uphold the providence of the Forefather, then they must say that the Pleroma was projected so as to provide a template for creation. But in this case, although the h armony of the cosmos is preserved, the Pleroma exists not for itself but for that which should have been its image. The Pleroma is then inferior to creation, as if it were a clay model, made only so as to build a gold, silver, or brass statue. In sum, if the Pleroma is a template for creation, then the Father created something inferior to what the Demiurge created.

37 Back to Ibid. 2.15.2.

38 Ibid. 2.24.5. 39 Ibid. 2.15.3.

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153 If they don't agree that the Pleroma was made for creation, then they must postulate a higher reason or cause for the projection of the Pleroma.40 But this is to postulate a system more spiritual and more powerful than the Pleroma. In this scenario Depth uses a higher pattern to shape and arrange the Pleroma. A vicious regression begins, since you must ask why this Superpleroma was made. The same line of questioning can lead to super­ Superpleromas, and so on. Irenaeus argues, you must either accept one God, who made the world, taking the pattern for the creation from his own power and his own self, or move the slightest bit away and end up always asking and seeking out how and from what source the highest being patterned his creation, upon what he styled the number of projections, and from where he derived the substance that was used. If they try to argue that Depth perfected the design of the Pleroma from himself, then it should be allowed that possibly the Demiurge too patterned the world, not from the Pleroma, but from himself. But if they insist that creation is an image of the Pleroma, then what is to bar the Pleroma itself from being an image, and so descend into an endless regress of images of images? Throughout his argument, Irenaeus has Valentinian number symbolism in mind. Numerical patterns and structures are central to their theology, and they must be used to test their claims that there are innate, direct connections between creation and the Pleroma. That there are differences in the natural patterns and the divine raises questions. Why those numbers in particular? Where did the numbers come from? Are they intrinsic to the highest reality, or merely accidental parts? Irenaeus argues that the heretics make number external to the deity, which is why they always try to trump each others' numerical systems.

40 Ibid. 2.16.1 .

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154 Basilides claimed 365 heavens, over whom the Power called Ineffable and his dispensation govern.41 Irenaeus says and that this large number was a direct response to inadequacies in the Valentinian Pleroma. But Basilides cannot escape this problem, either. He says that Ineffable got the pattern for emanating the heavens from his dispensation. But where did that dispensation come from? Ineffable had to have created the dispensation either from himself, or from a yet higher power. If the former, then one might as well abandon the entire theological complex of aeons for simply the one God, who created the one world from a numerical pattern of his own design.42 If the latter, then the endless regress resumes. Irenaeus mocks the ever-more complicated systems of his opponents.43 Just as the Valentinians accused less-spiritual Christians such as Irenaeus of remaining in the Hebdomad, so the Basilideans could accuse the Valentinians of remaining at the level of the Triacontad, and not ascending to the forty-five ogdoads, then the 365 heavens. But this too, Irenaeus says, could be trumped by inventing a system of heavens or aeons numbering 4380, the number of daytime hours in a year, and then, by including the nighttime hours, an even greater number. This endless one-upmanship means that the Valentinians and B asilideans must always remain in an intermediate state since they will always be unable to rise to the highest conception of the number of heavens or aeons. The creation of a new level above our world is an invitation to descend into endless levels of worlds.44 Irenaeus returns to this theme in the fourth book, where he advises that anyone who seeks after a Father beyond the one Father of the Scriptures will need to seek a third, fourth, 4 1 Ibid. 2.16.2.

42 Ibid. 2.16.3. 43 Ibid. 2.16.4.

44 Ibid. 2.35.1.

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1 55 and so on.45 Such a person will never rest in one God, but will drown in a Depth without Limits, until repentance brings him back to the place from which he was cast out, the one God. In his admonition, Irenaeus symbolizes the one God with the garden of Eden, the place of single simplicity. To develop other gods or aeons is to begin a bottomless journey into a pit of multiplicity, a transience ended only by returning to the garden of God's unity.

In his fourth line of argumentation Irenaeus deals with the numerous specimens of Valentinian exegesis of numbers in the Bible presented in book one (see chapter 1). Throughout books one and two he attacks their hermeneutical principles as being arbitrary and inconsistent. According to the Valentinians, the prologue of the Gospel of John justifies the names and sequence of the aeons of the Ogdoad.46 Irenaeus answers, John introduces the terms in a sequence quite different from theirs. If the structure of their Pleroma is so important, surely John would have preserved this sequence, and even preserved the conjugal unions, and mentioned every aeon's name specifically (Church, Man's consort, is never explicitly mentioned in John 1). To the notion that Judas represents Wisdom, the fallen twelfth aeon, Irenaeus responds:47 Judas was indeed expelled, but never reinstated, as Wisdom allegedly was. Since Matthias took Judas's place (Acts 1 .20), their myth ought follow the same outline and have another aeon projected to replace Wisdom. Furthermore, they say Wisdom suffered, but

45 Ibid. 4.9.3. 46 Ibid. 1 .9.1 . See above, p. 33. 47 Against Heresies 2.20.2. See above, p. 35.

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156 then they themselves admit that Jesus, not Judas, suffered. How can an unsuffering traitor be the image of a suffering aeon? After mentioning other dissimilarities between Judas and Wisdom, Irenaeus calls the Valentinians to account for their miscounting.48 True, Judas is the twelfth, but they teach that Wisdom was the thirtieth. Even if you accept the Judas-Wisdom connection, other problems in enumeration occur.49 They say that Judas's death represents the Inclination of Wisdom. But in their myth, Inclination returns to the Pleroma, unlike Judas, who is never reinstated to be with the apostles. If Judas represents the Passion of Inclination, then they invoke a third, distinct aeon, and their analogy completely dissolves, since under the best interpretation of what they mean to say, there are two biblical figures, Judas and Matthias, who are somehow supposed to stand in for three aeons, Passion, Inclination, and Wisdom. Two does not equal three. Moreover, if the Valentinians want the twelve apostles to represent Man and Church's projected twelve aeons, to be consistent they should produce ten more apostles to represent the other Decad of aeons, emitted by Word and Life.50 It is unreasonable that the Savior signified the youngest aeons but overlooked the elder ten. The same applies to the Ogdoad, which ought to have been numerically signified by the election of eight apostles. Indeed, their system can make nothing of the seventy other apostles the Lord sent after he commissioned the twelve, since seventy prefigures neither an Ogdoad nor a group of thirty. If their reasoning is correct, that the election of the twelve apostles signifies the twelve

48 Against Heresies 2 .20.4. 49 Ibid. 2.20.5. so Ibid. 2.21 . 1 .

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157 aeons, then they must hold that the seventy apostles were chosen because of seventy aeons. If this is the case, then we have eighty-two aeons, far beyond the canonical thirty. The Valentinians claim the woman with the twelve-year flow of blood to symbolize the restoration of Wisdom.51 Irenaeus argues that the story is inconsistent with their system, which holds that eleven of the twelve aeons in the Dodecad were impassible, and that only the twelfth suffered.52 But the woman who was healed experienced the opposite. She suffered for eleven years and was healed in the twelfth. Irenaeus admits, a type or image differs from the truth it represents according to the material and underlying substance, but the type must nevertheless preserve the form and outline of the truth. A type should make evident by its presence that which is not present. (Recall Irenaeus' s analogy, of the relationship between a clay model and the gold statue upon which it is made.53 Both objects have a different material cause, but nevertheless share an identical form.) Furthermore, the Valentinians do not apply this exegetical principle consistently. What do they do with the woman who suffered for eighteen years '?54 If one woman is a type of the aeons, then the other should be, too. The same goes for the man who was healed after being sick for thirtyeight years.55 Since these two examples have no bearing on their system, then neither should the woman healed from her twelve-year illness.

51 Ibid . 1 .3.3. See above, p. 35. 52

lrenaeus, Against Heresies 2.23.1 . 53 Ibid. 2.15.2, discussed above, p. 152. 54 Lk 13.6; lrenaeus, Against Heresies 2.23.2. 55 Jn 5.5.

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158 To the Valentinian appeal to the numbers in the Mosaic Law as symbols of the Pleroma, Irenaeus offers numerous counterexamples.56 According to their system, the dimensions of the ark of the covenant ought to be especially congruent with the Pleroma. But its dimensions are two and a half by one and a half by one and a half cubits, numbers that fit in no way their theology. The same thing applies to the mercy seat (two and a half by one and a half cubits) and the table of the showbread (two by one by one and a half cubits). All these vessels are in the holy of holies, whose numerical dimensions prefigure neither the Ogdoad nor the Pleroma. The seven-branch candelabra fits nowhere in their scheme; if it were meant to be a type then it ought to have been made with eight lights, not seven, to typify the primal Ogdoad.57 They appeal to the ten curtains as a type of the ten aeons, but they neglect the skin coverings, eleven in total, and the length of the curtains, twenty-eight cubits.58 Although they say the ten-cubit length of the columns typifies the Decad of aeons, they cannot explain their one-and-a-half-cubit width.59 Furthermore, they cannot account for the oil, which consists of five hundred shekels of myrrh; five hundred, of cassia; two hundred fifty, of cinnamon; and two hundred fifty, of calamus. These four ingredients plus the oil make five, a number that doesn't fit their scheme. It is absurd that the most sublime parts of the Law have no types in their system, yet they obsess over any other number, no matter how insignificant, that matches their Pleroma. All numbers occur throughout Scripture in different ways, such that anyone could derive not only an Ogdoad, Decad, and Dodecad, but whatever number one might like. 56

Irenaeus, Against Heresies 2 .24.3.

57 Ex 25.31-37. 58 Ex 26.1, 7, 2 . 59 E x 26.16.

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159 Irenaeus argues that their application of finger calculation and psephy is inconsistent.60 To say that the Savior came to gather the hundredth lost sheep and to transfer to the right hand the ninety-nine that are on the left does not mesh with their own analogy. According to them, anything on the left belongs to corruption, in which case it is not the hundredth but the ninety-nine who are lost, since they are the ones who exist on the left hand. Furthermore, since the psephic value of ayim:11 (love) is ninety-three, it too must reside on the left side, as must aAr'J8 na (truth), which is sixty-four, and anything else adding to less than one hundred. Marcus's dichotomy resembles techniques in secondcentury dream interpretation, which treated one hundred as an auspicious number.61 To emphasize that Valentinian exegesis has missed the dominant numbers in Scripture, Irenaeus mockingly presents the wonders of five, a number that fits nowhere in the structures of Valentinian theology.62 Five is used repeatedly in Scripture. I:wn'JQ, Tian'JQ, and ayan11 all have five letters. The Lord, blessing the five loaves, feeds the five thousand . There are five wise virgins and five foolish. There are five men with the Lord a t the Transfiguration. The Lord is the fifth of those who entered the house of the ruler whose daughter was ill.63 The rich man in the infernal regions says he has five brothers.64 The pool at Bethzatha has five porticoes.65 The cross consists of five parts: the four arms and the

60

Ibid. 2.24.6. See above, pp. 66 and 97.

61 Artemidorus, Dream Book 2.70, 3.34, says that numbers should be reduced to 1 00 to be suitable for

interpretation, and that the number 1 00 is especially auspicious. The ideas resemble Marcus's but the differences are greater: Artemidorus does not treat numbers less that 100 as unlucky. See below, p. 377. 62 Irenaeus, Against Heresies 2 .24.4. 63 Lk 8.51 . 64 Lk 16.19-31 . 65 J n 5.2.

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1 60

center. Every hand has five fingers (note how Irenaeus's proofs have moved from the Bible to the natural world) and there are five senses and five internal organs: heart, liver, lungs, spleen, and kidneys. There are five divisions in the body and five phases in human life.66 Moses gave the Law in five books (note now Irenaeus's tum to the Old Testament, sarcastically imitating the Valentinians)67 and each tablet contained five laws. Five priests were elected in the desert- Aaron, Nadab, Abiud, Eleazar, and Ithamar - and the ephod and breastplate were made of five materials - gold, hyacinth, porphyry, scarlet, and fine linen. Joshua surrounded five kings of the Amorites. The list could go on, Irenaeus notes, with examples collected from Scriptures and the works of nature. Nevertheless, this vast array of fives is no basis for claiming a divine group of five aeons. Irenaeus sarcastically uses their own exegetical technique against them. In the Scriptures, an exorcized spirit of ignorance finds those who were formerly possessed "striving not after God but after cosmic inquiries, and brings along seven other spirits more wicked than himself."68 One spirit plus seven others makes eight. Ergo, a demon has left the Valentinians but returned and found them ready to be inhabited, and so has taken along "seven other spirits, thus constituting their Ogdoad of spirits of wickedness." Their 66 lrenaeus's list, infancy, childhood, youth, adulthood, and old age, falls short of Solon's (frag. 1 9 Diehl) and Hippocrates' (On Hebdomads 5 ) more famous model, o f seven phases in human life. But cf. Theon of Smyrna, Mathematics Useful for Reading Plato 98.1 3-14, which divides human life into four, a tetraktys (see excursus B3). 67 Here, in Against Heresies 2.24.4, Irenaeus proves the excellence of the number five from three sources: the New Testament, the natural world, and the Old Testament. This mirrors the order and sequence of the Valentinian exegesis Irenaeus presents in book one, where the New Testament proof texts for the Pleroma are at chaps. 1-3 and 8, natural world proofs are at chap. 1 7, and Old Testament proof texts, at chap. 1 8. This is evidence, both of the sequence of the argument of lrenaeus' s source, and of the basic integrity of the authorship and sequence of Against Heresies 1 .1-22.2. See excursus E. 68 Mt 12.43. Irenaeus, Against Heresies 1 .16.3.

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1 61 arrogance is so great that, in enumerating seven heavens, they presume to have surpassed the apostle Paul, who ascended only to the third heaven, four short of the highest level.69 The Valentinians contravene not just Scripture but other parts of the rule of faith. Referring to a creedal-like recitation common in the churches, Irenaeus notes that the Valentinians " confess with the tongue one God the Father," Creator of all things?0 Yet they offend the Church's tradition by maligning the Creator. They similarly "confess with the tongue one Lord Jesus Christ, the Son of God" - once again invoking the liturgical tradition - yet they split up the titles of Christ into assorted independent projections. Thus, they pay mere lip service to their confession in church of the unity of God and his Son, and in reality they have fallen away from the unity of God .

All four lines of argumentation boil down to charges of incompleteness, inconsistency, and arbitrary methods. It is impossible to evaluate the accuracy of Irenaeus's critique. True, he defeats the system as he presents it. But we do not know how Valentinians might have responded to these charges, to know if Irenaeus was treating them fairly. Although we cannot broker the dispute, we can see if Irenaeus lived by his own principles.

IRENAEUS'S ALTERNATIVE As vigorous as Irenaeus's reaction is, Valentinianism does not define his theology. On occasion he becomes so engrossed in presenting the orthodox vision of God that his original heresiological interests fade into the background, or they become pretexts for other 69 2 Cor 12.2; Irenaeus, Against Heresies 2.30.7. 70 Irenaeus, Against Heresies 4.33.3.

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1 62 theological topics that interest him. Books four and five are full of discourses that transcend his immediate concern with Marcion and other heretics. In those places Irenaeus draws from many earlier Christian texts, most of them unacknowledged?1 Even though Against

Heresies is the earliest treatise of its kind we have, its numerous references to and citations of earlier Christian authors, including heresiologists, shows that it was part of a welldeveloped theological tradition. Irenaeus' s musings on numbers in theology is part of this tradition. He sees an operative rule at work in the churches, governing the appropriate role of numbers in theology. This rule allows for number symbolism in theology, but requires that it be anchored in the unity of God the Father and his Son, and that it respect the orthodox interpretation of Scripture. Irenaeus first alludes to the number symbolism permitted by the rule of truth in book one.72 He accuses the Valentinians of behaving like those who create bizarre centos of Homer, where assorted lines drawn from multiple places in the Iliad and Odyssey are stitched together in order to tell a story unrelated to the main narrative of the poetry. Irenaeus provides an example, a cento about Hercules that consists of ten lines taken from various places in the two epics. The practice, Irenaeus says, resembles someone who encounters a skillfully made mosaic of a king and rearranges it to resemble a dog?3 Anyone experienced with Homer's plot will know that the proper way to understand each line of

71 See, e.g., excursus E, on Irenaeus's use of an unnamed heresiologist for the catalogue of heretics in

book one. Some of Irenaeus's other unnamed sources are discussed at Forster, Marcus Magus, 1 3-15, 22-26 and Hill, Lost Teaching. 72 1 .9.4. 73 Ibid. 1 .8.1, 1 .9.4.

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1 63 Homer is in context, in the narrative from which it is drawn?4 In the same way, anyone who preserves unchanged within himself the canon of truth assumed in baptism will recognize the names, terms, and parables of Scripture, and that the Valentinian version does not match this canon of truth. Irenaeus applies this canon of truth, a critical component in his theology, to Valentinian number symbolism in book two?5 There he considers an important response to his criticism of Valentinian exegesis of numbers in the Bible: Are the placement of names, the election of apostles, and the acts of the Lord and his deeds recorded for no reason whatsoever? Irenaeus replies, Not at all. Rather, everything God does -whether ancient or anything accomplished by his Word in recent times- is harmonized and well ordered with abundant wisdom and precision. And these things should be yoked, not with the number thirty, but with the underlying narrative of truth. And they should not undertake an investigation about God on the basis of numbers, syllables, and letters. (For this is unsound because of their multifaceted and variegated nature, and because any narrative - even one that someone cooks up today - can gather out of the same [numbers, syllables, and letters] proof texts contrary to the truth, in that they can be manipulated to many ends.) Rather, they should fit to the underlying narrative of truth the numbers themselves and the things that have been done. For the rule does not come from numbers, but numbers, from the rule (non enim regula ex numeris, sed numeri ex regula). Neither does God come from creation, but that which is made, from God . For everything is from one and the same God?6+ 74 Ibid. 1 .9.4. See also Unger and Dillon, St. lrenaeus of Lyons, 1 82 n. 22. 75 Unger and Dillon, St. lrenaeus of Lyons, 1 82 n. 23. 76 Against Heresies 2.25 . 1 : Non quidem, sed cum magna sapientia et diligentia ad liquidum apta et

ornata omnia a Deo facta sunt, et antiqua et quaecumque in novissimis temporibus Verbum eius operatum est. Et debent ea, non numero XXX, sed subiacenti copulare argumento sive rationi, neque de Deo inquisitionem ex numeris et syllabis et litteris accipere- infirmum est enim hoc propter multifarium et varium eorum, et quod possit omne argumentum hodieque commentatum ab aliquo contraria veritati ex ipsis sumere testimonia, eo quod in multa transferri possint- sed ipsos numeros et ea quae facta sunt aptare debent subiacenti veritatis argumento. Non enim regula ex numeris, sed numeri ex regula, neque Deus ex factis, sed ea quae facta sunt ex Deo: omnia enim ex uno et eodem Deo. Rousseau and Doutreleau' s reconstruction of the Greek, with my own conjectures in angle brackets: Ov 1-lTJV aMa !-lETa !-1EYLXAT)c; aocj:>[ac; KC
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1 64

No other passage is as important for understanding Irenaeus's theology of arithmetic. He claims here that numbers, syllables, and letters are composite and that they have many different qualities. Such a claim was contestable. For by the very name given to them, O'TOLXELa, "elements," letters were considered de facto to have no parts. Being elements, letters were the building blocks of the linguistic universe. Numbers, too, shared in this simplicity. So Irenaeus's suggestion, that numbers and letters have multiple parts and qualities, suggests that both categories can be further analyzed, reduced to yet other, more fundamental, categories. Irenaeus reduces them to terms derived from the narrative of truth, the rule of faith. Irenaeus's first critique here, then, is that the Valentinians have not appropriately understood what an element is, that is, what is neither compounded nor subject to change. Numbers and letters are not elements in the true sense of the word. The second critique is that anyone can dream up a narrative and find witnesses in the world of numbers and letters to corroborate them. That is, numbers and letters lend

U/10 'TOU E>mu iyivE'To, 'Ta 'TE CxQXlXLlX KiXL n'x oaa EV iaxa'TOLc; KalQOLc; 6A6yoc; iXlJ'TOU b1QaE,EV" ocpdAoucn bE avn'x flTJ 'TcfJ CxQL8fl0 'TWV 'TQlcXXOV'TiX <'TctJ 'TQliXKOVTabt?>, ixAAa 'TlJ U 710KElf1EV1J auvan'TELV uno8[aEL 'Tijc; ixATJ8 E iac;, flT)bE 71EQL 'TOU 8mu C,r'J'TTJaLV [E, CxQL8 f1WV KiXL avAAa�wv Kai YQUflflliTwv avabixEa8m- aa8Evic; yaQ mum bta To noAvflEQEc; Kai noAUI10LKlAov atJTWV KiXL 'TO bvvaa8m miaav un68EatV KiXL aTJflEQOV TrlXQEnLVOOVflEVT)V uno nvoc; avaAr'J8nc; EE, iXlJ'TWV Aafl�UVE LV fliXQ'TUQLac; thE E ic; noAAa flE8lXQflOC,wem bvVlXflEVWV- ixAA ' lXV'TOVc; muc; iXQL8flOUc; KiXL 'TcX YEYOVO'Ta icpiXQflO(.E LV ocpd Aoum 'TlJ U710KElf1EVlJ Tijc; MTJ8dac; vnoeiaEL. Ov yaQ un68wtc; f_E, CxQL8f1WV, ixAA ' CxQL8f10l iE, vno e EaEwc;, ovbE: E>n)c; EK YEYOVO'TWV, aMa YEYOVO'TiX EK E>mu· TraVTa yaQ E_E, [voc; KiXL 'TOU iXU'TOU E>mu. For my first conjecture, see 1 .1 6.1 . 1 1, where XXX numerus is a redundant translation of r'J TQLiXKOVTac;. There is no "number of the thirty" in Valentinian theology, but rather a Triacontad, within which are many numbers. On my second conjecture, see 1 .1 0.3.1 157. The sexual connotation ofcopulare, alluding to the Valentinian syzygies, suggests a word stronger than avvan'TELV. What I translate as "narrative," un68Emc;, can be translated "plot," "argument," or "doctrinal system" equally well. Irenaeus uses the same word frequently at 1 .9.4 to describe the narrative structures of the Iliad and Odyssey, and to this discussion he no doubt alludes here, at 2.25.1 . See Rousseau and Doutreleau 2.1 (SC 293): 296-99.

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1 65

themselves to arbitrary justifications. Note that Irenaeus here accuses the Valentinians of an arbitrary set of witnesses, drawn, not from Scripture (although he does accuse them of this more specific charge elsewhere throughout books one and two), but rather from numbers and letters. That is, Irenaeus portrays numbers and letters (and not the Bible) as the Valentinians' fund from which they pull examples seemingly to justify their narrative. The examples may be instantiated as Scriptures or observations of the natural world, but nevertheless these examples, Irenaeus contends, are drawn from preconceived arithmetical ideas. Irenaeus answers V alentinian number symbolism with his own, alternative principle. A narrative should not take shape from numbers, but vice versa. His analogy is God and creation. The latter comes from the former, not the other way around?? Thus, God is to creation as the narrative of truth is to numbers. Just as all things come from one and the same God, so numbers - or at least their proper, intended use - emerge from the underlying narrative of truth, the canon of faith borne by the Church.

Irenaeus' s doctrine of God is based on this principle. The only number symbolism he applies to God is that of the number one, and he points whenever possible to the Bible. He says, "John preached one God Almighty and one Only Begotten Jesus Christ," in direct opposition to Valentinian interpretations of the same Gospel?8 Paul's phrase, "one God the Father" (Ephesians 4.6), is evidence of the Church's belief in only one God?9 The tradition of

77 The extended argument is at Against Heresies 2.15-16. 78 Ibid. 1 .9.2. Cf. Proof of the Apostolic Preaching 5. 79 Irenaeus, Against Heresies 2 .2.6.

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1 66 belief in one God has existed throughout history, from the protoplast Adam, through the prophets, to the age of the universal Church.80 That Church, he says, received a common faith in one God the Father almighty and one Jesus Christ, the Son of God.81 Elsewhere throughout the Against Heresies Irenaeus frequently insists on the unity of God.82 The unity of God spills over into the rest of the tradition. As a reflection of the one God, the Church, though dispersed, dwells as if in one house, possesses one soul, and proclaims with one mouth. The Church's tradition has a single power, and her faith is one and the same.83 Although Irenaeus roots his doctrine of the oneness of God in the rule of faith, the mathematical expressions he uses reflect his concern with Valentinianism. His insistence on there being but one Father responds to claims that there are two; his proclamation of only one Son counters the claims that there are multiple beings who bear names and titles ordinarily given only to Jesus Christ. But Irenaeus is silent about the unity of the Holy Spirit. In book one, he presses home "faith in one God the Father Almighty . . . and in one Jesus Christ the Son of God . . . and in the Holy Spirit." The Valentinians had challenged only the numerical integrity of the Father and the Son, so Irenaeus says nothing of the number of the Holy Spirit. In light of Irenaeus' s fight with the Valentinians, the lack of a confession of belief in "one Holy Spirit" in the Nicene-Constantinopolitan Creed is more intelligible. Irenaeus' s concern with Valentinian arithmetical theology is evident, too, in that he never uses 'rQLac; ("trinity") to describe the relationship among the Father, Son, and Holy

8o

Ibid. 2.9.1. Ibid. 1 .10.1, Irenaeus's adaptation of an early creedal statement shared by the churches. Its outline is evident in the Nicene-Constantinopolitan Creed . 82 See, e.g., ibid. 2.1.1, 2.11 .1, 2.16.3, 4.38.3. 83 Ibid. 1 .1 0.2, 3. 81

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1 67 Spirit. He clearly teaches that all three are the one God, but he shies away from the term, even though it was in use in his day.84 To some readers, Irenaeus's omission of the term confirms the slow, late development of the doctrine of the Trinity. But this is to ignore that for Irenaeus 'rQLLXc;; was too likely to have Pythagorean overtones. Irenaeus claims that Valentinianism's emphasis upon arithmetical terms such as Dyad and Tetrad to describe the Pleroma makes arithmetic its determinant factor. That is, it sets the creation over the creator. To describe the persons as a Trinity might make the godhead look Valentinian, as if the Father, Son, and Spirit were subject to mathematical abstractions.

As a corollary to his general principle, that numbers should emerge from the tradition, and not vice versa, Irenaeus claims, "And therefore parables ought to be harmonized with unambiguous things."85 That is, the more veiled, opaque passages of Scripture should not be used to decipher the parables. Not to heed this principle is to risk justifying any doctrinal system one likes. The passages that are clearest should be the interpretive key to the more obscure. He concedes that there may be Scriptures we don't understand, but this is to be expected, since there are also many things in the natural world we do not understand.86 A difficulty in Scripture is no reason to invent other gods. Just as a proper understanding of numbers should emerge from the narrative of truth, so too should a proper understanding of obscure passages emerge from the clear.

84 Theophilus of Antioch, To Autolycus 2.15, dated to just after 1 80. See also, e.g., Irenaeus, Against Heresies 4.38.3; Proof of the Apostolic Preaching 4-8. ss Against Heresies 2.27.1. 86

Ibid. 2.28.2-3.

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1 68 These two principles are at work in the several places where Irenaeus interprets numbers in the Scriptures. How do his principles justify his interpretation? In Isaiah 1 1 .2-3 there are seven virtues that come upon the Messiah: wisdom, understanding, counsel, might, knowledge, piety, and the fear of the SpiritP Irenaeus takes these characteristics to refer to the seven heavens. It is the model Moses used for the sevenbranched candlestick, in obedience to the command to fashion things as a type of what was revealed to him on the mountain.88 Here Irenaeus interprets not just Isaiah but the natural world. He takes the accepted datum that there are only seven planets, and uses Scripture to explain those planets. His principles are at work, since he is using numbers in the rule of faith to explain the Scriptures and the natural world. According to Irenaeus, Rahab, who welcomed the three men spying out the entire inhabited land, reveals in herself the Father and the Son, with the Holy Spirit; the fall of Jericho indicates the seven last trumpets.89 Thus, the capture of Jericho symbolizes the final age of history, when salvation will belong only to those who embrace in their hearts the three divine persons. Irenaeus' s principles are evident in this interpretation. There are some obscure numbers in the story of Jericho-why are there three spies and seven marches around the city? - and to interpret them, Irenaeus calls upon the rule of faith to find clearer numerical symbols for three and seven.

87 Irenaeus, Proof of the Apostolic Preaching 9. 88 Ex 25.40. 89 Jos 2, 6; Irenaeus, Against Heresies 4.20.12. Note that Jos 6.5 (LXX) speaks of only one trumpet, whereas Irenaeus speaks of seven (and he calls them "final": 1 Cor 15.52), explainable only because to him Jericho foreshadows the end-times trumpets of Rev 8.2, 6.

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1 69 When d iscussing God's command to Gideon to break up the altar of Baal and cut down the Asherah, Irenaeus interprets his taking ten men as a prophecy of Christ.?0 By the number ten, Irenaeus says, Gideon appeared to have Jesus as his help. That is, the number ten is written with an iota, which is Jesus's initial. It is likely that Irenaeus' s Bible had the alphabetic numeral instead of /Jten" in Judges 6.27: KCX L i:Aa�EV [EbEWV L' avbQac;. Although Irenaeus is inconsistent here (see below), he still draws from his two exegetical principles. Ten as a symbol of the name Jesus is an instance of numerus ex regula, since the rule of faith and the fame of the name Jesus associate him with the number ten.91 This clearer, more famous association clarifies this more obscure reference to the number ten. As for the New Testament, Irenaeus interprets the thirty-, sixty-, and hundredfold fruit in the parable of the sower as three levels of reward in the hereafter ?2 The hundredfold represent those who will be taken up into the heavens, the sixtyfold, those spending time in paradise, and the thirtyfold, those inhabiting the city (i.e., the heavenly Jerusalem). To corroborate this interpretation, Irenaeus claims as his authority the elders who were disciples of the apostles. According to them, the rank and pattern of those being saved is to advance by stages, through the Spirit toward the Son, and through the Son toward the Father. Thus, Irenaeus explicit calls upon a well known oral tradition to elucidate a parable whose interpretation is not immediately clear. Note also Irenaeus's reluctance to find any symbolism in the numbers themselves. He is more interested in their structure.

90 Judg 6.27 (LXX Vat, not Alex); Irenaeus, frag. 18 (Harvey). The syntax of much of this passage is unintelligible, despite attestation in 3 mss. 91 See above, pp. 34, 94, and below, pp. 192, 340 n. 37. 92 Mt 13.8; Irenaeus, Against Heresies 5.36.2.

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1 70 Irenaeus reserves his most sustained number symbolism for his eschatological exegesis. An extended part of the end of book five treats numerous passages in Daniel and Revelation, which prominently feature symbolic numbers. Irenaeus suggests that, because one day is as a thousand years to the Lord, so the world must come to an end after six millennia, reflecting the six days in which it was created.93 I have already mentioned how Irenaeus takes the seven marches around Jericho to represent the trumpets of the end of time, another instance of an eschatological number. The greater share of his remarks, however, is preserved for the very contentious issue (both then and now) concerning the interpretation of the number of the beast (Revelation 13.18). He begins by noting that the name of the beast is fittingly 666 since the number shows how he sums up in his person the pervasive spread of wickedness prior to the deluge.94 Noah, after all, was six hundred at the time of the flood (Genesis 7.6). And the beast, the sum of idolatry, is symbolized by Nebuchadnezzar's image, which had a height of sixty cubits and a breadth of six. Six hundred, sixty, and six make 666, QED. This recapitulation, Irenaeus continues, where six reappears in monads, tens, and hundreds, signifies the recapitulation of the apostasy at the beginning, middle, and end of history .95 True to his principles, Irenaeus draws from the Scriptures, choosing verses whose treatment of the number six allows for a broader, moral treatment of Revelation. Note, he does not appeal to the number six as a falling short of the perfection of seven, nor does he suggest the beast's number has anything to do with 888, the psephic value of 'IYJaouc;. The

93 2 Peter 3.8; Irenaeus, Against Heresies 5.28.3. 94 Irenaeus, Against Heresies 5 .29.2. 95 Ibid. 5.30.1.

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1 71 first of these explanations would have been a difficult sell, since six was considered a perfect number, and it had only positive connotations in number symbolism.96 Although Irenaeus recognizes that the number 666 indicates the psephic value of a name in Greek, the second explanation would have veered too close to Marcus's techniques. It also would have only encouraged the kind of speculation he found so exasperating. So Irenaeus opts to avoid psephy altogether, to break the number into three parts, and to interpret these in light of other Scriptures that shed light on the theological and moral significance of the number. Some Christians, probably a sizeable minority, held that the number of the beast was 616.97 Irenaeus criticizes this position, partly because the number disrupts a numerical pattern symbolizing the recapitulation of evil, partly because this reading depends upon textual corruption. Irenaeus says that the number results from a common error, a xi unraveling so as to look like an iota.98 Those who depend upon this reading may search out for a sure and certain interpretation, but in so doing they open themselves up to deception. They are working off a deficient manuscript, they have not consulted the oral tradition of the apostles, and they have ignored the proper, moral significance of 666.99 As for the proper interpretation of the names, Irenaeus pleads for temperance.100 He discusses several possibilities- Euav8ac;, Aa'rEi:voc;, and TEi:1:av - each of whose psephic value adds up to 666. TEt'rav too has the added bonus that it is composed of six letters.

96 Theology of Arithmetic, s.v. 97 Along with Irenaeus's testimony, several New Testament fragments confirm this variant reading. See Nestle ed., s.v. Rev. 13.18. See also below, p. 339. 98 Or a copyist may have inserted this comment, Harvey's suspicion (Sancti Irenaei Episcopi, s.v.). 99 See Rousseau and Doutreleau's ed., 5.1 (SC 152): 331-33. 100 Against Heresies 1 .30.3.

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172 D espite these possibilities, Irenaeus says, we should not endanger ourselves by claiming with certainty that we have the name. If it had been imperative that the name be clearly proclaimed now, the seer of the revelation would have said so. Recall here Irenaeus' s admission that some obscure numbers may not allow for an immediate, transparent interpretation. Irenaeus's most outstanding specimen of number symbolism is his argument for there being four and only four Gospels.101 Responding simultaneously to those who held to more Gospels (the Valentinians) and to those who held to a much smaller number (Marcion), Irenaeus claims that the Gospels had to have been four, no more and no less. There are four regions of the world and four universal winds.102 The Church is spread throughout the whole earth and the gospel is the "column and support" of the Church and the spirit of life.103 Because of all these things, the Church fittingly has four columns, from all directions breathing incorruption and granting people life. From this it is evident that the Word, the craftsman of all things, after manifesting himself to humanity, gave a quadriform gospel encompassed by a single Spirit. The Word sits on the cherubim and the cherubim have four faces.104 These faces are images of the activity of the Son of God. Following the language and order of Revelation 4.7 (and not Ezekiel 1 . 1 0), Irenaeus interprets the lion, ox, man, and eagle as, respectively, John, Luke, Matthew, and Mark, an assignment made on

101 Ibid. 3.1 1 .8. Cf. an Armenian abridgement, frag. 6 atPatrologia Orientalis 1 2 (1919): 737. 102 See Theology of Arithmetic 24. 1 0, 29.15. 103 DvEVfllX L;wf)c;. The pun and intent in relating the Scripture to world geography is better seen in the

translation "wind of life." "Column and support" refers to 1 Tim 3.15. 104 Ps 79.2; Ezek 1 .6, 10.

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1 73 the basis of the opening lines of each GospeJ.l 05 The four animal shapes reflect the four activities of the Son of God, and the four Gospels. For the same reason, four covenants were given to humanity, the first before the deluge, the second to Noah, the third to Moses, and the fourth is that which "renews man and recapitulates in itself everything, through the gospel raising and granting wing to men for the heavenly kingdom." Thus, everyone who nullifies the shape of the gospel and introduces greater or fewer faces of the gospel are foolish and ignorant.1 06 Those who have more (the Valentinians) claim they have found something greater than the truth. Those who have fewer (the Marcionites) nullify the dispensation of God. After criticizing both groups' treatment of Scripture, Irenaeus claims that the abundance of reasons he has presented demonstrate that the four gospels alone are true, certain, and admit neither increase nor decrease. Since God himself creates all things to be harmonious and well fit, the form of the gospel too had to be harmonious and well fit. How well does this argument for the four Gospels conform to Irenaeus' s principles? He doesn't seem to appeal to the rule of faith, and it looks like the argument arises from a predilection for number symbolism. Is this a case of regula ex numeris?

CONSISTENCY IN IRENAEUS'S THOUGHT Irenaeus claims that the Church's teachings, unlike those of the Valentinians, are well fitted.1 07 He calls the Church's proclamation a rhythm, fitted to the things that have been created by the rhythm.1 08 That is, the rule of faith conforms exactly to the contours of ws See Stevenson, "Animal Rites." 106 Against Heresies 3.1 1 .9. 1 o7 Against Heresies 2.15.3. ws apta est inem haec rhythmizatio his quae facta sunt huic rhythmizationi.

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1 74 creation because it is the very rule by which creation was shaped. Creation is well ordered, and the tradition fits the order of creation.109 The sentiment is less an argument than a pair of self-referential claims, akin to the early-Christian notion that by the Word all things were made, and that this very Word is that which the Church proclaimsP0 The two claims form a circle. The causes underlying the structure of the world reside within the Church, and the Church's proclamation is made manifest in the structures of the world. Throughout Against

Heresies, Irenaeus expounds the rule of faith and emphasizes its internal consistency. But is Irenaeus consistent? How well fitted is his rule of truth to the principles he outlines? More specifically, Irenaeus charges the Valentinians with mishandling scripture, and with putting numbers and doctrine in the incorrect order. But has he himself committed this very error? Does his treatment of numbers contradict his own principles? If so, then why the inconsistency? If not, what is the unifying principle at work? Our aim is not to measure Irenaeus by our own ideals. Rather, our concern is whether Irenaeus, in formulating principles against Valentinianism and Marcion, observes or neglects those ideals in other contexts. Recall the four main lines of Irenaeus' s substantive criticisms of Valentinian number symbolism. First, their method of numbering and organizing the Pleroma leads to grave inconsistencies. Second, their system is based upon changing culture-bound habits of language and enumeration. Third, their use of numbers conflicts with the structures of the natural world. Fourth, their exegesis of Scripture has been selective, arbitrary, and ignorant

109 Contra Perkins, "Beauty, Number, and Loss of Order," 279, who says that Irenaeus argues against

the Valentinians by affirming the disharmony of the lower world. 110 Jn 1 .3 and, e.g., 1 Thes 2.13.

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1 75 of the context of the narratives. Each of these criticisms can be inverted into corollaries, positive principles that Irenaeus defends. First, the numbers in one's taxonomy of the godhead should be consistent. Second, theology should not derive from and depend upon the changing linguistic or mathematical habits of a particular society. Third, the numbers in one's theology should correspond to the organization of the natural world. Fourth, numbers in theology should emerge from the entire body of Scripture, and proof texts should be used with regard to their context. This last principle is especially key for Irenaeus: numbers emerge from the rule of faith (the Scripture being part of that rule) not the other way around. How does Irenaeus's symbolic use of numbers fare against these principles?

Principle one. The numbers in one's taxonomy of the godhead should be consistent. Note how Irenaeus applies numbers to the godhead. First, he focuses on one Father and one Son, and not on the oneness of the Holy Spirit. This emphasis on the oneness of the Father and Son spills over into his description of the Church and baptism, in part to criticize V alentinian separatism, in part to reflect the Christian traditions he was taught in the Church and in the New Testament.111 Second, he never uses numbers to describe the relationships among the Father, Son, and Spirit. He shies away not only from Trinity, but from other terms that might suggest that the Father is to the Son as the Monad is to the Dyad. True, his exegesis of Joshua 2 likens the three spies to the Father, Son, and Holy Spirit, but his language there is oblique. He uses 'rQELs instead of 'rQLac;, that is, three individuals, not a Triad.1 12 Throughout his discussion of God, redemption, and purification, m

See, e.g., Eph 4.3-6.

1 1 2 See also his Proof of the Apostolic

Preaching 1 00.

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1 76 Irenaeus avoids any language that refers to God as the One, an association common in other early Christian authors. Thus, Irenaeus steers away from using numbers to describe the godhead. He is consistent with this first principle, since he avoids any kind of arithmetical taxonomies in his theology.

Principle two. Theology should transcend human conventions of grammar and enumeration. Irenaeus' s interest in grappling with Christian psephic practices developed to interpret Revelation 13.18 should be barred from consideration here. The original author of the verse, after all, plays with the Greek psephic convention, and expects his readers to d o so a s well. This becomes evident when the language of Revelation 13.18 i s compared with the numerous other psephic riddles and discussions (see excursuses C and D). But Irenaeus' s treatment of Gideon is more difficult to understand. He says that Gideon took ten men, a number he chose not at random but to make it evident that he had Jesus as a help. It was known in the late second century, as it is today, that habits of numeration in Gideon's time were far different than those in the second century.113 So Irenaeus appeals to a contemporary Greek technique to interpret an event that occurred in ancient Judaism. His observation resembles Barnabas's "masterful teaching" on the 318 servants of Abraham, or Marcus's use of the Greek translations of Hebrew names to derive psephic values.114 But to be fair, Irenaeus may have been thinking here of the Hebrew use of m

See, e.g., Aelius Herodianus (fl. 2nd c. CE), nEpi dpt 811wv (TLG no. 87.42).

1 1 4 See p. 340 n. 37.

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177 alphabetic numeration. Hebrew alphabetic numeration was introduced probably in the first century, modeled on the Greek prototype, and by the late second century its recent invention may have been obscured (see excursus C). Possibly Irenaeus was thinking of Gideon's ten men as a yod, which, like the iota, stood for the number ten. But even if Irenaeus was thinking of a Hebrew convention, the Valentinians or Monolmus would have seen little methodological difference between Irenaeus' s treatment of Judges 6.27 and their own connections between alphabetic numbers and theology. Because Irenaeus never clarifies this matter, at least in his extant works, he seems somewhat inconsistent on this principle, or else not completely fair to his opponents.

Principle three. The numbers in theology should correctly reflect the natural world. That there were four winds and four cardinal points was accepted as undeniable fact in Irenaeus' s day, an aspect of the natural world subject to neither change nor social convention. Grant him the science. Is it any reason to justify four and only four Gospels? Recall that he criticized the Valentinians for justifying their various levels of the Pleroma on the basis of inappropriate divisions of time. Has Irenaeus committed the same fault here? A Valentinian, for instance, could have argued for the five Gospels - Matthew, Mark, Luke, John, and the Gospel of Truth -on the basis of the five senses, the same basis upon which deutero-Simon argues for the perfection of the Pentateuch. Whose argument is stronger? Are the Gospels more like geography or sensation? A Valentinian could also argue that if the Gospels resemble the four winds, then how do the number of epistles or other books fit into that analogy? Why the specific number of letters by Paul and other apostles? Why the number of Old Testament books? If the

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1 78 Gospels represent the four winds, what do the other books represent? After all, Irenaeus insists that if they find evidence for the Dodecad in the calendar year, then they must find prototypes of the Decad and Ogdoad as well, to be consistent. Strictly speaking, Irenaeus has not violated his principle, since he does not refer to numbers in the natural world beyond the safe, uncontested four winds. But he has criticized the Valentinians for not executing their analogies completely. So it seems, as in the second principle, that Irenaeus has been unfair to his opponents, since he expects their number symbolism to be not only consistent with the material world but complete, as well.

Principle four. Numbers should come from the rule of faith, not the rule of faith from numbers. According to Irenaeus, you should work with the numbers latent in the tradition and work outwards. Thus, the thirty-, sixty-, and hundredfold fruit are taken not as numbers in their own right but as codes for the tripartite afterlife taught in the Scriptures and handed down by the elders who knew the apostles. The numbers in Joshua 2 Irenaeus interprets in light of other symbolic numbers common in the tradition. The various numbers in the epochs of human history Irenaeus tries to distill from Scripture. Numbers that appear in Daniel and Revelation he interprets in light of other eschatological Bible verses. In each case, one Scripture is brought to bear on another. A seven found in one verse is explained in light of another verse with the number seven. Even Irenaeus's numerical treatment of the four gospels depends upon this principle, since ultimately Irenaeus holds to four Gospels not because of patterns in the

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1 79 weather but because that is the number of Gospels the churches have received.1 15 That is the tradition he received from the elders. The apostolic rule of faith is Irenaeus' s foundation. And if the rule of faith preserves four and only four books, then that is a clear, firm part of the tradition that enlightens other, more obscure parts. The four Gospels explain the meaning of the four faces of the cherubim, as well as of the four covenants God gave throughout human history. From the tradition, whether Scripture or not, one develops numerical connections and associations that explain other parts of the tradition. Here an imaginary Valentinian may object, claiming that they were also working from within a tradition, albeit one lately revealed to them. Irenaeus' s counterargument, however, is strong. The tradition respects the narrative structures of the Scriptures, and it engages in the entire breadth of the Tradition. It flows out of the tradition, not into it. The tradition does not depend on any one person, school, or movement, but is the corporate experience of all the churches. The Valentinians cannot claim to follow this rule, otherwise there would be a place in their system for the sacred number five. They would also be able to point to the churches everywhere to show that their tradition was taught by the apostles.1 16 Moreover, the Scriptures they use to justify the numbers in the Pleroma are inseparable from their contexts. When read in their original setting, these verses undermine the doctrine of the Pleroma. It is evident that Irenaeus's treatment of this fourth principle is circular, but consistent. He sees the rule of faith as a given constant consisting of the Scriptures, the oral tradition, and the life and teaching of the churches founded by the apostles. Numbers 1 1s Irenaeus, Against

Heresies 3 . 1 .

1 16 Ibid. 3.1--4.

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1 80 should be treated as a part of that rule, and numbers from another rule should not force their way in. He treats various numbers in Scripture not as proofs of his system but rather as implications. The four animals of Ezekiel 1 and Revelation 4 do not justify the claims that there are exactly four gospels; rather, these verses are intelligible in light of that part of the tradition. Irenaeus's language of inference: KlXL yaQ and KlXL bu:X 'rofno does not look backward, as if to a basis for belief, but forward, as if to its implication. Throughout Against

Heresies Irenaeus uses inferential language for two purposes, one for proof and the other to show off the system's explanatory power. In his explanation of why there are four and only four Gospels, he is using only the second technique. He is not proving the number of Gospels but rather explaining them. He cloaks his explanation with clauses of inference, and thereby strengthens the power of his rhetoric, albeit at the expense of clarity. His clause of inference, E:nd yaQ, does not justify but explicates.117 For this reason, Irenaeus' s number symbolism is consistent with his fourth principle.

Overall, then, Irenaeus sticks close to his principles about the theology of arithmetic, or at least he tries to do so. His occasional indulgence in number symbolism and the alphabetic numbers suggests that he too found attractive the exegetical techniques used by the Valentinians, Mono1mus, and others. That they all share the same techniques highlights Irenaeus' s occasional tendency to be unfair to his opponents, expecting them to meet standards that he doesn't, elsewhere. But this has to do with techniques, not conclusions.

m Ibid. 3.11 .8.176-77.

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1 81 Ultimately, Irenaeus's complaint is with the origin and substance of the Valentinian system, foreign to the Church. By arguing that Irenaeus' s theology of arithmetic is internally consistent, I have not suggested that his critique succeeds against the Valentinians. After all, they may have followed coherent principles that guided their use of number symbolism, principles not reported in Against Heresies. Or, they may not have. Unfortunately, the sources we have are silent about this. How representative was Irenaeus of this approach to numbers among the orthodox? That is, how closely do these four principles describe an orthodox theology of arithmetic? To answer that requires the study of Irenaeus' s near contemporary, Clement of Alexandria, the subject of the next chapter.

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8 Clement of Alexandria

Very little is known of Clement, who flourished in late second-century Alexandria. He was probably raised in Athens, where his grandfather owned a library just south of the Stoa of Attalos.1 Clement used his social status to travel in pursuit of his education. Clement credits teachers from across the Roman world - Greece, Italy, Lebanon, Syria, and Egypt- with his training in Christianity, particularly a certain Pantaenus, whose missionary travels to India are mentioned by Eusebius.2 In Alexandria, Clement conducted what was probably an informal school for Christians, a school not to be confused with the famous academy that started under the auspices of Origen.3 After the persecution in 202 Clement left Alexandria, and died presumably shortly after.4 Several of Clement's writings survive, the most important of which for this study is his trilogy: Exhortation to the Heathen, The Instructor (The Pedagogue), and Stromateis (The

Miscellanies). Exhortation to the Heathen is an apology directed toward educated Hellenes, challenging them to embrace and follow Christ the Logos. In The Instructor Clement

1 Merritt, Inscriptions, no. 32, citing Hesperia 5 (1936): 41-42; suppl. 8:268-72. 2 Clement of Alexandria, Stromateis 1 .1.11; Eusebius, Church History 5.10-1 1 . 3 Jakab, Ecclesia alexandrina, 93-106. 4 For more on Clement's life, see DECL, s.v., and works cited there.

1 82

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1 83 presumes an audience of beginning or intermediate Christians, and instructs them in the ways of the Logos, focusing on morals and appropriate behavior. The last part of the trilogy,

Stromateis, is an intentionally unordered patchwork of discussions on various theological topics, intended for more-advanced Christians.5 Evident in Clement's writings is an unflagging commitment to Christian orthodoxy. His style and spirituality differ from his contemporaries, Irenaeus and Tertullian, but he nevertheless identifies himself with them and the Church. To understand all of Clement's number symbolism would require a separate study. Rather, I analyze here Clement's discussion of the Decalogue, found in Stromateis book six. It is his richest, most sustained foray into number symbolism. In this complex passage (whose structure I explain in excursus G) there are three major areas of his number symbolism especially relevant to this study: his fascination with the number ten, his treatment of the number seven as an intermediate stage to perfection, and his use of number symbolism to reinterpret the account of the Transfiguration. All three areas deal with themes found in the authors of previous chapters, so understanding how Clement handles his number symbolism provides a more complete account -more complete than one based solely on Irenaeus's testimony - of how the orthodox of the second century handled Valentinian number symbolism. Before turning to Clement's treatise on the Decalogue, however, I conduct a brief overview of Clement's doctrine of the nature of God and its relation to the

s For more on Clement's literary corpus and his theological thought, see Quasten, Patrology, 2:5-36,

with updated bibliography in TRE, s.v., and DECL, s.v.

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184 world of arithmetic. This sets Clement in relation to Irenaeus and the Valentinians and makes his excursus on the Decalogue more comprehensible.

NUMBERS IN CLEMENT'S DOCTRINE OF GOD Of second-century orthodox Christian authors Clement indulges more than most in number symbolism. This indulgence, however, is not reflected in his theology. Although, as we shall see, Clement ordinarily revels in patterns of sixes, sevens, eights, and tens, the only number he applies symbolically or otherwise to the godhead is one. Clement, like Irenaeus and Justin Martyr, holds to a single God, the Father, and a single Son, the express image of the Father. As an "ecclesiastic" he uses the various titles for God and his Son or Word to describe single subjects.6 Unlike the Valentinian use of the same terms, Son of God, Christ,

Savior, Instructor, and Jesus all describe the same person. He holds to no theology of emanations from God, and so there is no system of aeons organized into numerically symbolic groups? But unlike his orthodox predecessors, Clement is more adventurous in using arithmetic to describe the movement from the godhead to the structures of creation. Below the Father and the Son are numerous beings that form an elaborate hierarchy extending from heaven to earth, but their source of being is unity, and so is their goal. Clement says that these lower beings are saved by each other and save each other "from One and through 6 Clement prefers to d esignate himself and other orthodox churchmen by describing themselves "of the Church," in distinction to Valentinians and other opponents. See Kovacs, "Concealment and Gnostic Exegesis," 4 1 5 n. 5. 7 For a complete survey on all the differences and similarities between Clement and the Valentinians, see Davison, "Structural Similarities and Dissimilarities," and Edwards, "Clement of Alexandria."

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1 85 One."8 "From one" refers to the Father; "through One," to the Son. This unity of God, according to Clement, Abraham embraced in the alteration of his name from Abram, since the alpha that was inserted into his name represents his knowledge of the one and only God.9 Clement's sense of the unity of God is so strong that he calls him "the One" and applies the attributes of the number one to the godhead: just like the number one, God "the One" is indivisible, and therefore infinite, realized in his lack of extension.10 Clement even claims that God "calls himself one" on the basis of John 17: "In order that all might be one, just as you, Father, are in me and I in you," and so forth.1 1 Lest it be thought that God is the One, Clement interprets John so as to affirm that God transcends all number: "God is one, and beyond the One, and above the Monad itself."12 This refers to the common belief that the monad transcends the hen (see excursus Bl)P God, Clement says, stands not only above the One (the highest principle for a pure Platonist) but above the Monad itself, and is therefore beholden to no number. Despite any arithmetical metaphors he uses to describe God, Clement nevertheless cautions readers that the epithet One for God is an approximation, and not a true predicate of he who cannot be named.14 Such negative theology was a standard feature of the middle Platonism of his day. But Clement presents this idea of the indescribability of God, an idea

8 Clement of Alexandria,

Stromateis 7.2.9.3.

9 Ibid. 5.1 .8.6. 10 Ibid. 5.12.81 .6. For discussions of the philosophical dimensions of Clement's use ofone see

Choufrine, Gnosis, Theophany, Theosis, 165-66, 174-75, 1 86-88. John 17.21-23; Clement of Alexandria, Instructor 1 .8.71 .1 . 12 Clement of Alexandria, Instructor 1 .8.71 .2. See below, p. 295. 1 3 Choufrine's discussion (see n. 1 0, above) does not take this distinction into account. 1 4 Clement of Alexandria, Stromateis 5.12.82.1 . n

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1 86 that becomes quite important in Plotinus' s writings, not to press Christianity into a Platonic mold, but to prevent people from straying from belief in the transcendence of God. For Clement there is no category, including number, that comprehends and stands over his nature. His metaphors and pedagogical tools may be philosophical in origin, but in the substance of his theology, Clement stands with Irenaeus as a Christian monotheist, not a Platonist.1 5 Although God stands above arithmetic, Clement finds arithmetical unity a helpful metaphor of the divine, and he states that man's goal is a similar kind of unity. As a person becomes divinized into a state of dispassion, he becomes purely "Monadic."16 This unity is epitomized for Clement in the Church, "For just as God is one and the Lord is one . . . that which is most highly treasured is praised for its solitude (f.16vwmv) since it is an imitation of one principle (aQxi)c; 'ri)c; f.l llis). Thus, the one Church also has a portion in the nature of the One, which nature the [heretics] strive to chop into many heresies."17 This joint share in God's unity allows the Church to collect people "into the unity (E:v6Ttl'fa) of the one faith

( n(aHwc; f.! Lac;) of its proper testaments-rather of the one testament from different ages-by the will of the one God, through the one Lord."1 8 Thus, the Church, which is the earthly image of the heavenly Church, reflects precisely the unity of God, and humanity's return to that unity.19

1 5 See Edwards,

Origen Against Plato. Stromateis 4.23.152.1 .

16 Clement of Alexandria, 1 7 Ibid. 7.1 7.107.4. 1s Ibid. 7.17.107.5.

1 9 Ibid. 4.8.66.1 .

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1 87 The language Clement uses to describe the unity of God, the Lord, and the Church, is already in the New Testament.2° The same themes appear in Irenaeus (see chapter 7). There is in Clement very little, if any, polemic against the Valentinian Ogdoad and Pleroma. But his insistence of the unity of God is as strong as Irenaeus's, evidence that orthodox emphasis on God's unity was not conditioned by Valentinianism.

THE ANTHROPOLOGICAL DECALOGUE In his introduction to his excursus on the Decalogue (§§133.1-137.1) Clement carefully constructs three lists consisting of ten elements -types of decalogues, all of which, he says, the Decalogue encompasses (§133.3, 4: 7TEQLEXEL).2 1 The first, the heavenly decalogue, has exactly ten elements: sun, moon, stars, clouds, light, wind, water, air, shadow, and fire.22 So too the second decalogue has exactly ten items, this time relating to earth: humans, cattle, reptiles, beasts, fish, whales, carnivorous birds, birds of a delicate palate, fruit-bearing plants, and plants with no fruit. The first decalogue does not seem to follow a specific order, but the second list follows an order roughly the reverse of the d ays of creation.23 Genesis 1 goes from plants (day three), to reptiles, birds, and fish (day five), to quadrupeds, land

20 See, e.g., Eph 4.4-5; 1 Cor 8.6; Jn 10.16, 1 7.21 . 21 In this chapter, the symbol § refers to Clement of Alexandria, Stromateis book 6. 22 See above, p. 34. 23 Possibly the first decalogue, too, follows the opposite order of Genesis. But there are noticeable differences: fire and clouds are not mentioned until Gen 1 1 .3 and 9.13, respectively, and lif]Q doesn't feature in LXX Genesis at all. These three items excepted, the order in Genesis would be shadow, wind (= spirit), water, light, sun, moon, and stars. Possibly Clement considered fire and air to be implied in the first day of creation, and clouds in the second. If so, then the heavenly decalogue, like the earthly one, follows the days of creation in reverse order. Compare the imperfect order of the anonymous Valentini an text at Irenaeus, Against Heresies 1 .18.1, discussed above, p. 34.

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1 88 reptiles, beasts, and humans (day six). The correspondence is not exact, but close enough to suggest that Clement took the Genesis account and reshaped it so as to yield for heaven and earth exactly ten members each. The third decalogue Clement presents (§134.2) is that of the human being, who, he says, consists of the five senses, along with the ability to speak, the ability to generate, the formed spirit, the ruling faculty of the soul, and the characteristic mark of the Holy Spirit (a mark applied through faith).24 This anthropological decalogue, which features prominently elsewhere in Clement's writings, provides an important comparison to similar structures in Valentinianism and Stoicism. Fine details of this decalogue illustrate how he subtly used numbers to articulate profound points about the creation and salvation of the world. In book two, in his interpretation of Exodus 1 6.36 ("The omer was the tenth of the three measures"), repeating Philo nearly verbatim, Clement identifies the three measures as sense perception, reason, and intelligence, as well as the intended objects of these three faculties.25 He then adds his own thoughts to Philo's discussion. The Gospel teaching, "It is not what enters into the mouth that defiles a person, rather, that which exits a person's mouth is that which defiles a person," is the true and just measure.26 Clement brings up again this same anthropological decalogueP That same measure is the "decad that

24 T(J bux n1c; T[ LCJn:wc; ITQOCJ)'LV0!-1-EVOV ayiov ITVEl.J!-1-lXTOc; XlXQlXKTTJQLCJTLKOV ibLW!-1-lX. "Formed spirit" : literally, "that which is spiritual/breathing according to the formation" (To KaTix TJlV ni\amv ITVEU!-1-lXTLKOV). 25 Philo, On the Preliminary Studies 1 00. 26 Clement's rendering of Mt 15.17-18, at Stromateis 2.11 .50.2-3 .. 27 Ibid. 2.1 1 .50.1 .

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1 89 encompasses the human being." Clement claims that the three measures of Exodus 16.36 allude in summary form to that decad.28+ He then explains what that decad consists of.

ELTJ b' av CJWf..UX '[f KiXl \]Jvxi] ai' '[f rrfV'[f aicr8T]CJW ;; KiXl 'rO <j:>WVTJHKOV KiXl CJITEQf..WHKOV KiXl 'rO bLaVOTJHKOV Tl rrVEU f.liXHKOV ij onwc; Kat f3ovt\E L Kat\ELV.29

That might be both the body and the soul: the five senses, the vocal faculty, the generative faculty, and the faculty of understanding or of the spirit, or whatever you want to call it.

Clement then notes the need to overleap all these faculties so as to stand at the mind, as if overleaping the nine portions of the universe. The nine portions of the universe, according to Clement, are the four elements (that is, earth, the sublunary region: portion 1), the seven planets (portions 2-8), and the "unmoved ninth" (the fixed sphere of stars: portion

9). What he has just termed the mind -the tenth portion, the complete number- resides above these nine, and is the arrival at the knowledge of God.30 Thus, the nine faculties of the human being, capped by the tenth, the mind, resemble the structure of the universe, in which nine celestial levels are subordinate to God as tenth.31+ Although Clement's 28 Ibid. 2 .. 1 1 .50.3. In Stahl in's edition, the true measure is not equated with the decad: TOtJT OLf.HXL, n) KlXTlX 8EOV UAJ18LVOV KlXL CJLKlXLOV f.lETQOV, <}> f.lETQELTlXL TCt f.lETQOVf.lEVa, lJ TOV av8QWTtOV auvi:xouaa bEKa�, ilv irri. Knpa,\a(wv Ta TtQOELQJ1f.lEVa TQLa ibf],\waEv f.lETQa. The relative pronoun 1J has no feminine antecedent. It makes sense to convert this to the definite article, 1'1, as in Mondesert's ed. This puts the decad in apposition to the measure. 29 Clement of Alexandria, Stromateis 2.11. .50..4 .. 30 Ibid . 2.11. .50.4-2 .. 1 1. .5 1. . 1. . 31 A t 2 .. 1 1 .50 ..4, there is some admitted confusion .. The five senses plus what seems like three other faculties adds to eight. The wording seems to suggest that btaVOJ1TLKOV and rtVEUf.llXTLKOV are equivalent terms for the eighth faculty. At 2.1 1 .51..1 the mind is called the tenth faculty, in analogy to Philo's cosmological decalogue. Where is the ninth? The answer is found at Stromateis 6.16.134.2, where the faculties of understanding and of the spirit represent the eighth and ninth levels. Clement's offhand remark, at 2 .. 1 1. .50..4, "or whatever you want to call it," suggests that there was a difference of ·,

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190 cosmological d ecalogue depends directly upon Philo, his anthropological one d oes not. It may be original to Clement.32 Back to book six. In the excursus on the Decalogue, Clement twice identifies the mark of the Holy Spirit explicitly as the tenth number or element in the human being

(§134.2: b€K£nov and §135.1 : 'l"OV b£Ka'I"OV cXQL8 f16v), thus emphasizing afresh his tenfold anthropology. This point is easily missed when reading §135.1 . This terse passage describes the ninth and tenth human elements (ruling faculty and the characteristic mark of the Holy Spirit) as agents that perfect other activities. The text is difficult to translate without some expansion.

inaaKQLVnm bi: i] ¢uxi]. Ka i 71QOE LUKQLVE'ra L33 n) fJYE flOVLKOV, clJ b La;\oyL£:6f1E8a, ou Ka'I"a 'I"ijv 'I"OV anEQflCX'I"O� Ka'I"a�o;\ijv YEVVWflEvov, W� auvayE<J8m KC:X L lXVEU 'l"Otnou 'l"OV bEKCX'I"OV cXQL8f-10V, bL' WV fJ mxaa EVEQYEW: 'I"OV av8QW710U i mu;\{i'rm.

The soul is added [to the senses and limbs]. And the ruling faculty, by which we reason, is added prior to this, and is begotten, not by the casting of seed [d. Heb 1 1 .1 1 ], just as the tenth number [i.e., the characteristic mark of the Holy Spirit] is brought in without it [i.e., seed], by which things [i.e., the ruling faculty and the characteristic mark of the Holy Spirit] every activity of a person is perfected.

In this terse passage (made difficult by the vagueness of wv) Clement notes that the ninth and tenth elements- the ruling faculty and the characteristic mark of the Holy Spiritare not dependent upon physical generation but are bestowed from above. They are,

opinion, between those who wished to suborn the spiritual faculty to the faculty of understanding and rank them eighth and ninth respectively, and those who wished the opposite. See below. 32 Philo, On the Preliminary Studies 102-6. 33 nQOELGKQLVETCXL Descourtieux, nQOGE LGKQLW:nu Stahlin.

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191 together, agents of perfection. These two highest faculties stand above and apart from the lower eight. These three passages show that Clement regarded the anthropological decalogue an important model. This was not Clement's only anthropological model based on decalogues. At §134.3 he states that the law was laid down for the ten parts of the human and he restricts the list to the five pairs of sense organs - sight, hearing, smell, touch, and taste.34+ The doubled sense organs resemble the two tablets upon which the Decalogue was inscribed. But Clement does not mention the higher faculties of the soul itemized in his main anthropological decalogue (§134.2). The two lists differ, but they are not incompatible, since they both emphasize that the tenfold division within human beings is natural. They both simply highlight different ways the decad can be identified within the human being.

34 The passage is ambiguous. Ell 71QOC: TOlJTOLC: b[Ka naiv av8QW71ELOLc; flEQEaL 71QOGTaaanv i] VOf108WLCX cpa[vnm. TlJ TE OQUGEL KCXL tXKOJJ KCXL TJJ oacpQTJGEL acpfl TE KCXL yn)an KCXL TOLe; TOUTWV vrwvQyo'ic; 6Qyavmc; bLaao'ic; oum, XEQa[ TE Kai rroa[v. "Again, the laying of the law seems to be given to these certain ten human parts: to sight and hearing, to smell, and to touch and taste and their accompanying organs, being double, both to hands and feet." Does this mean the five senses plus the four limbs? Or does it mean each of the five sense-perceptive faculties understood "doubly," with the hands and feet a later scribal gloss? Under the first option, the total comes to nine, not ten. Under the second option, it is hard to see where all the "double organs" are. Even though there are two eyes, two ears, and two nostrils, it is unclear what pairs of sense organs belong to touch and taste. Possibly Clement has garbled the Valentinian account, where the four senses of sight, hearing, smell, and taste (divided into bitter and sweet) have two organs each, an image of the upper Ogdoad. See Irenaeus, Against Heresies 1 .18.1 and discussion above, p . 31 . At Theology of Arithmetic 68.3, there are said to be seven orifices in the head, probably counting the tongue singly. Possibly, however, it is the symmetry (and therefore doubleness) of the sense faculties that is key in Clement. Note, too, Clement's order of the senses differs (as does Plutarch's: The E at Delphi 12 [390B]) from that found in the Paraphrase of the Apophasis Megale. See above, p. 129 n. 48. A third interpretation, which adds to the second, seems most likely to me: Clement is referring to the ten toes and ten fingers. Thus, he draws up three physical decalogues found in the human being: the senses, the fingers, and the toes.

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192 THE INSPIRATION FOR CLEMENT'S ANTHROPOLOGICAL DECALOGUE That Clement chooses the decalogue to structure his anthropology is not surprising. The symbolism of the number ten runs throughout Clement's works. Later in this excursus (§145. 7) he notes that the Decalogue, because of the iota -the Greek numeral for ten invokes the blessed name ]esus.35 Clement earlier (§84.5) calls the number ten "all perfect."36

In book two he likens the number ten to reaching the knowledge of GodP For Clement this level of perfection explains why a tithe (and no other denominator) was to be given to God, and why the Paschal feast starts on the tenth of the month.38 The parallels with Monolmus (see chapter 3) are noteworthy. Both authors are interested in plumbing the books of Moses to locate patterns and groups of ten. Both play on the role of iota as a Greek numeral. Yet despite their mutual interest in the number ten, they approach the matter very differently. Monolmus begins with the glyph l as a symbol of the relationship that holds between the two supreme beings and their emanating powers. Clement, on the other hand, is interested in ten qua number or qua numeral, but not qua glyph. Further, he does not share Monolmus' s metaphysic, so he uses ten as a symbol mainly of the structures of creation and their interrelated connection to Scripture, not of the godhead. Clement does not seem to be interested in connecting this scheme with other philosophical decalogues, for instance, with Aristotle's categories. And, unlike Monolmus,

35 See above, pp. 34, 94, 169 and below, 340 n. 37. 36 Tj DEKCxC: b[ Ofloi\oy{i-rm ru:xv-rii\noc: Elvm. See above, p. 50 n . 125. 37 2.1 1 .51 . 1 . 38 2 . 1 1 .51.2. Tithe: Ex 29.40, Lev 6.20; Pascha: E x 12.3 (see above, p . 1 12).

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1 93 who never uses the name Jesus, Clement sees the iota in the Decalogue and the Psalms as prefiguring only Jesus.39 Also comparable to Clement's anthropological decalogue is the tenfold list culled by a Valentinian comparing the first things of creation to the Decad of aeons.40 Both Clement and the Valentinian school sought in the Scriptures patterns of ten. But the Valentinian decalogue is so dissimilar in its details and organization from any of Clement's decalogues that any question of borrowing can be rejected. In some respects, Clement's interest in relating the Decalogue to anthropology compares more favorably with Heracleon, his contemporary and rival. Heracleon was probably part of the Valentinian school, and possibly flourished, at least for a time, in Alexandria.41 Both Clement and Heracleon shared an interest in number symbolism. Important for this study are Heracleon's comments on John 2.20 ("The Jews said, 'This temple was built in forty-six years . . . " ) , which parallel Clement's anthropological decalogue.42 Claiming that the temple is an image of the Savior, Heracleon analyzes the constituent parts of the number forty-six. He says that six refers to matter or substance

(uAYJ), that is, the formation of man (nAaof.la). Forty, "which is the Tetrad . . . which does not admit union," refers "to the infusion, and the seed in the infusion."43

39 Clement of Alexandria, Instructor 2.4. 40 Irenaeus, Against Heresies 1 .1 8.1 . See above, p. 34. 41 Clement, Stromateis 4.9.71 .1, calls Heracleon the "most approved of the school of Valentinus." On Heracleon see above, p. 12 and n. 6. 42 Heracleon, frag. 1 6 ( Origen, Commentary on John 1 0.38.261). For other aspects of Heracleon's number symbolism see below, p. 203. 43 Ibid., trans. Heine (FOTC 80). "a TETQac; icn(v," ¢11aiv, "i] anQoanAoKoc;," Eic; n) E f1cpDCJY1f1G Kat n) EV -r4J E flcpVaTJflGTL CJ71EQf1G. =

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1 94 Heracleon' s number symbolism makes important theological points. His term for " does not admit union," anQ6aru\oKoc;, is reminiscent of the language of Ptolemy, who uses

aavfl n;\oKoc; three times in his Letter to Flora as a quasi-technical epithet for the Decalogue, the most perfect of the three parts of the law .44 Both Heracleon and Ptolemy share a common vocabulary and express an interest in the number ten. To Ptolemy the Decalogue is "not interwoven" with evil. Heracleon's use of anQ6arrAoKoc; suggests that he regards the Tetrad as the highest principle, corresponding to the place Ptolemy assigns the Decalogue.45 If the connection between Heracleon and Ptolemy is real, then Ptolemy's placement of the Decalogue at the highest place in the tripartition of the Law may be mirrored by Heracleon' s placement of the Tetrad at the head of a decalogue, also divided in three. Heracleon identifies the Tetrad with the "infusion" (E fl
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1 95 Any reconstruction of Heracleon' s views on this matter must be tentative, but it seems that what he is proposing is this. The forty-six years of the temple are an image of the Savior, who is himself the perfect synthesis of the Tetrad and the number six, corresponding respectively to man's two parts, his higher infusion and his lowly matter. If the Savior synthesizes these two elements - a synthesis represented by the number forty-six - then, of course, he embodies the number ten. Heracleon, like Clement, embraced an anthropological decalogue. Heracleon sees the division between the higher and lower faculties of a human being at four and six, whereas Clement divides the human being into two higher faculties and eight lower. Whether Clement knows of, and now answers in his own orthodox fashion, the anthropological decalogue Heracleon based on John 2.20, it is too difficult to determine based on this hypothetical reconstruction. The opposite, that Clement is merely repeating the anthropology taught to him by his teacher, Pantaenus, and that Heracleon represents a departure from that earlier tradition, is just as likely. Stoic anthropology would have been the basis for any Christian anthropology ­ whether orthodox or Valentinian - that carefully enumerated the parts of the human being. As part of their program to show the essential material unity of the human soul, Stoics divided the soul generally into seven parts, all governed by an eighth. A number of such lists are extant, and they sometimes differ, both in their specific terminology, and in the order of the sixth and seventh elements. But all sources generally agree that there are eight parts and that they sit in a hierarchy, with the seven lower faculties - that is, the five senses, the voice, and the capacity for reproduction - governed by the higher one, the ruling faculty

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196

(TJYEflOVLK6v).47 Earlier Stoics rejected the tripartite soul taught by the Platonists, but in late antiquity some Stoics began to accept this and other ways of dividing it.48 Clement expands the eight Stoic parts of the soul into a decalogue by introducing two modifications. He moves the ruling faculty from the eighth to the ninth place and then inserts two new faculties: the formed spirit in the eighth position and the mark of the Holy Spirit in tenth. To understand the significance of these modifications, we must understand Clement's ideas behind his two new faculties, the formed spirit (eighth) and the mark of the Holy Spirit (tenth). Both new faculties are discussed in book four, where Clement discusses the gnostic's potential to become a god, then contrasts the composition of the human being in general with that of specific individuals. "So the human being in general, is formed ( nMaaerm) in

47 Sometimes discrepancies occur in the same source: Diogenes Laertius, Lives of the Philosophers 7.1 1 0 ( = Chrysippus, frag. 828 [SVF 2:226]) contrasts with ibid. 7.157 (ibid.). The primary sources that attest the canonical eight parts are numerous: Zeno, frag. 143 (SVF 1 :39 = Nemesius, On the Nature of Man 96); Chrysippus, frag. 827 (SVF 2:226 = Aetius, Placita 4.4.4); idem, frag. 830 (SVF 2:226 = Porphyry, On the Soul in Stobaeus 1 .49.25a); idem, frag. 831 (SVF 2:226 = Iamblichus, On the Soul in Stobaeus 1 .49.34); idem, frag. 832 (SVF 2:226--27 = Philo, Questions and Answers on Genesis 1 .75); idem, frag. 833 (SVF 2 :227, assigned to various passages in Philo); idem, frag. 836 (SVF 2:227 = Aetius, Placita 4 .21); idem, frag. 879 (SVF 2:235-36 = Chalcidius, On the Timaeus 220); Philo, De opificio mundi 1 1 7; Iamblichus, On the Soul 12 (Finemore and Dillon trans., 37). For discussions of the Stoic division of the soul, see Safty, Psyche humaine, 293-97; Dillon, Middle Platonists, 1 02; and Stein, Psychologic der Stoa, 1 :1 1 9-25.

48 On the rejection of the Platonic tripartite soul see Chrysippus, Fragment 829 (SVF 2:226 = Origen, Against Celsus 5.47). On variations in the Stoic tradition see Schindler, Stoische Lehre von den Seelenteilen, 326-45, 53-70; van Straaten, Panetius, 1 19-29; Spanneut, Stoicisme, 96; and Pohlenz, Die Stoa, 2:100-1 12. The variations are dependent almost wholly upon Tertuallian, On the Soul 14, whose intent on making the Stoics contradict each other probably skews the picture. See also Dillon, Middle Platonists, 1 74-75, who lists the various divisions of the soul - sometimes contradictory systems­ taught by Philo. This difficulty shows that Philo was not confused or capricious but was aware that "each of these divisions expresses some aspect of the truth" (ibid., 1 75).

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197 accordance with the form (lb£av) of the connate spirit."49 He associates this spirit with the shape of the human being, both in essence and in physical form, and he says it explains why man lacks neither form nor shape "in the factory of nature."50 Thus, the " connate spirit" here corresponds to the eighth faculty in his anthropological decalogue, since it is higher than, but nevertheless affects, the physical shape of human beings. In contrast to the general human being, " the individual man is characterized (xaQaKTflQLi:;am) by the impression

(n)nwmv) of his choices entering into (t:yyLVOf..tEVflV) the soul."51 The parallel terminology to §134.2 (nQOayLvowvov, xaQaKTflQLGnKov), where the tenth part, the mark of the Holy Spirit, is discussed, shows that the faculty that "impress[es one's] choices" in the soul in book four is the same as the tenth element in Clement's anthropological decalogue. This is confirmed further on: "By this [impression] we say that Adam, as regards his formation, was perfect. For he lacked none of the things that characterize (xaQaKTflQLi:;ovTwv) the form and shape of a human being."52 At the root of both this description and that of the tenth and highest part of the anthropological decalogue is the idea of a person freely choosing the things that characterize or - to capture the overtones of xaQaKTTJQ -inscribe themselves into a person's soul. Further into his excursus on the Decalogue Clement returns (§136.4) to this contrast between the lower eight and the upper ninth and tenth human faculties. The two tablets on which the Ten Commandments were written are said to indicate that "the commandments

49 Stromateis 4.23.150.2. 5o Ibid. 51 Ibid . s2 Ibid . 4.23 .. 150.3.

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198 are given to the two spirits, both the one formed and the ruling faculty (TJYE!-lOVLKcfJ)." The difference between the two spirits corresponds to the difference between sense perception and the mental process (§137.1). This describes the eighth and the ninth faculties of the anthropological decalogue. The eighth element is conceived as part of the realm of sense perception. The tenth element is referred to earlier in book six (§103.5), where Clement compares the perfected gnostic to Moses, whose face shone.53 This glorified face is called the "characteristic mark (i.blwf.la xaQctK'rT)QLanK6v) of the just soul." This depends directly upon his terminology for the tenth faculty. For Clement a person incorporates this faculty into his life as his highest divine power. When the gnostic is perfected as far as his human nature allows, this radiance unites him to God.54 To bring all these threads together: Clement's eighth faculty is the breath or spirit that God breathed into man at his creation.55 It is common to all people, and it provides for them their structure, both their physical makeup and their essence. This formed spirit is part of the faculties of sense perception, although it is the highest of these, placed above language (i.e., the voice) and the capacity for procreation. The Stoic ruling faculty, the TJYE!-lOVLKOV, the governor of all sense perception, is Clement's ninth faculty. His tenth faculty, the characteristic mark of the Holy Spirit, is the highest divine principle, applied by a person as he chooses the things he wishes to imprint upon his soul. The mark of the Holy Spirit transcends the ruling faculty, since it allows a person to be assimilated to God, as far as human nature allows. 53 Ex 34.29. 54 Stromateis 6.12.104.1. 55 Gen 2.7.

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1 99 The distinction between the eighth and tenth faculties mirrors one of Clement's more important theological themes, the distinction between the image and the likeness in God's creation of humanity. Clement takes image in the Biblical text to refer the state of man at his creation, and likeness, to his eventual acquisition of perfection.56 This distinction between image and likeness, along with its variations, runs throughout the patristic tradition.S7 It is no different here: the eighth faculty, the formed spirit, corresponds to the image of God; the tenth faculty, to the likeness. Clement's anthropological decalogue shows that he regarded the standard Stoic anthropology as incomplete, lacking two prominent aspects of man taught in the Scriptures. By inserting into the Stoic scheme the faculty of the formed spirit (his new eighth element), Clement teaches that the divine form is common to all people . His inclusion of the mark of the Holy Spirit as the tenth and highest faculty shows that Clement regarded the ruling faculty (the hegemonikon) alone as unable to account for the way people could be assimilated to the likeness of God. There must be a faculty higher than the hegemonikon. After all, everyone has a ruling faculty, but not everyone who diligently exercises it becomes divine. At the same time, Clement's preference to subordinate the spiritual faculty to the ruling faculty, and not vice versa, shows that he held God's spirit to be an essential part of every human being, and not just the elect. For Clement the spiritual faculty is more central

56 Gen 1 .26; Clement, Pedagogue 1 .1 1 .97.2, 1 .12.98.3; idem, Stromateis 2.22.131 .2, 6. 57 There are many studies devoted to this theme. See, for example, Crouzel, Theologie, 67-70; Graef, L'image de Dieu; Hamman, L 'Homme image de Dieu; Ladner, "Image of God"; Merki, Omoiosis Thea, 4459.

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200 and basic to human existence than is even governance over the senses. It is possible to detect here a tacit criticism of Valentinianism, which sorted people into three categories ­ corporeal, soulish, and spiritual - and which taught that only the elect were spiritual. For Clement, the only faculty of the anthropological decalogue that might be missing from, or at least minimized in, a person is the tenth, since in book two, discussed above, he urged his audience to overleap the nine faculties to the tenth, the mind.58 Life in the tenth element is not guaranteed without effort. But the spirit, imparted in creation, is found universally. For Clement all people are inherently spiritual, in that they bear the breath of God. Clement developed his intricate anthropological decalogue to provide a coherent and distinctively Christian account of the world, an account that did not merely repeat the philosophical tradition, but challenged it with an alternative structure that was just as, if not more, numerically harmonious.

SIXES AT SEVENS, SEVENS AT EIGHTS Back to the excursus on the Decalogue. To discuss the Commandment relating to the Sabbath (§137.4), Clement adopts the strategy of Jewish and, possibly, Christian predecessors who sought to establish the philosophical soundness of the Mosaic Law. God needs no rest, he argues, so the rest the Sabbath provides is really our enlightenment by knowledge and our establishment in dispassion. Clement then indicates that his discussion (§138.5: A6yoc;) has slipped into the theme of the hebdomad and ogdoad (the hexad is not a matter of concern until the next sentence), and that the discussion is something of a tangent

ss See p. 189, above.

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201

(rv 7HXQEQY
( iAaa116v), which makes acquisition of the promise possible, is brought on the eighth day (a point not specified in the Septuagint). According to Clement, Ezekiel's references to seven and eight days point to the doctrine of the hebdomad and ogdoad. In all three of these examples a certain theme emerges: the hebdomad symbolizes rest, but is surpassed by the ogdoad, wherein is the promise of gnostic perfection. Clement does not consider this to be his personal opinion. Quoting from Clement of Rome, he discusses his namesake's treatment of Psalm 33.13 (34.12): "Who is the man desiring life I yearning to see good days?"61 Breaking into the quotation, Clement comments, 59 Stromateis 5.6.36.3.

Stromateis 4.25.158-59. 61 Clement of Rome, Letter to the Corinthians 22, cited in Clement of Alexandria, Stromateis 4.1 7.109.1-2. 60

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202 "He then adds the gnostic mystery of the hebdomad and the ogdoad," then resumes his citation of Clement of Rome and Psalm 33: "Stop ( navaov) your tongue from evil I and your lips from uttering deceit I Turn away from evil and do good I seek peace and pursue it." Presumably, the mystery of the hebdomad is in the verb navaov, translatable as "rest!" Which words or ideas in this quotation refer to the ogdoad is more obscure. It may be the commands in the last verse, to turn away (£KKAtvov), seek ((iyr11aov), and pursue (blcvl;ov), presumably to the realm of the ogdoad. The grammatical subject of Clement's comment inserted after Ps 33.13 (34.12) is ambiguous, probably intentionally so. By it he suggests that both David and Clement of Rome composed literature with an awareness of the doctrine of the hebdomad and ogdoad. The lesson Clement tacitly drives home is that the gnostic Christian should be sensitive enough to the doctrine to detect it in certain keywords that would elude the careless or less-disciplined reader. The technique resembles Valentinian exegesis.62 Even Plato was sensitive to the doctrine of the hebdomad and ogdoad. Clement cites Plato's Republic: "Now when seven days had reached the [spirits] that were in the meadow, on the eighth they were obliged to proceed on their journey and arrive on the fourth day."63 He claims that Plato here prophesied of the Lord's Day, where "seven days" refer to the motions of the seven planets, hastening to their goal of rest. The meadow constitutes the eighth, fixed sphere (Ti]v anAavf) acpai:Qav), and the journey represents the passage beyond

62 See above, pp. 32-38. 63 Plato, Republic 10.616b; Clement of Alexandria, Stromateis 5.14.106.2-4.

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203 the planets to the eighth motion and day. This eighth level, the fixed sphere, Clement elsewhere calls Atlas, the dispassionate pole, and the unmoved aeon.64 Clement was not alone. Heracleon and Theodotus also taught variations on Clement's doctrine of the hebdomad and ogdoad. Heracleon, when commenting on John 4.17, the account of the Samaritan woman, claims that she had six, not five, husbands.65 He takes the six husbands to refer to all material evil, and he claims that the woman didn't technically have a husband, since her true husband resided in the aeon. Since for Heracleon six symbolized material evil, it is likely that he assigned seven (that is, the Samaritan woman's seventh husband, in the Pleroma) to a more perfect nature. This is hinted at in the remnants of Heracleon' s discussion of John 4.52, when he explains why the official's son was healed at the seventh hour: "Through the seventh hour the nature of the one healed is depicted."66 Elsewhere Heracleon assigns eight to an even higher, spiritual nature.67 Six, seven, and eight symbolize the stages from the material world to spiritual perfection.

Stromateis 5.6.36.2. 65 Heracleon, frag. 18 ( Origen, Commentary on John 13.69-72). On Heracleon's apparent departure 64

=

from the text of the New Testament in this passage, see Ehrman, "Heracleon, Origen," 112-13. 66 Heracleon, frag. 40 (= Origen, Commentary on John 13.416-26). Wucherpfennig, Heracleon Philologus, 320-21, denies that this passage refers to the doctrine of the six, seven, and eight, and suggests, rather, that it refers to the seventh day of Creation and God's restoring human nature to its original good standing. But frag. 40 (at Origen, Commentary on John 13.424) discusses a nature that is "depicted" (XCXQCXKTT)Qti:;erm), not "restored." In this passage natures are not transformed (as Wucherpfennig's reading would require), they are revealed. True, the first to describe the royal official's son's nature as "psychic" is not Heracleon but Origen (idem, 13.431), but it appears, from the ensuing polemic, that Origen introduces the term at Heracleon's prompting. 67 Heracleon, Fragment 15 ( Origen, Commentary on John 1 0.248-50), treating Jn 2.19 ("Destroy this temple and in three days I will raise it up." Heracleon takes [v TQlCJLV to mean [v TQtTq, which he in turn takes to mean not only the day of the Resurrection, but "the spiritual day," wherein "the resurrection of the Church is made manifest." In the same fragment, Heracleon describes the first and second days (= Friday and Saturday, the sixth and seventh days) as "of clay" (xo·iKTjv ) and "of the =

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204 The same doctrine was part of the theology of Theodotus, a second-century Valentinian.68 According to Clement's notes, the Excerpts from Theodotus, Theodotus held that the rest (avarravcnc;) of the pneumatics - elect and spiritually advanced Christians - lay in the Lord's Day, the ogdoad. For those psychics who were faithful, their souls would eventually, at the time of perfection, ascend from the presence of the Demiurge to the realm of the ogdoad.69 The Demiurge was symbolized by the number seven in Valentinianism. Thus, for both Theodotus and Clement, the hebdomad and odgoad were places of rest and perfection, respectively. Of course, Theodotus assigns the realm of the odgoad primarily to his own circle of pneumatics, an elitism Clement criticizes throughout the Stromateis. But this shows only that Clement and Theodotus were using the same number symbol, but to different ends. Clement finds the association of seven with eight in the Scriptures, in ecclesiastical authors, and in philosophy, whether or not the hebdomad and ogdoad are explicitly mentioned.7° Because the notion of transition from rest to gnostic perfection, symbolized by seven and eight, is so dominant, Clement looks for the theme wherever he reads. This, then, explains why Clement felt his exposition of the Sabbath had led to a critical subexcursus. Treating the themes of seven and rest, Clement, out of habit, considered it imperative to also

soul," (lf!uXLKfJv) respectively, thus reinforcing his view, that the eighth day symbolizes spiritual perfection. 68 On Theodotus, see DECL 571 and below, excursus F. 69 Excerpts from Theodotus 3.63. 7D For more examples (such as Stromateis 7.10.57.4-5) and analysis of the seven and eight in Clement of Alexandria, see Itter, "Method and Doctrine," 43-55.

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205 consider the role of eight (§138.5, lines 1-3). But to understand why six and seven are also invoked (lines 4-5), we must first explore his discussion of the Transfiguration.

THE ARI1HMETIC OF TRANSFIGURATION Clement's subexcursus on the relationships of seven to eight and six to seven (§§138.5-145.7) has been studied most thoroughly by Delatte, who was also the first to recognize that Clement's exegesis of the Transfiguration depends upon the teachings of Marcus?1 Delatte's commentary is perceptive, and I shall include some of his observations as I proceed. Clement begins (§138.5) with the cryptic claim, "The odgoad is likely to be chiefly a hebdomad, and the hebdomad, a hexad, at least apparently. The first is likely to be chiefly the Sabbath, but the hebdomad, a woman worker."72 In the remainder of the excursus Clement sets out to explain the paradox of how an eight can be considered Sabbathlike, and seven, workerlike. Clement itemizes the various properties of each of the numbers six, seven, and eight (§§138.6-140.2).73 He spends the most time on the number six, pointing out its role in the cosmogony, the course of the sun, and the cycles of plant life. He appeals to the importance of six in embryology and to the arithmetical properties that led the Pythagoreans to make it a symbol of mediation and marriage. Six is a function of generation and motion. Seven is depicted as motherless and childless, an allusion to its arithmetical properties, since seven

71 Delatte, E tudes, 229-45. 72 Woman worker: iQya:w;;; see Prov 6.8a LXX. 73 Delatte, E tudes, 234-35, identifies Clement's sources. See also parallels in the sections of the Theology of Arithmetic devoted to the 6, 7, and 8.

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206 neither is the product of, nor produces, any of the numbers in the Decad?4 Seven was traditionally assigned to Athena, the virgin born without a mother. Clement, however, takes the Pythagorean epithet to refer allegorically to the Sabbath and the form of rest in which "there is neither marrying nor being married."75 The ogdoad is briefly described as the cube, the fixed sphere, and a participant in the Great Year?6 Delatte notes that Clement is drawing here, and in a later passage concerning the excellence of seven (§143.1-145.2), from a Jewish tradition of arithmology, evident in the writings of Philo and Aristobulus, who argue that Jewish law and custom harmonize with Hellenic philosophy. Although Clement uses Aristobulus, this is probably mediated through someone like Hermippus of Berytus, a grammarian (possibly Jewish or Christian) of the early second century, whose lost treatise

On the Hebdomad is mentioned in §145.2. Up to this point, Clement has marked only the differences between six, seven, and eight. There is nothing up to this point to justify his claim at §138.5 that there is an identity between them, or a transformation from one to another. To make this connection Clement turns to the Transfiguration (§140.3). He locates the event on the eighth day, and the Lord as the fourth person (after counting Peter, James, and John). The Lord ascends the mountain

74 There are dozens of ancient references. See, e.g., Aristotle, frag. 203 (= Alexander of Aphrodisias, Commentary on Aristotle's Metaphysics 38); Philo, On the Creation of the World 1 00; Theology of Arithmetic 41 .30; Theon of Smyrna, Mathematics Useful for Reading Plato 1 03.14-16; Nicomachus of Gerasa in Photius, Biblioteca 1 44B. 75 Mt 22.30.

76 Fixed sphere: TTJV ani\avi) . . . cnpaiQCXV: see Stromateis 5.106, cited above. Because of precession, the drifting of the earth's axis across the stars, the zodiac appears over the centuries to rotate slowly around the earth. The time it takes for one house of the zodiac to return to the place where it started from, calculated by modem astronomers at 26,000 years, is called the Great Year. The length of the Year was a very old topic. See, e.g., Plato, Republic 8.546.

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207 and, at the appearance of Moses and Elijah (i.e., two more persons), becomes the sixth. The voice of God Clement reckons as the seventh character, and Jesus is made manifest as the eighth, God. The explanation depends upon Marcus (see chapter 2). But is Clement following Against Heresies or do Irenaeus and Clement depend upon a common source? Delatte suggested the latter, since both authors give details lacking in the account of the other. Most recently, Forster has suggested that Clement depends on only Irenaeus since Clement does not otherwise employ Marcus's doctrine?? Forster's view seems correct. In the recent past scholars have observed Clement's overt and tacit use of Irenaeus.78 In the clearest parallel between the two, the interpretation of clean and unclean animals in the Law, Clement adapts Irenaeus' s vocabulary and thought, occasionally quoting nearly verbatim, at other times adding his own explanations?9 As we shall see, this is how Clement handles Marcus's teaching. Sometimes he quotes Irenaeus verbatim, other times he adds to Irenaeus' s account, so as to revise the interpretation and make it his own. Compare the passages:

[§140.3, line 10; gray shading indicates textual parallels] TatrrlJ TOL 6 KUQLOs TETaQTOs ava � ixs c is '[0 OQOs EKTOs y(vETaL Kal cpunl 7IEQIAcX�-t7IETaL 7IVEU!-1£X'rlKcfl, TTJ V bvva�-tLV TTJ V an' atnov naQaYV!JVWaas c is oaov ol6v TE T]v tb{iv wis 6Qav £10\cycim, bt' £�b6�-tTJs

So on this [eighth day]82+ the Lord, as the fourth, after ascending the mountain becomes a sixth and is radiated by a spiritual light, making bare his power - as far as it is possible for those who have chosen to see to perceive-and heralded

77 Marcus Magus, 252, n. 207. 78 See Behr, Asceticism and Anthropology; le Boulluec, "Exegese et polemique antignostique," 707-13; and Patterson, "Divine Became Human."

79 Clement of Alexandria, Stromateis 7.18.109.2-1 10.1, adapting Irenaeus, Against Heresies 5 .8.3.53-84. The parallel is analyzed in Hort and Mayor, Clement of Alexandria, and Patterson, "Divine Became Human."

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208 avaK11QU000f1EVO(_; [line 15) ti'Jc_; ¢wvflc_; ULO(_; dvm 8 wu, tva bl) o'i flEV avanavawvrat rraa8£vrEc; nEQl. a{rwv, CfrJ+ b£, bu't ycviaEwc;, f)v ebf)i\waEV i] n;ac;, E7TLOllf10c_;81+ oyboac; vnaQxwv ¢avrj, 8Eoc; f.v aaQKLc}> 'ITJV bvvaflLV EVDE LKVVflEVO(_;, ClQL8f10Uf1EVO(_; flEV we; aV8QW7TO(_;, KQU1T'!OflEVO(_; bi: oc; llV"

by the seventh, the voice, to be the Son of God, so that those who are persuaded about him might rest, while he, being an episemon ogdoad, might be manifest through his generation (which the hexad clarifies) as God, demonstrating his power in a bit of flesh: numbered as man, but concealed as he was.

[Irenaeus, Against Heresies 1 . 14.6.272-77] Tou'!ou '!OU i\6you Kal. TfJc; OLKOVOflLac; '!aVnJc; KaQn6v ¢TJaLV ev OflOLWflan ELK6voc; nE¢TJVEVaL EKEi(vov) '!OV flE'!a '!ac; eE, tlflEQac; '!E'!aQ'!OV avaf)av'!a de; '!0 OQOc; Kai ycv6f1Evov EK'!ov, '!ov Ka'!af)av'!a Kai KQa'!YJ8Ev'!a f.v '!� 'Ef)boflabL, EITLOll flOV 'Oyboaba vnaQxov'!a Kal. £xovra f.v £au'!cf1 '!OV a navra '!�JV G'!OLXE LWV ClQL8 f10V.

[Marcus] says that the fruit of this account and this plan is that he was manifest in the likeness of an image (Rom 1 .23), he who, after six days, ascended the mountain as the fourth and became a sixth, he who descended and was held in the Hebdomad, being an episemon ogdoad and possessing within himself every number of the oral letters.

Delatte pointed out that the two passages complement and explain each other. Clement's description of Jesus as f.n(aT]flOc; is intelligible only when we consider that Marcus calls Jesus this because his name consists of six letters.83 Likewise, the peculiar suggestion in Irenaeus' s report of Marcus's doctrine, that Christ was held in the hebdomad,

so Substituting Delatte's 6 for the 6 in SC and the oi- dittography from the line prior- in the

manuscript. 81 I delete the comma here, following Sagnard, Gnose valentinienne, 378, and Dupont-Sommer, Doctrine gnostique, 47. On the coined phrase, episemon ogdoad, see above, p. 9 1 . 82 The precise referent of TatYI:lJ i s missing from the A N F and SC translations. I t must refer t o the odgoad because that was the topic of the previous section and because TaUTTJ corresponds to Marcus's pna TtXC: E:l; fJf.lEQac:. It may possibly refer to the last word of §140.2, avTanobOm:wc;, but even this term Clement gives the nuance of eightness. But my reconstruction makes sense in light of Lk 9.28, which places the Transfiguration on the eighth day, unlike Mt 1 7.1 and Mk 9.2, both of which place it "after six days." Clement follows Luke; Marcus follows Matthew and Mark. 83 Delatte, E tudes, 238. Irenaeus, Against Heresies 1 .14.4.

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209 is intelligible only in light of Clement's version, where the seventh is identified with the voice, which possesses Jesus and declares him to be the Son of God at his baptism.84 Delatte argued that, for both Clement and Marcus, Christ is represented inclusively as six, seven, and eight, numbers that symbolize the Incarnation. Thus, according to Delatte, Clement's version of Marcus's account of the Transfiguration synthesizes the previous sections discussing the properties of six, seven, and eight (§138.5-140.2), and help demonstrate Clement's claim, since Christ himself is six, seven, and eight. The problem with Delatte's interpretation is that, strictly speaking, Christ is identified by Marcus and Clement, not with seven, but only with six and eight. The seventh character is reserved in Clement for the voice of God, not Jesus. Thus, six, seven, and eight are not indiscriminately all symbols of Jesus, as Delatte claims. Also, what started Clement on this tangent in the first place was the proposal that the ogdoad is a hebdomad, and the hebdomad, a hexad (§138.5). This requires a transitive relationship, of 6 ----* 7 ----* 8, or 8 ----* 7 ----* 6. But neither Clement's nor Marcus's account of the Transfiguration suggests that Jesus went from being the sixth to becoming the eighth, via the seventh. Clement may have originally (§138.5) proposed to demonstrate a transformation of six into eight, but that does not occur here, at §140.3. The only transformation of numbers in this passage is from four to six, when Jesus becomes the sixth after the appearance of Moses and Elisha. Clement states (as does Marcus) that Jesus is concurrently six and eight-the episemon ogdoad -without implying any transition between the two (at least, not in §140.3). Even if a transition could 84 Although his comparison seems to be correct, Delatte, E tudes, 238-39, does not explain specifically

how the voice "possesses" Jesus, in either the Transfiguration or the Baptism. The puzzle still remains.

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210 be established, there i s nothing to suggest that i t happened via seven, which i s assigned, as already mentioned, to the voice. Both passages emphasize the differences, not the transformations, among six, seven, and eight. Clement's version in particular constitutes a Christian parallel to the arithmology of §§138.6-140.2, which lists the distinct properties commonly known in the Greco-Roman world among six, seven, and eight. Clement uses a single event, the Transfiguration, to depict the Christian understanding of the symbolic significance of six (generation), seven (the voice), and eight (divinity), arraying the symbolism for all three numbers in a single, static image.

A closer look at the vocabulary of §140.3 bears this out. We have mentioned above the care Clement shows when he reads other authors and "discovers" in them the doctrine of the hebdomad and ogdoad. Sometimes there are key words that make this explicit, such in Plato's Republic. Other times, there is little or nothing to make this association explicit, most notably his treatment of Clement of Rome and Psalm 33 (34), where a word reminiscent of seven, navaov, spurs Clement to invoke the doctrine of the hebdomad and ogdoad. Clement considers Scripture to have been written with extreme care. There are no superfluous words, and each word is chosen for its symbolic overtones. I suggest that Clement composes his explanation of the Transfiguration with the same care. He chooses words that have subtle overtones of number symbolism, and thereby gives a fuller Christian arithmology of six, seven, and eight. Clement gives to Christ the epithet episemos ogdoad. This epithet, which features prominently in Marcus's theology (see chapter 2), conjoins six and eight, a mathematical and theological paradox. Six represents the created, m aterial world; and eight, spiritual perfection, the divine realm. Notice how the paradox is reflected at the end of §140.3, where

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21 1 Jesus is "numbered as man," but hidden "as he was." Six corresponds to "man," and eight, to "as he was," i.e., God. Between these two phrases, however, is 8coc; f.v craQKL4J -olv

buvaf.HV E.vbnKVVflEVOt;, a phrase that can also be interpreted as a cipher for six-eight: craQKLCfl is six; 8E6t; and buvafl Lt;, eight. The entire clause, from 6 bt to the end, reiterates in three compact phrases the mystery of the Incarnation as a combination of six and eight. Likewise, the first instance of buvaflLs (line 13), just as the second (line 1 8), should also suggest the number eight. This is consistent with Clement's exposition, since this first instance describes how Christ laid bare, as much as his companions could manage, his divinity. Divinity is often represented as the number eight in Clement. The spiritual light in which Jesus is cloaked, then, is the radiance of this "eightness." This entire phrase alludes to the eightness of the Transfiguration, and complements the next phrase, which explicitly identifies seven with the voice that permits his disciples to find rest: E:[3b6f1lls, <j:>wvf]c;, and

avanaucrwvrm all resonate with each other. By finding rest, the disciples, who are products of generation, and therefore symbolized by six, move from the realm of six into seven. Read this way, the unshaded text in §140.3, which has no parallel in Marcus/Irenaeus (from KaL <j:>W'rL to ITEQL av'fov) constitutes a miniature Christian arithmology on eight, then seven. It moves on to six - the generative aspect of Jesus -where Clement picks up again from Irenaeus' s text, and then ends in a terse meditation on the Incarnation as a combination of six and eight. Thus, the material in Clement but not in Marcus/Irenaeus is to be attributed not to teachings of Marcus unreported by Irenaeus yet reproduced by Clement- the scenario endorsed by Delatte -but to Clement's careful rewriting of Irenaeus' s version of Marcus's account

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212 THE EPISEMON: THE TRANSFIGURATION OF ARITHMETIC Clement's account of the Transfiguration moves, not to the baptism of Jesus, as Marcus's does, but to the order of the alphabet and numerical notation. This, too, is a theme upon which Marcus touches, but Clement pursues the matter further. He begins by explaining how six is included in the order of the numbers, but the sequence of the alphabet shows that the episemon is not written with a letter. That is, numerals, using the alphabetic system of numeration, follow the sequence a', W, y ', b', E ', c; ', (, , r (, and so on. The number six is '

represented by the episemon. But when the alphabet is written out-a, �, y, b, E, (,, 11, and so on - it shows that the episemon is unwritten. He explains that the difference between the two sequences is created by the intrusion of the episemon, which disrupts the alphabet, a disruption that he takes as a cipher for his doctrine of the six and seven, and subsequently of the seven and eight. Here is the relevant text.

[§140.4] TlJ f.l EV yaQ 'ra�El 'rWV lXQL8f.1WV

For the [number] six is included in the cruyKa'raA£ynm Kai. 6 £�, � bi:: 'rwv CY'rOLXE LWV order of the numbers, but the sequence of aKoAov8 (a E 71 LCY11f.10V YVWQL(,El '[Q f.l� the oral letters makes known that the episemon is unwritten. Thus, according to yQa¢6f.1Evov. [§141.1] ev'rau8a Ka'ra f.lEV the numbers themselves, each monad is 'rove; lXQL8f.10Vc; at)'[OVc; crc}J(,E'raL 'rlJ 'ra�El preserved in sequence, up to the EKaCY'rll f.lOVac; de; [ �bOf.laba '[E Kai. oyboaba, hebdomad and the ogdoad. But according Ka'ra bi:: '[QV '[WV CY'rOLXE LWV lXQL8 f.10V EK'[OV to the number of oral letters, the zeta y (vE'raL 'rO C,i]'ra, Kai. E.�bOf-lOV 'rO f} [2] becomes sixth, and the eta, seventh. But 'E KKAanEV'roc;85 b' OUK otb ' onwc; '[OU EnLCYTJ f.lOU de; u)v yQa¢i]v, eav oih-wc; when the episemon - I don't know how ­ i:: n wwea, EK'rll f.lEV yivnm � [�bof-lac;, slips into86 writing (should we pursue it in £�bow1 bi:: � oyboac;· this manner) the sixth [letter] becomes the

ss M s reading. Stahlin: Eicnv\an£vwc;. 86 Or "slips out of." See discussion, below.

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213 hebdomad, and the seventh, the ogdoad.87+

To unravel this cryptic passage, preliminary comments on two aspects of Greek grammar are in order. First, as already discussed, crrOLXEiov, the oral letter, was distinguished from YQll!-1!-HX, the written.88 Clement also seems to hold the grammarians' distinction between spoken letters and written letters. The phrases 'l"O 1-1� yQa¢61-lEvov and

de; 'r�V yQa¢r1v show that he sees the episemon as dwelling in the written sphere, not the oral one. That is, the episemon is a written letter, not an oral one. Second, Clement is not discussing the digamma, the archaic Greek letter derived from the Phoenician waw. His comments here are frequently misread because modem readers conflate the episemon and the digamma. It is common knowledge today that the earliest Greek alphabets included in the sixth place the Phoenician letter waw, first written like a Y, but later, as F.89 When the digamma dropped out of use, the written letter was preserved in the Milesian system of numeration. The episemon is seen as the direct

87 This last clause, at first glance, seems as if it should be translated, "the hebdomad becomes sixth and the ogdoad, seventh." But it is nearly impossible to make sense out of this. The episemon is a numeral (see above, p. 91). Hebdomad and ogdoad always refer to numbers, not numerals or serial rank. For the number seven to become sixth would require the loss of another number, not a numeral. This reading would also require the text to be emended to EK 'rfJc; yQacpfJc; (on which possibility see below). Even then, it is a stretch to make sense of the loss of the numeral episemon as altering the numbers. Thus, in my view, this clause makes best sense when EK'rll and i'(3Mf-!ll (sc. yQacpl'J) are taken as the subjects. These symbols "become" the hebdomad and the ogdoad by virtue of their new symbolic values. They lack articles since ordinal numbers often do, and their predicates have definite articles because they are well-known abstractions. See Smyth, Greek Grammar, 1125c, 1125n, and 1 152. On the ambiguity of subject and predicate in Greek see Kahn, Verb "Be, " 39-40. 88 See above, p. 83 and n. 13. 89 Hence, the term, digamma, attested in the post-classical period, since the character looks like one uncial gamma superimposed on another. See L SJ 752a, s.v., "p" and Larfeld, 294.

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214 descendant of the obsolete waw. But late antique and medieval treatments of the digamma show no awareness of its association with the number six. Greek grammarians in late antiquity did not even assign the digamma a place in the sequence of the alphabet. Further, no ancient discussions of the parasema - the nonalphabetic numerals- mention the letter digamma.90+ One scholium on Dionysius Thrax states very clearly that the digamma was never associated with the number six. This scholiast entertains the theoretical objection that, because the digamma is a letter, Dionysius Thrax' s claim that there are twenty-four written letters must be faulty. The objection runs: both a xaQ£XK'rTJQ and an 6vof.la are concomitant with every oral letter; the digamma has both, so it too should be reckoned with the oral letters. The scholiast lays out several responses to this argument, one of which runs, "Again, every character (X£XQ£XK'rTJQ) of the oral letters designates a number. For the a indicates the

90 All ancient references known to me concerning the episemon are discussed above, pp. 86--S S.Scholia on Dionysius Thrax 1 .3 :496 .6--7 appears at first glance to identify the digamma with the Greek numeral for six. The scholiast entertains the question, Why are there twenty-four letters (yQcXf-lf-llXHX) when there are other characters and inscribed figures, and other nations have their own letters, and there are certain other figures: "the digamma, the koppa, the so-called parakuisma, the insignia, and things written alongside letters, and the crown?" l wx TL bi:: Kb ' i'¢11 Eivm Ta YQcXf.lfllXTa E i yag YQcXf-lf.llXTa Eicnv oi xagaKTijQEc; Kai oi E,vaf.lol, YQcXf.lfllXTa bi:: Kai Ta naga Xat\baimc; Kai AiyvnTimc;, KaL nva ETEQa, n) blyaf-lf-llX Kai To Konna Kai TO Kat\ovf.l E Vov nagaKv"iaf.la, Kai. Ta GllflEia, Kai. Ta 711XQEyyQacp6f.!EVIX Toic; GTOLXELOLc;, KIXL r'] KOQWvic;, KIXL El n TOL01�JTOV, lXTOnwc; ¢llai.v on Kb ' EGTLV. This passage has guided scholars, including LSJ 1 562a, s.v. "M" and LSJ, Supplement 1 14, s.v. "xnagaKv"iaf.la," to define naQaKv"Lafla as the term for the numeral q. The problem with this conjecture is that it assumes the author identified the digamma with the numeral c; and that the author intended to list all three non-alphabetic numerals. This is possible, but it should be demonstrated, not assumed. In this passage nagaKv"iaf.la - a hapax legomenon - can be read with biyaf.lfllX and Konna as a threesome, but this is not required. It might actually form a pair with TG Gllf.!Eia. Given the root meaning of naQaKv·iafla -a KVYlfllX is a fetus-it is very difficult to see how the character q could be inferred. Jannaris, "Digamma, Koppa, and Sampi," 39, suggests the q "is a naQaKt\ivov yivvllfllX, a slanting letter," but offers no explanation of how it resembles "offspring." In reality, we have no clue what naQaKv·iaf.la means. This scholium on Dionysius Thrax is the only ancient text that might possibly be interpreted to connect the digamma with the numeral six, a shaky foundation, given my arguments below.

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215 number one, and the (3, two, and so forth. So therefore, if the character of F doesn't indicate a number, it is clear that it is not an oral letter."91 The scholiast pursues several other arguments for not treating the digamma as a letter, of no concern to us here. This much is clear, that he regarded the digamma as having no corresponding numeral and therefore no place in the order of the alphabet. Other parallel scholia discussing the digarnrna do not repeat this argument, but they also do not associate the digamma with the number six or any ordinal place in the alphabet-92 This explains why Ptolemy, in his Harmonics, uses both the digamma and the episemon in the same sentence to refer to two different things: the digamma for a musical tone and the episemon for a numeraJ.93 Also relevant is a rather obscure Greek text, On the

Mysteries of the Greek Letters, extant only in a Coptic translation and preserved in a fourteenth-century manuscript-94 The text, which is little known today, has been dated to the fifth or sixth centuries, but I suspect it is even later.95 The author claims the Greek

91 Scholia on Dionysius Thrax 1 .3:187.22-25. "En nac;; XCXQIXKTllQ aTOLXElWV 01]!-llXLVEL cXQL8 !-16v· Kai yaQ n) a OIJ!-l lXLVEL n)v ifva cXQL81-16v, Kai n) � n)v Mo, Kai i:!;i)c;; · E i aQa ovv 6 XCXQCXKTllQ TOVF ov 0fJ!-11XLVC l cXQL8!-10V, bi);\ov on OVK [an GTOLXELOV. 92 Scholia on Dionysius Thrax 1 .3:34.15-23; 2.1 :76.32-77.12. At first glance, the Georgian alphabet seems to provide evidence that late antique grammarians knew about the connection between F and �. The fifth, sixth, and seventh letters are a [ e], 3 [v ], and 'b [ z], and the alphabet was used for numerals in the fashion of Greek. But Mouraviev, "Valeurs phoniques," has demonstrated that the placement of extra Georgian letters such as 3 in the alphabet had nothing to do with the Semitic alphabets, but was the careful, deliberate work of a phonologist. In Georgian, the phonetic equivalent of waw is the 22nd letter, ";:! [ii/w], assigned the value of 400 as an alphabetic numeral. 93 Ptolemy, Harmonics 2.1. 94 Hebbelynck's ed. Studies by Dupont-Sommer, Doctrine gnostique; Galtier, "Sur les Mysteres." 95 See Dupont-Sommer, Doctrine gnostique, 52, who affirms an early, ca. 5th-c. date. The text, however, plays with Syriac, Hebrew, and Arabic letters, suggesting that it was written after the rise of Islam. Further, the combination of theological polemic, letter mysticism, and interest in comparative linguistics is reminiscent of Jewish (and later, Christian) kabbalistic literature, dominant in the 13th c.

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21 6 philosophers moved the waw from its proper place and placed it after the nu, as part of their rejection of God, since God provided the waw as a prophecy of Christ.96 To this author, the Phoenician waw became not the digamma but the omicron! All these late-antique texts show that any original association there might have been between the numeral six and the digamma had been lost.97 This helps clear up a vexing textual problem at §§140.4-1 41.2. It is unclear whether Clement thought the letter slipped into writing, or fell out of it, since £1o\an£vroc; and de; 'rl)v yQacpi)v seem to oppose each other. Some scholars have argued that the text should read Eimo\an£vroc; (which would have Clement regard the character as entering the alphabet), others as

EK 'rflc; yQacpflc; (to

have Clement see the character fall into disuse).98 The former group seems not to have done so on the basis of the grammatical background, just discussed.99 Delatte's proposal, which depends upon the latter group, has Clement, in conformity with modem scholarship, meditate on the development of the Greek alphabet from its Phoenician roots. But this is not Clement's point. He is interested primarily in the difference between the alphabet and Greek numeration. Like the grammarians of his day, Clement saw no connection between the waw and the numeral six, since he considered the latter as a purely written, not spoken, 96 Hebbelynck ed., 27. 97 Given all this, we should guard against translations such as Williams, NHS 35:217 (Epiphanius, Panarion 34.6.4), which translates E ITLCJl'lflOV as "digamma." 98 Delatte, E tudes, 241 . 99 Delatte (agreeing with Serruys) rejected Stahlin's (agreeing with Lowth) argument for the first option, since it rested on the view that the last sentence in Clement's paragraph purports to say that the number seven then took the sixth place, and the number eight, the seventh. Stahlin argued for the first option by suggesting that the numbers themselves move. Of course, they do not. By affirming the second option, that the episemon fell out of writing, Delatte seems to have influenced the SC edition (446:342--43), which departs from Stahlin's text- otherwise the preferred edition -in favor of the manuscript Laur. V 3. But the French translation in SC reflects Delatte's preference.

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217 symbol. Thus, the text should read Eicnv\an:ivroc; b' ovK olb ' onwc; 'lOU £mm')flou de; 'l�V yQacpt1v.100+ The numeral six, the episemon, somehow entered into the writing system Clement admits his ignorance on the historical specifics-and thus disrupted the order of the alphabet. This emendation, in tum, makes Clement's illustration of his theology clearer: the episemon symbolizes Christ, who enters into the writing of the world and effects an alteration in the constitution of its oral letters/elements (cnOLXEia). Clement plays on the ambiguity of cnOLXEiov, treating it primarily as a letter of the alphabet, but also alluding to its alternate meaning as an element of the universe. He regards the inconcinnity between the alphabet and the numbering system to be the key to interpreting the effect the Incarnation had on creation. This same inconcinnity explains the numbers latent in the Transfiguration. There on the mountain, Jesus is revealed as the episemon ogdoad, the number eight in the guise of the numeral c;. The number eight is the unknowable God, the c; is his entry into the writing system.1 01 That intrusion causes the sixth element (a'LOLXEiov) to access the seventh, 100 There are other reasons for accepting the emendation. First, the alternate proposal, 'EKKi\anivTos

b' ouK oib onws wv i:mm'J1-1ou EK TTJs yQafJs, requires an alteration of three words, rather than just one. It seems to me more likely that a scribe wrote K for ta than the other possibility, that he wrote ta for K, plus two substitutions of v for a. Second, the last sentence in Clement's paragraph does not suggest what Stahlin said and what Delatte discounted (see previous n.); rather, as my translation and explanation propose, Clement sees the sixth letter becoming the hebdomad, which requires the standard twenty-four letter alphabet to antedate the alphabetic numerals. Third, the alternate proposal suggests that the episemon was originally in the alphabet, then disappeared, contradicting the previous sentence, which states that, prior to whatever happened to the episemon, zeta was sixth and eta seventh in the order of the alphabet. In light of these concerns, the episemon "slips into" writing. 101 Note here the contrast with On the Mysteries of the Greek Letters, which has the waw (episemon) represent Christ by virtue of its position after the first five stages of creation (alpha through epsilon) and before the two stages symbolizing Christ's advent (zeta and eta). In the Mysteries the episemon does not symbolize the lower of the two natures. Further, the Greeks are accused, not of dropping the ·

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218 and the seventh element (aTOLXEiov) to access the eighth. Thus, the apostles, b y trusting in him on the mount of Transfiguration, entered into the rest of the seventh. We would think that, by analogy, they would move from the seventh to the eighth, but Clement's interpretation of the Transfiguration (§140.3) does not state this, either explicitly or implicitly. But since he has now brought the subject up (§141 .2, echoing §138.5), Clement now turns (§141 .3-7) to Marcus's teaching on the number six. Clement draws from parts of Scripture that speak to the doctrine of the episemon, and then selects examples from geometry to establish the point he set out to make initially, that the ogdoad is likely to be a hebdomad, and the hebdomad, a hexad. His argument runs:

[§141 .3] bL<) KCXl EV TlJ EKT-r:J 6 av8QW7Wc:; A£yETCXL nEnon)a8m 6 T4J £ maiJf-l� maToc:; YEVOf-!EVOc:; we:; n)8£wc:; KUQLCXKf]c:; KAf]QOVOf-! Lac:; avanavmv i mo;\a�ELV . [4] TOLOl)'[OV '[L KCXL Tl fKTfJ WQCX Tf]c:; GWTfJQLOU oiKOVOflLac:; E f-lc}>a[vn, Ka8 ' ilv ETEAnw8fJ 6 av8QW710c:;. [5] vat f-!TJV TWV f-!EV OKTW CXL f-!Ea6TfJTEc:; y[vovTm i:nTa, Twv bi: i:nTa cpa[vovTa L dvm TlX bLCXGTTJ f-lCXTa lE,. [6] aMoc:; yaQ EKEivoc:; A6yoc:;, E71ClV i:: � bOf-!Clc:; boE,a(-r:J TTJV oyboaba KCXL "oL OUQCXVOL TOLe:; ovQavoic:; bLfJYOtJVTCXL b6E,av 8 wu . " oL TOlJTWV CXLG8fJTOl TlJ710L TCl 71CXQ' TJf-llV cpwvi)EvTa aTOLXEia. [7] ouTwc:; Kat avToc:; E LQfJTCXL 6 KUQLOc:; "aAcpa Ka i w, cXQXTJ Kai. '[E;\oc:;," "bL' ou '[Cl navTa EYEVETO KCXl XWQtc:; CXUTOU EYEVETO ovbi: EV."

[3] So also, it is said that in the sixth [day] the human was made, becoming faithful to the episemon, so as to receive straightaway the rest of the Lord's inheritance. [4] Even the sixth hour of the divine plan of salvation indicates this sort of thing; in it the human was perfected. [5] Indeed, there are seven intermediates of eight things, and there seems to be six intervals of seven things. [6] For there is that other saying, "When the hebdomad glorifies the odgoad and the heavens declare to the heavens the glory of God." (Ps 18.2) The oral letters that are our vowels are perceptible types of these things. [7] So also the Lord himself is said to be "alpha and o[mega ], beginning and end," (Rev 21 .6) "through whom

letter, but of rearranging its position, to fall after the nu. See Hebbelynck's ed., pp. 156-58. For other ancient Christian associations of Christ and the waw, also without overtones of number symbolism, see Danielou, Symboles chretiens primitifs, 150-5 1 .

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219 everything came into being, and without him not even one thing came into being." (Jn 1 .3)

The parallel from Marcus runs:

[Irenaeus, Against Heresies 1 .14.6.280-85] Kat btlt ·rofno Mwvata f.v TTJ EKTIJ �f.lEQ0 ELQT]KEVCCL TOV av8QW7WV ycyovtvm· KCCL TTJV OLKOVOf-1 LaV bE. EV TTJ EKTIJ '[WV �f.l EQWV, line;; fG'rlV � 11CCQCCUKEVTJ, lJ "(()V EUXCCTOV av8QW110V de;; avayivVT]aLV TOU 71QC�nou aV8QC�mou 71Ecj:>T]VEVCCL, f]c;; OLKOVOf-!LCCc;; UQXTJV Kat TEAoc;; TTJV EKTT]V wQav dvm, f.v 1J 71QOGT]Aw8T] Tc}J E;vA4-J.

And because of this, Moses said that the human being came into existence on the sixth day, and the divine plan, on the sixth day [of the week], i.e., the day of Preparation, in which the last human being is manifest for the rebirth of the first man. The beginning and end of this divine plan was the sixth hour, when he was nailed to the wood .

[ibid., 1 .14.8.320-25] Kaewc;; ovv ai f.rrTa, cpf]aLv, bvvaf.lnc;; bo�a(ovm "(()v A6yov,

He [Marcus] says: Therefore, just as the seven powers glorify the Logos, so also the soul in infants, crying and wailing, glorify Marcus himself. Because of this, David also said, "From the mouth of infants and sucklings, you have perfected praise," (Ps 8.3 [8.2]) and also, "The heavens declare the glory of God." (Ps 18.2 [19.1])

ovTwc;; Kai � l(Jvxi] £v Toic;; (3Qicpcm KAa(ovaa Kai 8QTJVOl)aa MaQKOv bo�a(n a-ln6v. bli'x TOVTO bt Kai. Tov �avib E LQT]KEVCCL" "'EK GTOf-lCCTOc;; VT]71LWV KCCL 8TJAa(6vTwv KCCTTJQTLaw aivov," Ka t rraAtv· "oi OVQCCVOL btT]YOUV'[CCl b6�av e wv."

Clement's version is an orthodox, ecclesiastical variation of Marcus's teaching. He notes, in Marcus's words, that the human was created on the sixth day. By omitting any mention o f Moses he identifies from the beginning the sixth day o f creation with the day of Christ's crucifixion. Clement unpacks the phrase "in the sixth [day] the human." Using the same order of cases - dative, then nominative - Clement explains what sixth day and human mean. The sixth day of creation/redemption is the episemon, and in that day man becomes

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220 faithful to him. Clement, again departing from Marcus, says that the purpose of the creation/redemption was to have the human being straightaway enjoy the rest of the Lord's inheritance. His wording is precise. In a single phrase he uses ciphers of both seven

(avanavmv) and eight (KVQLaxfJc:; MYJQOVOf1 Lac:;).102 Thus, Clement restates that the goal of humanity is to move from the sixth day of creation, through the Sabbath rest, into the rest of the eighth day. He regards the connection between these days of creation as tight as the geometric relationship between points and the intervals between them. To illustrate his point Clement appeals to Psalm 1 8 (19), which he emends so that the heavens declare the glory of God to the heavens (not in the Septuagint), just as the hebdomad glorifies the ogdoad. The image invoked here is that of the seven planets glorifying the fixed sphere, an image he uses to interpret Plato's Republic, discussed above. Throughout ancient number symbolism the seven planets were closely associated with the seven vowels. So the Lord, who is called alpha and omega, is symbolized in the Psalms by the heavens. The Lord, the creator of all things, is the beginning and the end of all seven vowels. The thrust of §141.6-7 is that Christ constitutes the harmony of the spheres, the one who communicates to all the glory of God. Marcus's numbers in this passage are more static than Clement's. In the first paragraph, he is concerned with the number six and with showing the relationship among the sixth day of Creation, the crucifixion on the sixth d ay of the week, and the nailing of Jesus at the sixth hour. He claims the sixth hour was the beginning and the end of

102

KvQLO:KTJ and KAllQOVOf1LO: are ciphers for the Lord's day, the eighth. See Stromateis 5.14.106.2, 6.14.108.1, 7.12.76.4, and Excerpta ex Theodoto 3.63.

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221 redemption, alluding to the Pythagorean idea of the perfection of the number six.1 03 Six does not become anything. The second paragraph, which concerns itself with the number seven, has no sign of the motif running throughout Clement's version of numbers changing and turning into each other, in imitation of the divine plan and the incarnation of God. Clement has taken two unrelated passages by Marcus and spun them into a new narrative, a narrative of the orthodox vision of God becoming man so man might attain divine unity .104 The numbers in this new narrative symbolize the vertical transition of the faithful, as they ascend from the material world to the spiritual. The remainder of the excursus on the Decalogue (§§141 .7-142.1) consists of a long explanation of the meaning of rest and the number seven. The material, much of which probably derives from Aristobulus, is not of immediate concern, since it relates more to Philo's number symbolism, not the Valentinians' .1 05

TRANSFIGURATION OF ARITHMETIC Having read Against Heresies, Clement would have known Irenaeus' s saucy rhetoric against Marcus, his sarcasm, and his reductiones ad absurdum. Clement, however, seems to take Marcus's exegesis seriously. There is no express sarcasm or criticism, no attempt to show the arbitrary methods of his opponent. Throughout the Stromateis Clement uses knowledge

(yvwmc;) so as to reclaim it from the heretics, those who called themselves spiritual, on 1 o3 S ee p. 50 n. 125. 1 04 S ee above, p. 1 86. 1os See Delatte, E tudes, 233, for the scope and evidence of Clement's direct or (more likely) indirect use

of Aristobulus. Compare also Stromateis 5.14.107.1-108.1, Clement's catena of quotations from classical authors who praise the number seven.

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222 behalf of his own "ecclesiastics." So here he robs Marcus of the episemos ogdoad, to make of it a sign of Jesus's Incarnation, not of his emanation from and return to the Ogdoad. Both M arcus and Clement consider Jesus to be "noteworthy" because of his association with six. But for Marcus, the sixness is found most immediately in the number of letters in Jesus's n ame, the number needed to augment the twenty-four letters of the alphabet so as to achieve the Triacontad, the collection of the aeons. For Clement, the sixness lies not in letter counts but in its symbolism of the human nature of Christ, of the rupture in human discourse that brought about salvation. He ignores any sense of thirty, twenty-four, eight­ hundred and one, or any other number appealing to Marcus. Marcus focuses on the connection between the aeons and the alphabet. Clement, on that between the Incarnation and redemption. Both use the symbolism of the episemon, but to different ends. Clement shares with the Valentinians, Monolmus, and deutero-Simon a fascination with arranging Scripture into arithmetically harmonious structures. Just as they do, when he approaches the text, he takes along a preconceived, well-developed number symbolism. He massages the terminology he finds in texts, peers behind individual words, and chases down their overtones, so as to show how the Bible reveals those structures. The technique works outside the Bible, too. Clement reads ecclesiastical and philosophical literature with an eye to hidden number symbolism. His finest example is his investigation of Stoic anthropology, which he transforms into a Christian one by supplementing the missing parts and molding the structure into a pattern that better resembles the patterns he finds in Scripture. The tactic resembles those of his theological opponents. For Clement, this is no problem, since their error comes from their theological conclusions, not from the tactics used to justify or adorn them.

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223 What would Irenaeus have said of Clement's number symbolism? Like the V alentinians, Clement draws from human conventions in grammar and numeration to illustrate his theology (contra Irenaeus's second principle). Clement also quite openly takes preconceived number symbols into the Scriptures and the ecclesiastical tradition, rearranging a bit of the furniture along the way (contra Irenaeus's fourth principle). So there are two specific ways in which Clement and Irenaeus seem to differ. Other aspects of Clement's number symbolism match Irenaeus' s. He has no mathematical arrangement of the godhead, and the symbolism he draws from numbers found in the natural world is safely based on the science of his day (Irenaeus's first and third principles). If Irenaeus were to have any problem with Clement's number symbolism, it would probably revolve around exegetical matters. But we have already noted how Irenaeus bends his second and fourth principles, and is somewhat uncharitable in the third. So if Irenaeus believed that Clement was rooted in the apostolic rule of faith - as Clement probably hoped Irenaeus would have believed - then it is quite probable that Irenaeus would have shown him the same leniency he shows himself. For his part, Clement does not directly criticize Irenaeus. His criticism is tacit. He faces the same opponents, but does not use against them standards to which he does not presume to attain. Marcus and Clement emphasize different numbers. Marcus focuses mostly upon even numbers, especially two, four, six, eight, twelve, twenty-four, and thirty, to tie together language and the aeons. Clement, however, is concerned mainly with six, seven, and eight, seeing in the three numbers a kind of symbolic path of gnostic perfection. He shows little interest in other numbers, aside from the oneness latent in God, and its extension in the perfect number ten. Theodotus and Heracleon were also interested in the transition of six,

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224 seven, and eight, but Clement uses the number symbol to oppose, or at least to dampen, Valentinian theology and protology.

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9 Platonism

Like Christians from the same period, Platonists of the second and third centuries frequently used number symbolism, and even argued over the proper role numbers should be given. The disputes among Irenaeus, Clement, and the Valentinians were not exclusively part of the rhetorical and theological baggage of early Christianity. Rather, Christian debates over the theology of arithmetic were part and parcel of contemporary intellectual discourse. To illustrate this point I present here three different non-Christian Platonic texts and authors, each with distinct parallels to the Christian number symbolism discussed in earlier chapters. The first, Marsanes, a Nag Hammadi text datable to the late third or early fourth century, exemplifies a strain of Platonic thought strikingly similar to that of Marcus. The second, superficially similar to both Marsanes and Marcus, is a treatise by the fourth-century philosopher Theodore of Asine, with whom Iamblichus, his teacher and fellow Pythagorean, vehemently disagreed, most notably on the role that numbers should be allowed to play in philosophy. Third are the writings of Plutarch, who displays several different attitudes to number symbolism, ranging from skepticism to credulity. The first two examples fall slightly after the late second to early third century, the chronological bounds of this study; the third and last example, after it. This slight departure from the main time period under investigation is no obstacle to the m ain purpose of this 225

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226 chapter, to show that in late antiquity Platonists and Christians were working with a similar vocabulary and confronting similar problems. Naturally, the differences between the two groups should not be minimized -in this chapter I highlight the ways Platonists used their vocabulary distinct from Christian -but the common threads help explain what Irenaeus, Clement, and the Valentinians were arguing over.

MARSANES The Nag Hammadi text Marsanes purports to recount a revelation to the Syrian teacher Marsanes, after whom the treatise is named.1 This teacher, who seems to have been regarded in some circles as a prophet, ascends through the various levels of the universe and along the way learns about its structure and the seals through which he must pass to ascend to the highest level. Unfortunately, the once-lengthy text is lacunose, and only about a third of it can be meaningfully understood. What we have suggests that the treatise was intended for an intermediate or advanced audience, readers who had already been grounded in certain doctrines of the so-called Sethians.2 Sethian texts are often Christian or Jewish in content, but not necessarily so, as is the case in Marsanes, in which there are no direct or indirect references to Christian doctrines or texts. The few Jewish references are superficial, restricted to the names of Jewish prophets or mythic figures who had been a longstanding part of Sethian mythology. Although the geme 1 See chap. 7 in the untitled treatise in the Bruce codex; Epiphanius, Pan arion 40.7.6; and Pearson's ed.,

230-33. 2 Turner, Sethian Gnosticism, 122. The term Sethian was devised by scholars who, aware it was a neologism, attempted to explain important recurrent themes found in the heresiologists and in the Nag Hammadi library. Often the heavenly savior Seth lies at the center of these texts, but there are numerous other parallels. For a complete list, see ibid., 63-64.

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227 of Marsanes - a philosophical, apocalyptic ascent narrative-may suggest parallels with Christian apocalypses and Jewish hekhalot literature, this alone shows less the Christian and Jewish influence than the broad popularity of the genre. According to Turner, one of the most recent and most thorough commentators on the text, the absence of explicitly Jewish or Christian elements points to a late stage in the history of the Sethians, when they were estranged from Christianity.3 Should Turner's proposed reconstruction of Sethianism not be persuasive, or should the entire category Sethian be abandoned or drastically revised,

Marsanes would still, for other reasons, suit best the late third or early fourth century, that is, after the death of Plotinus.4 The author of Marsanes frequently invokes numbers to develop ideas about the structures of the universe . Marsanes presents thirteen levels of reality, one above the other, extending from the worldly, material realms to the highest realm, that of the unknown silence.5 To move from one level into another a traveler must pass through various seals. The lowest three seals are devoted to the worldly and material realms, the fourth, to the supercorporeal, and the fifth to conversion. The sixth seal is given to incorporeal being, a level whose self-begotten residents exist in the truth of the All. Thus, the first six levels are devoted to realms inhabited by groups of entities or by abstract notions. The remaining seals, however, are devoted to individual aeonic beings, similar to those found in Valentinianism. The seventh seal is for the triple-perfect, self-generated power. The eighth

3 Ibid., 257-60. Turner suggests six phases in the community's development, starting from a fusion of

Christian and Jewish groups in the second century, and ending in the late third or early fourth century with Platonists who had no formal religious affiliation. 4 Funk, Poirier, and Turner, Marsanes, 1, 229-30; Turner, Sethian Gnosticism, 189-94. 5 Marsanes (NH 10.1) 2.12-4.23.

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228 seal is given to the male intellect, Protophanes, who is part of an incorporeal and intelligible world.6 The ninth seal, as best we can understand the text, is given to Kalyptos, and the tenth seal goes to the aeon Barbelo. Above her are the invisible, triple-powered being, and then the spirit without essence. The thirteenth seal is devoted to the unknowable silence? This thirteenth realm is the most transcendent, the pinnacle of the ascent. A universe consisting of thirteen levels has not been seen in any of the texts so far discussed in this study. In texts from late antiquity the number thirteen is of very little interest as a symbolic number. For instance, Zostrianos, a Sethian text with many affinities to

Marsanes, ends only at the eleventh and twelfth levels, with no suggestion of anything beyond.8 Two texts, however, offer parallels to Marsanes' thirteen levels: the Books of feu and

6 Throughout this chapter I use intelligible if and only if vonoc; or a cognate is used. For VOEQOc; I use intellectual. Platonist philosophers in late antiquity sharply distinguished the two terms, assigning them to different realms of reality. Although the distinction is more important for my discussion of Theodore of A sine, I note the terminology here, where the distinction might also be at work. 7 A synopsis of the structure: 13 cnyfj? Silence Unknown Spirit without essence nVC!Jf..la clVOUCHOV? 12 the Invisible (who has three powers) aoQawc; 11 Barbelo. Virgin? Aeon? B A P B HAID 10 [Kalyptos?] Kai\u7noc;? 9 male intellect 8 Protophanes incorporeal and intelligible world self-generated power atnoycvi]c; bUva1-uc; 7 triple perfect [TQh:oc;] TiAnoc; self-begotten atnoyivvr]TOL 6 incorporeal being clOW!-!lXTOc; OUOLlX those who exist in the truth of the All conversion 5 super-[ corporeal?] 4 material, worldly 1-3 8 Funk et al., Marsanes, 379.

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229

Pistis Sophia. In the Books of feu, dated to the early third century, the Father is said to emanate twelve places, and he himself stands in the thirteenth place, analogous to the role of Christ over the twelve apostles.9 The thirteenth region is the culmination of the journey through the twelve previous regions, each of which requires a password for entry .1 0 A gnostic hymn in the same text gives praise to the first mystery, who established the thirteenth aeon and the gods within.n In Pistis Sophia, from the late third century, the thirteenth level is a dominant, almost overpowering themeP There resides the transcendent being, governing twelve other lower aeons.13 These twelve aeons are in no special hierarchy, although they seem to form two groups, one of five and another of seven members.14 According to the main story the thirteen levels are of paramount importance: Pistis Sophia, the main figure in the text, falls from the thirteenth realm, and the twelve lower aeons persecute her for trying to regain her lost position.15 Throughout the text, this thirteenth realm is epitomized as the place of superperfection. Common to all three texts is the idea that the thirteenth aeon transcends all other levels. The lower twelve are associated, both implicitly and explicitly, with the zodiac,

9 LThK 5:848; Books of feu 1 .39, 2.42. There are other texts that focus on a group of 12 governed by a single entity (think of the apostles and Christ) but these do not talk about the number thirteen per se. See Danielou, Symboles chretiens primitives, 131--42, esp. 136, where he notes that Ephrem the Syrian calls Christ the 13th, a variation on the theme apostles and Christ, and not directly relevant here. 10 Books of feu 2.52. 1 1 Bruce codex, fol. 37, treated by Schmidt as separate from the Books offeu. 12 For the date see DECL 491, LThK 8:317-18. 1 3 Pistis Sophia 1 .1 0 and passim. 14 Ibid. 1 .86, 2.96. 1s Ibid. 1 .30-31.

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230 which means that the thirteenth level transcends the material heavens. This sheds light on the trope already discussed, of the number eight symbolizing the superperfection of seven. Seven is, of course, the number of planets. Since Marsanes, Books offeu, and Pis tis Sophia all postdate Clement, who so frequently uses the trope seven ---* eight, the notion twelve ---* thirteen seems to be modeled on this earlier Christian motif. This means, then, that just as eight is symbolic for its supersession of seven, so in Marsanes thirteen is a symbolic number only because it represents the transcendence of twelve. But Marsanes' arrangement of the inner structures of the thirteen levels differs considerably from the other two texts. Pistis Sophia and the Books of feu treat the lower twelve realms or aeons as an undifferentiated mass that resides above the material world.

Marsanes, however, presents the thirteen realms as steps on a ladder stretching along a metaphysical hierarchy, extending from the lowest realm, the material, up to the highest, that which transcends all apprehension. The text is very fragmentary, but what we have suggests that the first twelve stages are placed in four groups of three, an arrangement that would be very much in line with the text's tendency to triads (see below). This shows that

Marsanes is a Platonic ascent text, concerned with the process of upward ascent via triads.16 Also important in Marsanes' teaching are the relationships formed among the monad, the dyad, and the triad. In previous chapters I have emphasized the relationship between the monad and the dyad. All that Marsanes says about the matter is that the monad and dyad are the first to exist, and that the dyad divides from the monad P This is not enough information to locate Marsanes on the monadic/dyadic scale I created for 1 6 See Finamore, "Iamblichus, the Sethians, and Marsanes," esp. 256-57. 1 7 Marsanes 32.12-17. See esp. Funk's ed. and commentary, on the dyad, 446.

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231 Valentinianism (see table 1 ). It may be that the passage dwelling on the origin of the dyad is no longer extant, or that it was never a central topic. If the case is the latter, then the recurrence of the triad is all the more important, since threes play a much more significant role in Marsanes than do twos or ones. There is the triple-powered one ('rQLC'n)vcq.wc;), a recurring figure who stands between the Invisible Spirit and the aeon of Barbelo.18 Marsanes is given a third of the power of the one who possesses this triple-powered one, and a lengthy discussion, now lost, discusses the threefold composition of this being.19 The triad is also taken to be the point of departure for the other numbers: the monad, dyad, tetrad, hexad, heptad, ogdoad, and so on, up to the dodecad.20 In this section, what is comprehensible of the fragmentary text suggests that the triad, the first one that is good, gets its existence from a synthesis of the shape (axfJf.la) of the monad and the substance of the dyad.21 The emphasis on threes is suggestive of other Neoplatonist schemes from the third and fourth centuries.22 Distinct echoes of Marcus's system can be seen in Marsanes' doctrine of the soul's shape. Marsanes claims that there are five different arrangements of the soul, only the first three of which are discussed. In the first arrangement the soul takes on the form of the

1 8 Marsanes 6.18-20; Funk et al., 390; Pearson, 266-68.

1 9 Marsanes 1 0.7-11 and fols. 14-15. See also Funk et a!., 396 on the triple series associated with the top tier of Marsanes' hierarchy. 2o Marsanes 32.7-33.5. 21 Ibid. 32.7-12. This is my own conjectural reconstruction ofMarsanes' argument, based on oyq
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232 simple vowels,

a,

E, T), L, o, u, and w;23 in the second, the diphthongs, which Marsanes lists in

their entirety, and then some:

yyy, yyy, m au,

a

a L, au, a

EU, T)U, ou, wu, OL T) L, U L WL,

au a,

EU T) L, O L ou, yyy,

EU, T)U, Ol ou, wu, yyy, yyy, au E L EU, OL ou, T)U.24 The third shape of the

soul consists of the simple vowels, but in triplicate:

aaa,

EEE, T)T)T), and so on.Z5 The fourth

and fifth shapes also consist of diphthongs, but Marsanes says he is not allowed to discuss everything about them.26 Presumably these last two shapes consisted of strings of, respectively, four and five vowels. Around this fivefold scheme Marsanes weaves a complex theory about the letters, which are divided into vowels, semivowels, and consonants. But unlike Marcus, who places the nine consonants above the eight semivowels, and these above the seven vowels, Marsanes follows the traditional hierarchy, attested to by Philo, Plutarch, and others: vowels over semivowels, and these over consonantsP Other aspects of letters, such as length, aspiration, and accent, also play important parts of Marsanes' discussion of the hierarchy of the letters. Similar to Marcus, Marsanes treats letters as constituent parts of the structures of the universe. Both Marcus and Marsanes depend upon formal grammatical distinctions in their explanation for the role and presence of letters in the universe and in anthropology. Both incorporate grammar so as to illuminate their theology, and this in tum prompts the reader to see traditional categories in a new light. Thus, Marcus's theology is not so unusual, as

23 Marsanes 26.4. 24 Ibid. 26.5-7, 28.5-1 1 . Concerning the triple gammas, see Funk et al, Marsanes, 60, and n. 29, below. 2s Marsanes 28.4, 17-22. 26 Ibid. 29.2-5. 27 Philo, Questions and Answers on Genesis 4.117; idem, On the Preliminary Studies 1 50; idem, Creation of

the World 126; Plutarch, Table Talk 9 .2.2, discussed below; Melampous, in Grammatici Graeci 1 .1 :42; anonymous, cited on p. 347. See Funk et al., Marsanes, 420-25 and Forster, Marcus Magus, 240-42.

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233

Marsanes and m any other comparanda show. But, whereas Marcus's alphabetical theology is integrated with his isopsephy and Valentinian numerical speculation, this is not the case with Marsanes. In Marsanes the number of letters in a given word is not important, and there are no examples of psephic calculation. Even Marsanes' itemization of the diphthongs, which begins with the canonical eleven, continues with a mishmash of letter combinations.28 Had the author of Marsanes been as obsessed with numbers as Marcus, such a list would evince pattern and order.29 Rather, the haphazard order of the list resembles the voces mysticae of magical texts, which also present unordered or semiordered lists of diphthongs.30 This is not to say that there are no numerical structures in Marsanes. After all, the thirteen realms are well ordered, and the soul is built out of vowels that are numerically harmonious. The vowels are introduced in an arithmetical progression. For the first shape there are individual letters; for the second, pairs; for the third, triplets. This progression, less

2s 28.5-1 1 . See Funk et al., Marsanes, 430-32. 29 Turner (Funk et al., Marsanes, 59-61) and Poirier (ibid., 430-32) argue for a planned, coherent

structure to Marsanes' list, which seems to substitute triple gammas for certain diphthongs. Poirier counts 27 sets, even though the lack of an overdot between his nos. 1 & 2, 8 & 9, and 10 & 11 would suggest either 24 sets (counting the overdots) or 36 (ignoring all overdots). Turner's attempt to show a pattern A B C A' C B' is daring but unconvincing, since the groups and ordering-neither self­ evident nor natural - are left unexplained. To interpret the gammas as numerals (Turner's suggestion) seems incorrect, since psephy is used nowhere else inMarsanes. And neither the numbers in Plato's lambda (Timaeus 35AB) nor the Timaeus itself are even alluded to in Marsanes, so Turner's suggestion that they are an interpretive key for Marsanes seems wildly off. It is more likely that the gammas indicate the scribe's omission of yQlXf-!f-!CX'ra, whether unintentionally or by his inability to read the manuscript he was copying. This suggestion is tentative; I think the text defies explanation. 30 Cf. PGM 2.128-33, which lists the psephic value of the name of a divine entity: ou Tj t(lf]tpoc; 87Z)Cj8'· nr LE" La " La.Tr LCX.c[·] LEU" Llla· LWCX" LEU" LllL" ll LCX" ca.· Ell" llf" Wll" llW" E llE" E Ell" llEE" aaw· Wca· Eaw· WL" WE" llW" Ell" ECXE" LLL" 000" UUU" WWW" LU" cU. OU" ll ca· Lllca· ECXE" na· LCXLE" Llla· LOU" LWE" LOU" ill· .Lll" ill· .LlliL Such similarity complements yet another between Marsanes and the magical papyri: both are interested in the association between the zodiac and numbers. For other parallels and contrasts between Marcus (esp. Irenaeus, Against Heresies 1 .14.5) and Marsanes see Forster, Marcus Magus, 239.

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234 complex a numerical device than Marcus's, nevertheless draws on a simple form of number symbolism. It is reminiscent of the magical alae or ladders (KALJ.laKa), where individual lines repeat select letters and get progressively longer, thus producing text shaped like a wing or ladder. For example:31 a

E

T) l 0 u w

w

T) T) l

0 u w

E

l

l 0

u

0 u

w

0 u

w

u w

w

There are no alae in Marsanes, but its description of the soul as an accumulation of one-, two-, three-, four-, and five-letter patterns of vowels shares the practice of alphabetic ascent, used so frequently in texts of ritual power.

THEODORE OF ASINE

Marsanes' interest in the alphabetic composition of the soul and in the thirteen levels of reality parallels the thought of Theodore of Asine (ca. 275/80-ca. 360). Theodore was a student of Porphyry, in Rome, and then of Iamblichus. He rejected the teachings of the latter and claimed to uphold those of the former, along with the doctrines of Numenius (fl. 2nd c.) and Amelius (fl. 3rd c.). Toward the end of his life, Theodore's followers still actively

31 PGM 1 .1 3-19. Other examples are legion.

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235 opposed Iamblichus's. Of his writings, we know of only two titles, On Names and That the

Soul is All the Forms (sc. of Life). Extracts, some lengthy, from these works are preserved by Proclus.32 Theodore's metaphysical system, rather neglected today, involves among other things a complex explanation of the origin and structure of the soul.33 The explanation bases itself on letters, their numerical value, and the symbolism behind the numbers. The bulk of this numerically oriented system is preserved in testimony six, worth quoting in full. Proclus, our source for the testimony, says:

Theodore, the philosopher of Asine, inspired by the discourses of Numenius, in a rather novel manner composed treatises concerning the generation of the soul, making his attempts from letters, written characters, and numbers. So that, then, we might have concisely his written opinions, come, let us make an overview, point by point, of everything he says. [1; my numeration, for later discussion] So then, the first is rightly hymned as being, for him, ineffable, inexpressible, fount of all things, and cause of goodness. [2] And after this [first], so exalted above all things, there is a triad that defines, for him, the intelligible plane. [The triad] he calls the One (TD "EN) since it comes [a] from a breathing that is somehow ineffable (which the rough breathing of "EN mimics), [b] from the loop of the E itself, on its own without the consonant, and [c) from even the N itself. [3] Another triad after that one defines the intellectual depth, [4] and another one, the demiurgical. The former is existence prior to being, thinking before mind, living before life. After these is the demiurgical triad, containing first, being, second, mind, and third, the fount of souls. [5] From that triad is another triad: absolute soul, universal [soul], and [soul] of the all. We have earlier discussed the distinction of these things, each of which proceeds from the entire demiurgical triad -that is, one from being, another from 32 On Theodore's life see DNP 12.1:328-30; PRE 5 (n.s.): 183�38 (Theodore, no. 35); Gersh, From

Iamblichus to Eriugena, 289-304. 33 Theodore has escaped inclusion in the TLG (as of 2005) and the OCD.

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236

mind, and the other from the fontal soul.34 Indeed, it was proposed to Plato to speak about this soul of the all, especially about the plain soul that comes from the fount of souls, about the universal [soul] and the [soul] of the all, and about the fount itself. For all things exist in all things, even if at one time in one way, and at another time, another: in the soul before the triad [all things exist in all things] in unity; in the plain [soul], [all things exist in all things] in wholeness before the parts; in the universal soul, [all things exist in all things] in wholenessfrom the parts; and in the third [soul], [all things exist in all things] in [wholeness] in the parts. [All this is said] on the basis that Plato classified all these things and needed to refer to every [soul] every ratio, ratios that allow no difference among them. And [Theodore] thinks it necessary to say first why [the soul] exists from three means. And indeed he says that the soul as a whole is a geometrical ratio, existing from both the first god according to being and the second [god] according to mind. For these very things are two essences, one undivided and the other divided. Both the arithmetical ratio (which bears the image of the first essence) and the harmonic [ratio] ([which bears an image of the] second [essence]) result in [the geometrical ratio]. The former is monadic, since it is without extension, the latter is discrete, but harmonically so. [7] Then, the entire number might be a certain geometrical number, since [the soul] is shown to be a tetrad, being from the tetrad of the elements/letters. But lest you suspect that this number is lifeless, taking for the third heptad the first, you will find life in the extreme letters. Rather, setting out according to its order the base of the first letter, you will see the soul is an intellectual life. E.g., Z, 0, 'I'. The middle [term, 0,] is the circle, being the intellectual one, since mind is the cause of the soul. The smallest [term, Z,] shows [the soul] geometrical, a kind of mind, through the attachment of the parallels and the diameter. [The mind] remains above and encompasses opposites and is shown to be a form of life, both oblique and not oblique. The largest [term, 'I',] is the element/letter of a sphere. So then the lines, bent into each other, will make the sphere. On top of this, the bases of the next letter, D., M, Y, are simultaneously three and tetradic. And because of this, as they beget the dodecad, they result in the twelve spheres of the all. The largest of the bases[, Y,] shows that its essence yearns for two certain things and stretch up toward two matters. Therefore some call this letter 34

He refers here to a discussion preserved in test. 22.

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237

philosopher. The [essence] of both flow to the lower [region]. So this is why we find the Y referred to by some of the noteworthy [authors of the past]. It is between two spheres, the 'I' and the X, the former being warmer (because of the breath) and more life-giving, and the latter having each [quality] to a lesser extent. Thus, there is again a mean to two minds, one earlier and the other later, and the middle character makes clear its property and relation to the other. Rather, even though the letter 'I' is a sphere, Plato assigned the X to the soul, so that it might show the equal balance of motion itself, since all the lines in the X are equal, and thus to make the automation of the soul evident. But if the Demiurge brings in the soul through existence itself, it is clear that he himself has ordered it in proportion to the X. After all, that is the foremost mind. And so, because of these things, he says that the soul, as it advances and brings itself out, is a certain middle essence of two minds. And this is the manner in which these things are to be understood . But through the last letter, the H, the advance of [the soul] up to the cube is to be observed. [8] And if it is a dyad because of the otherness of life, and it is a triad because of the tripartition of its essence, then it has, on the one hand, the ratio 3:2. But as it enters into itself and, through its entrance, applies the dyad to the triad, it begets the hexad. As it connects to the undivided and to the trisected the harmony that [comes] through these things in doubleness, it comes into existence. And since, on the one hand, the triad, as it turns into itself, results in the ennead, and the dyad, on the other hand, moving into itself dyadically always results in the octet, so from both it results in the ratio 9:8. The linear birth [of the soul] makes clear its indivisibility, and its thorough homogeneity (after all, every part of a line is a line), and that all the ratios are everywhere. But the split into two demonstrates that its form is dyadic. And its indivisible wholeness is an image of the first mind, whereas the unsplittable [wholeness] of the two (which he calls the circle of the same) [is an image] of the second [mind]. And the [wholeness] split into six [is an image] of the third [mind], the last to be calculated. And the octet becomes manifest from the dyad of the soul, whereas the heptad depicts in monads the first form of the soul; in decads, its intelligible [form] (because of the circle); and in hundreds, the soulish mark, the third one remaining. And [the soul's] straight, connate nature exists for the fixed [sphere], which begets; whereas the exit and indefinability [exist for] the wandering [sphere]; and the return after the advance [exists for] the life that wanders without wandering. And since on the other hand the shape of the soul is like X, and its form is dyadic (since the split is into two), and the dyad [applied] to the hexad (being primarily the base of X) creates the dodecad, you might take from that the first twelve ancient souls.

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238 A lthough the testimony continues, it is worth commenting on a number of ideas that emerge from this jumble. It usually takes several slow readings to understand much of Theodore's system. Proclus' s summary is terse, and even in faithful translations many ideas are incomprehensible.35 At the top of Theodore's system [1] is a transcendent entity, described in negative terms descriptive of its role as cause and source. Significantly, he does not call it "One."36 Rather, it is absolute, beyond names, beyond even spirit or breathF Below this transcendent entity is the intelligible plane [2], consisting of a triad that unfolds and manifests the primal entity in the letters of f.v. The rough breathing [2a], which Theodore claims is silent, mimics the ineffable breathing of the uppermost entity.38 This ineffable breathing is symbolized by the rough breathing, the dasia, which had not been pronounced for some centuries in Theodore's day. The unspoken dasia is the perfect symbol of the ineffable since it too is a paradox of unspoken speech. According to another testimony to Theodore's system, its combination with the €, shaped by a loop [2b] - it is important to remember that Theodore is commenting on uncial Greek letters, not the lowercase ones we are familiar with today - renders the vowel at once utterable and unutterable. The N [2c]

35 For other translations, of varying degrees of accuracy, see Proclus, Commentary on the Timaeus, trans. Festugiere, 3:318-21; Ferwerda, "Plotinus on Sounds," 51-52; Turner, in Funk et al.,Marsanes, 214-16. Taylor, the great English Platonist, left this part of Proclus's commentary untranslated, explaining, "Proclus gives an epitome of this theory, but as it would be very difficult to render it intelligible to the English reader, and as in the opinion of Iamblichus, the whole of it is artificial, and contains nothing sane, I have omitted to translate it." (Proclus on the Timaeus, 141 n. 1 .) 36 Contra Turner, in Funk et al., Marsanes, 214, 216, 227. In test. 9 Theodore explicitly denies that this highest entity has a name. 37 Theodore of Asine, test. 9 (Deuse). 38 Ibid.: sicut et spiritus tacitus and spiritum . . . indicibilem.

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239

rounds out the image of the ineffable made effable.39 The triad 'EN consists of two groups: a dyad and, above it, a monad.4o Beneath this level is the intellectual depth [3], consisting of a triad: existence, thinking, and living. Each of these three parts of the intellectual depth stand prior to and over the elements in the triad just below, the demiurgical depth [4], a triad that consists of being, mind, and the fount for souls. This fourth level seems to have been an easy target for Theodore's critics, who saw this doctrine, taken from Amelius, as an unnecessary introduction of three demiurges, in lieu of Plato's one demiurge.41 The threefold demiurgical level, however, sustains Theodore's commitment to a metaphysic of the triadic descent. It is also a critical explanation for the next level down, the realm of the soul [5], which consists of three kinds of soul, all derived from the demiurgical triad in general, and the fount of souls in particular.42 Each of the three aspects of the soul corresponds to a certain relationship between the whole and the parts, and to the three major kinds of ratios. What part of the soul corresponds to what proportion is treated in another testimony, where Theodore goes to some length to correlate the numbers one, two, three, four, and six to the four elements, and by extension, to the soul.43 For example, the series one, two, and four, a geometrical

39 Test. 9 is unclear. See Morrow and Dillon, Proclus ' Commentary, 590 and n. 1 1 3. Turner's suggestion (Funk et al., Marsanes, 216) that "EN represents point, line, and plane reads too much into the passage. 40 Test. 9 neither stipulates which letters are the monad and which the dyad, nor elaborates on how

the monad generates the dyad. 4 1 See test. 12, translations by Taylor, Proclus on the Timaeus, 260; Turner, in Funk et al., Marsanes, 218-

1 9; Festugiere (Proclus, Commentary on the Timaeus), 4:165-66. 42 For amplification on this level, see test. 22, which is translated by Turner, in Funk et a!., Marsanes, 221-23; Festugiere (Proclus, Commentary on the Timaeus), 3:262-65; and Taylor, Proclus on the Timaeus, 92-94. 43 Test. 22. See previous note.

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240

series (b I a

=

c I b), corresponds to earth because of its name, and so the number seven, the

sum of the series, also represents the earth. Theodore's very difficult, complex number symbolism, linking souls to the sublunary region, shows that he saw numbers as a key constituent in the formation, design, and explication of the universe. The most basic parts of this number symbolism are evident in the structures of his metaphysics, presented in testimony six [1-5], which may be diagrammed:

n) TIQ�n:ov lXQQT]TOV I The ineffable, first voryTov ru\aTo<:; I

'EN / ONE

intelligible breadth voEpov {Jaeos 1

dvm I existence

voEiv I thought

i:;f]v I life

ov I being

vouc; I mind

a.inot(luxij I absolute soul

Tj Ka.86Aou t(luxf] I universal soul

i:.wf], TITJYll n0v �mxwv, TIT]ya.ia. �mxf] I life, fount of souls, fontal soul Tj mu 71£XVToc; t(luxf] I soul of the All

intellectual depth ory11wvpytKov {Jaeos 1

demiurgical depth

Here it becomes apparent that Theodore, like other Neoplatonists, had a mathematically molded view of the divine realm.44 A comparison with Marsanes' thirteen levels is inviting. Both Theodore and Marsanes agree in the number of levels and in the transcendence of an ineffable entity located in the thirteenth place. But prominent differences should also be noted. Marsanes ' lowest realm is the corporeal world, not the soulish. And even though Marsanes teaches that the twelve stages leading to the thirteenth consists of four levels of triads, those triads do not follow the 44 See comparative schemes at Deuse, Theodoros von Asine, 22-24; Turner, in Funk et a!., Marsanes, 230; and Finamore, "lamblichus, the Sethians, and Marsanes," 256-57.

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241 consistent pattern found in Theodore: existence-thought-life. This regularity in Theodore's triads lends itself to depiction in a rectangle, where both horizontal and vertical relationships are important. Theodore, for instance, places living over life (the two names are cognates), but their correlatives in Marsanes, self-generated power/triple perfect and super-[ corporeal?] do not have this kind of vertical relationship. Marsanes presents the thirteen seals seriatim, a linear shape. The two systems are incommensurate. Nevertheless, they both attest to the importance of mathematically structured systems. Later in testimony six Theodore points to the soul as consisting of four elements or letters [7] - the play on the double meaning of G'TOlXELOV is evident- as the reason for calling the entire number of the soul a geometrical number. This introduces a letter-byletter, numerical explanation of the word WYXH, which is geometrical since it consists of four letters.45 Theodore's method is to take a letter, for example 'I', find its base, then list other letters that share the same base, in this case, Z and 0.46 He then uses each of the three letters, particularly their shape, to explain the letter as a whole. The combination of parallel and oblique lines in the letter form Z explains how the soul preserves both kinds of directions, as specified in Plato's Timaeus. The circle of the 0 represents the mind's generation of the soul. The W's crossarms, arching in toward each other, represent a sphere. For the Y in WYXH, its base of four, when multiplied by the three letters that share it as a

45 See below for Iamblichus's criticism, which confirms that Theodore's method focused on the number of letters in a word, not its psephic value. Sambursky, "Gematria," incorrectly suggests that Theodore of Asine, test. 6, preserves the earliest use of the term gematria. What very basic psephy there is at work in the passage has nothing to do with what Produs calls the "geometrical number." 46 Theodore's use of rru8f-lfJV to refer to not the base alone but its multiples of ten and one hundred goes against normal use of the word. See LSJ, s.v. and above, chapter 6, and below, excursus D.

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242 base, yields the "twelve spheres of the all," presumably the zodiac. Its shape too illustrates the philosophical dimensions of the letter, as its stem and arms portray the flow from upper regions to lower, and the retum.47 The final part of the testimony [8] deals with the Timaeus' s duple and triple progressions and identifies the activities of soul with the various numbers that make up the most basic musical intervals (e.g., 3:2 and 9:8, the fifth and whole tone).48 The passage is complex and difficult to understand without indulging in a very lengthy discussion about the entire Neoplatonic interpretive tradition of the numbers in the Timaeus, beyond the scope of this study. Nevertheless, it is important to note how deeply Theodore's explanation of the constitution of the world soul involves itself in arithmetic. Theodore is squarely in the center of Pythagorean Platonism, an interpretive tradition of the Timaeus spearheaded by Xenocrates, who identified number, combined with motion and the mixture of same and other, as the source of the soul.49 As part of this tradition Theodore made numbers and arithmetic a constituent part of every level of his philosophy. Theodore's letter and number speculation resembles that of Marcus, who identifies the number of letters in the name Jesus Christ as a symbol of the structure of the aeonic realm. Theodore finds the shape of the letters to symbolize important metaphysical truths,

47 See below, p. 347, where the Y is interpreted as a symbol of moral choice. Theodore's suggestion, however, is that the two arms of the Y stretch toward its companion letters, W and X, the former being more life-giving (as Theodore stipulates elsewhere, W recalls Z, the initial of ZO'H, "life''), the latter more soullike. 48 Plato, Timaeus 35b: 1, 2, 4, 8 and 1, 3, 9, 27. 49 Plutarch, Genesis of the Soul in the Timaeus 2, 22.

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243 just as Marcus locates in the divisions of the alphabet signs of Pleromatic emanations. Both use human conventions to symbolize the divine. Theodore also has a connection with Colarbasus. In psephic numerology names take on significance well beyond what is immediately apparent. Analysis of the numbers invested in a n ame allows one to discover hidden knowledge, and to learn more about the person or thing that bears the names. Theodore, like Colarbasus, sees the numerical value of names as providing the key to hidden knowledge. Just as Marcus's speculation became for Irenaeus a prime target, so Theodore's speculation earned him the reproach of Iamblichus, the Platonic philosopher who is reported to have been the teacher of Theodore. Iamblichus' s criticism is preserved in the last part of Theodore's testimony six. Proclus says:5°

Thus Theodore philosophizes these kinds of things about these matters, making his interpretations out of letters and utterances (to compare a few [ideas] among many). But the divine Iamblichus lambasted this sort of viewpoint in his responses, Against the Circle of Amelius (for so he titles the chapter) and indeed also [in Against the Circle of] Numenius. [Iamblichus] either -for I cannot say [which] - identified [Theodore] with these [two men] or had somewhere found them writing similar things about these matters. So the divine Iamblichus says first that you shouldn't make the soul the entire number or the geometrical number because of the quantity of its letters. For L.OMA [ "body"] too is made of the same [number] of letters, as is even MH ON [ "nonbeing") . So [by Theodore's reasoning] MH ON would be the entire number. You could find many other things that consist of the same [number) of letters yet are shameful and completely opposite to each other, all of which would certainly not be right to conflate and confound with each other. so

In addition to those listed in n. 35, other translations are in Dillon, Iamblichi Chalcidensis, 165-67 and Taylor, Proclus on the Timaeus, 141.

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244 Second, it is dangerous to try [to build a system] based on written characters. After all, these things are relative: the carving of an archaic [character] used to be one way, but is now another. For instance, the Z upon which that man builds his argument had neither parallels that were completely opposed, nor the middle diagonal bar. Rather, [the crossbar was] perpendicular, as is apparent from ancient steles. Third, to reduce [numbers] to their bases and to preoccupy oneself with them, [going] from one number to another or vice versa, alters our understanding. For the heptad in monads, the [heptad] in decads, and the [heptad] in hundreds are not the same thing. So if this [heptad] was in the term WYXH, why must he sneak in an account about bases? After all, using this same technique we might transform every thing into every number, by dividing or adding or multiplying. So much for the general [problems]. He also refutes [Theodore's] individual results, [showing them to be] fraudulent and insane. And everyone who would like to know the weakness of every point may easily acquire the treatise and read through the appropriate refutations of everything [taken] from [Theodore's] writings. This passage shows that Proclus, our source for testimony six, consulted a readily available work by Iamblichus, a book of polemic divided into chapters discussing and arguing against a series of philosophical schools.51 One chapter was directed against the circles of Amelius and another, against that of Numenius. What Proclus seems unable to determine is whether Iamblichus meant to identify Theodore with these two circles, or if he meant to refute only an approach shared by all.52+ This suggests to me that in his polemical

sJ

Here I agree with Festugiere against Dillon (Iamblichi Chalcidensis, 337), who understood the Greek text to refer to one title (Against the Circle of Amelius and Numenius), not two (as in my translation). Since Iamblichus' s text consisted of two chapters, and the titles describe their contents as being refutations, the passage is probably not from a commentary on the Timaeus, as Dillon supposed. sz My interpretation depends upon taking the TOtrrov of 2:277.30 with Theodore and the EKELvouc; of the same line with the circles of Amelius and Numenius. Dillon's reading (Iamblichus, Jamblichi Chalcidensis, 165, 337-38), which assigns TOVTOV to Numenius and iKdvouc; to the circle of Amelius is viable, but I feel the overall context of Proclus's report puts Theodore front and center, much closer

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245 work Iamblichus did not name Theodore specifically, but refuted Theodore's d octrine under the name of these two schools, leaving the reader to guess whether Theodore could justifiably be associated formally with the schools of Amelius or Numenius.53 In any case, Proclus, who knew Theodore's writings well, saw that Iamblichus' s critique clearly applied to Theodore. Iamblichus makes three criticisms of the method in general, then refutes specific claims that Theodore makes. Proclus reports only the general criticisms, three total. The first is Iamblichus' s contention that one cannot infer from the premise "soul consists of four letters" that the soul is the entire number, or that it is the geometrical number. He demonstrates the faulty logic with a reductio ad absurdum. Both body and non-being have four letters, so Theodore's method should allow one to conclude a similar, exalted position for corporeality or nonexistence. Iamblichus notes that a number of four-letter words, too rude to mention, could be inserted in Theodore's system. This first criticism deals with Theodore's fascination with the number of letters in WYXH. His critique has nothing to do with the practice of gematria.54 The second criticism is that letterforms are a faulty starting point because of their relative nature. Iamblichus focuses on how letterforms change, demonstrating it with the Z. He points out that the archaic form of the letter was I, a shape that undermines Theodore's interpretation of the soul being at once parallel and oblique. Note, the tendency of

(and therefore Toi:nov) than the more remote (at least in this context) Amelius and Numenius (and therefore iKEivovc;). 53 See Dillon, Iamblichi Chalcidensis, 338. 54 Contra Dillon, in Iamblichus, lamblichi Chalcidensis, 338-39 and Sambursky (see n. 45, above).

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246 letterforms to change in history is not necessarily the only reason Iamblichus dismisses the premise. Quite possibly he had other concerns- the fluctuation of letters and letterforms from one language to another, their very origin as a human artifact, and so on - but he expresses only this particular concern. Third, Iamblichus criticizes as valueless the practice of taking alphabetic numerals, finding their base value, and extrapolating from that base to other numerals that share the same base. He questions why bases should even be a point of consideration. The risk in the practice is that someone could take a word like soul and derive any preconceived result, by performing various mathematical operations. Iamblichus may be somewhat unfair here to Theodore, who seems to have moved from one number to another only by dividing or multiplying by ten. That is, Theodore's system has certain rules. But Iamblichus criticizes the practice for the arbitrariness of its results. Other numbers could easily be introduced to prove whatever one desired.55 Iamblichus was no enemy of number symbolism.56 His writings are full of Pythagorean number symbolism. For example, his magnum opus, On Pythagoreanism, is structured in ten books to pay homage to the perfection of the number ten.57 Each of the extant books in this series deals in some way with number symbolism. In the third book,

Common Mathematical Knowledge, for instance, Iamblichus focuses on the philosophical and

55 Hippolytus too criticizes Greek numerology for introducing new, strange rules to deal with results

that contradict reality (see chap. 5). The vast number of variations in Greek numerology, discussed in excursus D, suggest that numerologists had to tweak their rules as they went along, to get the right results. 56 For examples beyond those given here, see Shaw, "Eros and Arithmos." 57 For the structure of this work, see O'Meara, Pythagoras Revived. On the perfection of ten, see above, p. 50 n. 125.

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247 religious importance of numbers and mathematics, arguing against cynical attitudes, like those of Sextus Empiricus, that the four kinds of mathematical science are useless. In his response, Iamblichus defends the Pythagorean tradition of mathematics. He notes that there were two ways the Pythagoreans taught mathematics. The first began with first principles, and applied them to the efforts of the faculty of understanding. The earliest discoveries of mathematics were pursued in this fashion. The results were not used as if they had some kind of separate existence, but to see how something demonstrated in mathematics might come into existence.58 The second Pythagorean method taught mathematics through symbols, for instance, through the pentad of justice. This symbolic approach to pedagogy especially pervaded the Pythagoreans' philosophy since they thought the technique appropriate for the gods and naturally fitting.59 This second, symbolic approach fits well with Iamblichus' s more general conviction that each of the mathematical sciences purifies the soul and prepares it for union with the divine. Marking the entire path of theurgy are symbolic numbers. Although there is no stylistic reason for ascribing the anonymous

Theology of Arithmetic to Iamblichus, the substance of the treatise, with all its theological and scientific number symbolism, fits very well with his general outlook.60 58 Iamblichus, Common Mathematical Knowledge 18.7-17. 59 Ibid., 18.17-23. 60 Taran, Speusippus of A thens, 291-98 argues that the Theology of Arithmetic, traditionally dated to the fourth century, is probably the product of a later Byzantine compiler of a number of arithmological treatises, including those by Nicomachus of Gerasa, Anatolius of Laodicea, and Iamblichus. To make his point, however, Taran identifies Imablichus's On Pythagoreanism book 7 with excerpts from the Theology of Arithmetic. O'Meara's later study, Pythagoras Revived, reconstructs book seven on the basis of fragments from Michael Psellos (11th c.) and thereby shows that it differed considerably from the Theology ofArithmetic, thereby reaffirming the consensus about its 4th-c. date. In my opinion, many of Taran's observations have not been accounted for. The question of the date of the Theology of Arithmetic should be revisited.

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248 Like Theodore, Iamblichus engages in extensive symbolic analysis of the numbers in the Timaeus.61 Both men explain the generation of the soul in terms derived from arithmetical explanations for the generation of the dyad and triad from the monad.62 So Iamblichus's criticism of Theodore is not a criticism of number symbolism per se, nor even a criticism of wild number symbolism (to some sensibilities Iamblichus's number symbolism is also wild). His main complaint against Theodore's method is that it is capricious, bound to changeable human convention, and liable to lead one to all sorts of absurd conclusions. The method destroys the very essence of the symbol. Iamblichus prizes numbers as key symbols because of their inherent connection with higher realms of reality. Theodore had focused, however, on facets of numbers and letters that were inherently part of the human condition, the product of changing social conventions. In these contexts the symbol loses its power because it is rooted in temporal instead of eternal realities. To locate numerical symbols in the realm of the divine was completely justified and expected in the Pythagorean and Platonic traditions. But to root them in human convention, as Theodore did, was not. The debate between Iamblichus and Theodore compares favorably with that between Irenaeus and Marcus. Both lamblichus and Irenaeus deploy biting sarcasm in their reductiones ad absurdum to try to discredit a point of view that has threatened and obviated the rules by which one secures truth. Both writers criticize techniques that are custom bound and liable to lead a person to whatever preconceived idea they have, or to absurd, immoral positions. Both Irenaeus and Iamblichus participate in communities

61 Prod us's Commentary on the Timaeus depends considerably on Iamblichus. See Dillon, lamblichi Chalcidensis, 161, 322-25. 62 Jbid., 1 60-63.

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249 grounded in tradition, and they both work with systems and texts that were considered to have roots, so to speak, in upper, divine soil. For Irenaeus, this is the apostolic rule of faith, deposited in the churches and codified in the Bible; for Iamblichus it is the Platonic rule of faith, practiced in religious theurgy and enshrined in the writings of Plato. The analogy should not be pressed too far. Christians and Platonists had separate notions of community and tradition, and their self-identities cannot be compared easily. Nevertheless, both Irenaeus and Iamblichus characterize their opponents as having strayed beyond the acceptable limits of the tradition.

PLUTARCH Our last Neoplatonist for this chapter predates the main period of this study by half a century. Plutarch of Chaeronea (ca. 40s-ca. 1 20s) was a very prolific author; his extant works include fifty biographies and seventy-eight other works treating ethics, philosophy, and religion. He studied in Athens in the late sixties with Ammonius, an Alexandrian Platonist who was also fascinated by Pythagorean number symbolism. Plutarch's philosophical training was thorough, as shown by the breadth of his philosophical treatises, which frequently cite older philosophers from Platonic, Peripatetic, Stoic, and Epicurean schools. For most of his life he lived in his hometown, although he had a wide network of influential friends from across the Roman Empire. The majority of his extant writings were composed in the last decades of his life, when he was a priest at Delphi, to which he was resolutely dedicated, as an inscription there attests.63

63 Babbitt ed., vol. 1 (LCL 197), frontispiece. For more on Plutarch's life and works, seeOCD, s.v.

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250 Number symbolism pervades Plutarch's writings, evidence of the importance he placed in his studies with the mathematically inclined Ammonius. The titles of two treatises, now lost, reflect this interest: Whether the Odd or Even Number Is Better and Monads.64 The former, no doubt, would have treated the common Pythagorean association of odd and even with male and female. The latter presumably would have dealt with the symbolic and metaphysical properties of units. Both are themes that recur in his other writings, alongside many other instances of number symbolism.65 Three treatises are especially useful for this study, The E at Delphi, Table Talk (particularly book nine), and Isis and Osiris.

In The E at Delphi there are six named characters who take part in a discussion, styled as a Socratic or Aristotelian dialogue. Plutarch himself and Ammonius, his former teacher, are two of the participants. The subject at hand is the meaning behind an E inscribed at Delphi. The various participants note that the inscribed figure could be read as a number, or named as a letter (pronounced ee, not epsilon) and therefore equated with the homonyms if

(d) or you are (d). One by one they offer a series of seven possible solutions to the problem. The first answer, proposed by Plutarch's brother Lamprias, depends upon the E as a numeral, and he takes it to represent the five wise men of Greece: Chilon, Thales, Solon, Bias, and Pittacus, all of whom are reported to have met at Delphi, where they agreed to consecrate the letter in honor of their number.66 Ammonius dismisses the suggestion, as does an unnamed participant who offers his own alternative explanation, that as the second

64 Lamprias's catalogue, nos. 74, 163. 65 See excursus B2, and Plutarch, Roman Questions 1 02 (288D). 66 Plutarch, The E at Delphi 3 (385D-386A)

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251 of seven vowels the E represents the sun, second in position after the moon, and therefore ApolloP This suggestion too is dismissed. The Delphians agree that neither the appearance nor its sound should be considered as a key to interpreting the E, but rather the spoken name of the letter,

EL

This leads to the

third explanation, that the E represents either the word if (d), the key word used to discover from the god the outcome of a future endeavor, or the if of the optative mood, to indicate wishes or prayers.68 Another option, the fourth explanation, is that the if indicates the force of syllogistic logic.69 The conversation returns in the sixth explanation to E as a numeral, a symbol of the key number, "the pemptad" - an archaism of pentad and the root of the rare verb "to count on five fingers" (nq.tna(nv)?0 This explanation comes from an Athenian named Eustrophus, but Plutarch eagerly takes over the idea and the discussion. What follows is Plutarch's lengthy excursus on the mathematical and symbolic excellence of the number five. He notes that five is the sum of the first odd and even numbers, and is therefore called

marriage (see excursus D5)?1 Five is called nature since when multiplied by itself the product's final digit is always five; when five is multiplied by any other number it results in either the decad or itself; and this behavior resembles nature, which returns either to itself or to perfection.72 To answer the objection that this seems to have little to do with Apollo, the

67 Ibid. 4 (386A-B). 68 Ibid. 4-5 (386B-D). 69

Ibid. 6 (386D-387D).

70 Ibid. 7 (387D-F). The thought is repeated in Plutarch, The Obsolescence of Oracles 36 (429D). See also

idem, Isis and Osiris 56 (374A) . 71 Plutarch, The E a t Delphi 8 (387F-388c) . 72 Ibid., 8 (388c-E).

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252 god at Delphi (who was associated with the number one and seven, not five), Plutarch pursues a convoluted explanation that involves Dionysius and the harmony in the poetical measures and, finally, the ratio three to nine, seen in the relation between the creation and the conflagration.73 As if caught in the tangle of his own obscurity, Plutarch leaves this line of thought unresolved, and reverts to his original explanation of five's behavior of returning to itself or to perfection, an attribute of the divinity. So too, he goes on, five appears frequently in music, in the fifth (literally bLa nEV'rE) and in the five basic intervals74 Furthermore, Plato affirmed there to be five worlds, Aristotle taught five elements, and there are five fundamental geometrical shapes in the Timaeus.75 Plutarch lists each of the five senses and explains to what element each belongs, and he appeals to Homer, who divided the cosmos into five parts.76 Further, the succession point, line, plane, and solid must continue in its fifth phase to the level of soul. There are five classes of living things in the world - gods, daemons, heroes, people, and beasts - and the soul naturally divides into five parts?7 Plutarch notes that the number five is the sum of the first two squares, provided that one is willing to take the number one as a square78 After arguing that Plato makes his chief principles, causes, and categories five in number, Plutarch suggests that the Delphic

73 Ibid., 9 (388E-389c). 74 Ibid., 10 (389C-F). 75 Ibid., 1 1 (389F-390A), a meditation expanded in Plutarch, The Obsolescence of Oracles 32-33 (427A428B). 76 Idem, The E at Delphi 12-13 (390B-c). 77 Ibid. 13 (390C-F). The soul was normally trisected in the Platonic tradition, and, indeed, in Plutarch's other writings. Dillon, Middle Platonists, 194. 78 The E at Delphi 14 (390F-391A).

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253 inscription was set up by someone who had anticipated Plato's doctrine?9 The crowning point in Plutarch's rambling encomium- it has now taken up more space than all the previous five explanations combined -is a riddle. On the sixth day of the new month, the priestess is led to the Prytaneum, and the first of the three lots is given over to five sortitions: two for the inquirer and three for her. Nicander interjects that this is so, but warns that the reason should not be uttered. Smiling, Plutarch answers, "Until such time as we become holy men, and God grants us to know the truth, this also shall be added to what may be said on behalf of the Five."80 Ammonius responds to Plutarch's arithmetical encomium with the pleasure of a teacher observing an immature student speak his naivete sophisticatedly. Rather than argue the point directly, Ammonius notes that just about any number's praises could be sung, especially seven, Apollo's native number.81 For him, the more plausible explanation for the E is "you are" (d), and for the rest of the treatise Ammonius explains what it means to ascribe eternal, unchanging being to Apollo, given our own fleeting, fluctuating condition.82 The length of the sixth explanation shows that Plutarch was fascinated with numbers and their symbolism. But it is difficult to determine how seriously he regarded them. The mathematical interpretation of the E is the longest, but in the end it is trumped by Ammonius' s ontological explanation. Of all the participants, Ammonius, the Pythagorean mathematician, would be the one expected to emphasize the number symbolism of the E. At

79 Ibid ., 15 (391A-D). so Il Ef.t71aboc;. Ibid., 16 (391D-E).

81 Ibid., 17 (391E-392A). s2 Ibid., 18-21 (392A-394c).

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254 the end of The E at Delphi, the reader is left with a number of options, and no definite indication as to which is the true explanation. Lamberton, in his recent introduction to Plutarch, notes how difficult it is to interpret the Delphic dialogues, "deliberate but coy self-portraits," where "Plutarch remains a very elusive presence."83 The dialogues, in Lamberton's reading, dramatize inquiry and keep a single, dominating explanation at arm's length from the reader, emphasizing instead the importance of dialogue itself and the pursuit of truth. The difficulties that beset this pursuit are symbolized by the setting in Delphi, where the oracle speaks in riddles that have frequently been misinterpreted, and where the priests are not allowed to divulge the mysteries. Plutarch, a Delphic priest when he wrote the dialogue, would never have divulged the secrets of the priesthood publicly, so to search the discourse for the correct answer is a fool's errand.84 But if the arithmological explanation of the E is merely one installment in the search for truth, then why has Plutarch dwelt on it and at such length? What does he intend the reader to do with all this numeric lore? One obvious answer, in light of Lamberton's thesis, is that such insights would be entertaining, and should be part of any educated person's repertoire of knowledge.85 Such an attitude toward number symbolism - lighter than the attitudes expressed by other authors in this study -is illustrated best in the Table Talk, a collection of idealized conversations among friends after dinner. Number symbolism crops up in many of the discussions, and even in the structure of the work, which is organized

83 Plutarch, 5. 84

Ibid., 26, 149, 156-58.

85 Dillon, Iamblichi Chalcidensis, 1 90.

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255 into nine books, in honor of the nine muses.86 The playful use of numbers is portrayed as a diversion, as entertaining as the after-dinner game where guests challenge each other with isopsephic rid dles, a practice that Plutarch reports but unfortunately does not describe.87 In

one scene of Table Talk, two related questions are asked. Why is the alpha first in

the alphabet? Upon what proportion is the number of vowels and semivowels built?l8 The first of these two questions is posed by Hermeias, a geometer, to Protogenes, a grammarian. Protogenes's answer is that vowels take precedence over the consonants and semivowels, a hierarchy commonly taught in schools.89 Further, any vowel that can be either long or short (i.e., a, L, u) is superior to vowels that are only one or the other (i.e., short:

c:,

o; long: T], w).

Of the three vowels of ambivalent length, a is superior to L and u, since when a follows either, it never assimilates into a diphthong. This is something of a protest on the alpha's part for not coming first, where such assimilation does occur. That is, m and au are single syllables, but Let and vex are two syllables. Thus, on three counts of superiority, the alpha is given pride of place in the alphabet, as if the winner of a pentathlon. After Protogenes' answer two other possibilities are proposed. The first, from Ammonius, is that Cadmus adopted the Phoenician convention, which prized oxen as the first of necessities. This proposal, although historically correct, Plutarch - here a participant- sets aside for a phonologically based one, that the alpha is the most basic,

86 Plutarch, Table Talk 9.pref (763c); see also the lengthy discussion on the number of muses and its

significance at 9.14 (743c-748D). 87 Plutarch, Table Talk 5.pref (673A-B). 88 Ibid., 9.2-3 (737c-739A), upon which my description in the following paragraphs is based. 89 See n. 27, above.

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256 simplest sound to articulate. This is the reason, he says, that the names of the consonants, save pi, need the assistance of the alpha.90 After Hermeias accepts the competing theories as being of equal value, Plutarch challenges him with the second question, more appropriate to his job as geometer. Plutarch begins to answer his own question by noting that the twenty-four letters are divided into groups of seven, eight, and nine, which is the arithmetical proportion (c - b

=

b - a)?1 The

proportion is not mere chance, but reflects the most fundamental of all the ratios. Furthermore, the extremes of the series represent the nine muses and Apollo, traditionally assigned the number seven.92 Their sum is twice the middle number, symbolic of how semivowels share in the nature of consonants and vowels. Hermeias takes up Plutarch's explanations and expands on the number symbolism. Hermes, inventor of writing, is associated with the number four, the day of the month upon which he was bom.93 This explains why the earliest Greek alphabet- that of Cadmusconsisted of only sixteen letters. It also explains the additions to the alphabet made by Palamedes and Simonides, each whom contributed four extra letters.94 The sum of the

90 Of the nine consonants, �, y, b, 8, K, n, T, x, and ¢, two others besides pi lack alphas in their names: chi and phi. Plutarch's explanation is that phi is an aspirated pi, and chi participates secondarily in the alpha by virtue of being an aspirated kappa. 91 The grouping is already noted above, p . 88 n. 23. 92 Traditionally, that is, according to Plutarch (Table Talk 8.1 .2 [717D] and The E at Delphi 17 [391E392A], discussed above). Apollo is more often associated with the number one. See Plutarch, Isis and Osiris 10 (354F), 75 (381F); Theology of Arithmetic, s.v. 93 See Theology ofArithmetic 28.3. 94 On the wide variations in the ancient and late antique accounts of the alphabet, see above, p. 149 n. 29.

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257

letters, twenty-four, reflects the first two perfect numbers, three and six, both of which are factors of twenty-four.95 Zopyrio, a schoolteacher, laughs at this explanation, calling it total nonsense. The quantity of letters came about not by forethought but by chance. The harmonies found in the alphabet are as much a coincidence as the first lines of the Iliad and the Odyssey, which possess the same number of letters (as indeed do their last lines). And with this last bit of ridicule, the conversation drifts to other topics. Similar to The E at Delphi, the Table Talk puts no stock in any one conclusion. Plutarch colors his dialogues with an air of sport and riddle. Here Lamberton's thesis, that Plutarch is more concerned with the pursuit of truth than its acquisition, should be modified somewhat, since there is no suggestion that truth is on the agenda. Rather, the challenges the dinner participants present to one another are intended to elicit thoughtful and sometimes ribald responses, whose excellence is judged by their cleverness. There are several parallels to Valentinian number and alphabetic speculation. The vowels, semivowels, and consonants are ranked into groups whose numbers are considered significant, just as in Marcus's teachings. The comments by Hermeias on the early development of the alphabet are based on early lore about the development of the alphabet, yet he structures that lore so as to emphasize the alphabet's divine origin, signified by its dependence upon the number four. This compares favorably with Marcus, who circumvents history and plugs the alphabet's structure directly into the divine realm. Zopyrio, the critic at the end of the conversation, resembles Irenaeus and Iamblichus, with the notable

9s 3

x

8 24 and 6 x 4 =

=

24. On three and six as perfect numbers, see p. 50 n. 125.

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258 exception that Zopyrio does not take the matter so seriously. This is, after all, simply a dinner conversation. That he is a mere schoolteacher (yQa!-l�Hxna'rijs), and not an advanced philosopher like Ammonius, seems to be Plutarch's extra touch, to emphasize that speculation on the numbers and letters may be interesting, but is not likely to fool anyone. On their own these two texts suggest that Plutarch considered number symbolism interesting, but not a satisfactory way to explain the world. Such a conclusion would be hasty. Isis and Osiris, Plutarch's study and analysis of the history of traditional Egyptian religion and mythology, is filled with number symbolism. Some of this lore is no doubt trivia, but many other arithmological explanations are genuinely important to him. According to tradition Typhon, when hunting in the light of the moon, found and chopped up Osiris's corpse into fourteen parts. Plutarch relates this dismemberment to the lunar phases.96 Numbers and the lunar cycle fascinate Plutarch, who reports the belief that cats give birth to successively larger litters- one kitten, two, three, all the way up to seven kittens, thereby giving birth to twenty-eight in all.97 He admits that the story is a myth, but he finds it uncanny that cats' eyes dilate when the moon is full. Plutarch claims that the Pythagorean application of numbers to gods was inspired by the Egyptians. Apollo is the monad, Artemis is the dyad, Athena is the hebdomad, and Poseidon is the first cube, all because these motifs were etched into Egyptian religion.98 For similar reasons the Pythagoreans associated triangles with male deities and squares with female; and Plato assigned odd numbers to Olympian gods, but even numbers to

96 Plutarch, Isis and Osiris 18 (358A), 42 (368A). 97 Ibid. 63 (376E). 98 Ibid. 10 (354F). See below, pp. 301-302.

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259 demigods.99 B ecause Osiris died on the seventeenth of the lunar month the Pythagoreans abhor the number. Sixteen is a perfect square, and eighteen a perfect rectangle, in that both numbers form geometrical figures whose area is equal to their perimeter.100 Seventeen divides the two numbers, and can be divided into only unequal parts. Plato's nuptial triangle, a rectilinear triangle consisting of sides length three, four, and five, also derives from the Egyptian myth of Isis and Osiris.101 The vertical side of length three corresponds to the male Osiris, the source. The base represents the female Isis, the receptacle. The hypotenuse is Horus, their perfect offspring.102 Plutarch does not write all this off as mere mythology, interesting tidbits suitable only for chitchat around aperitifs. He treats the Isis and Osiris story as true; its greatest truths are latent in its symbolism.103 According to Plutarch there are two errors to be avoided: superstition and atheism.104 The middle course is piety, adherence to right belief.1os By adopting a philosophical and pious attitude to the various customs of the world, one finds the truth of symbols. Plutarch says that the world's various cultures give the gods different names, but they nevertheless all share the same gods, the same way they give the same planets and elements different names.106 But behind all these naming systems and

Ibid. 26 (361A), 30 (363A). See below, pp. 301-302. 4 x 4 4 + 4 + 4 + 4 and 18 3 x 6 3 + 6 + 3 + 6. 101 Plato, Republic 546B; Plutarch, Isis and Osiris 56 (373F-374A). 102 See below, p. 323. 103 See Gwyn Griffith's ed., 1 00-101 . 104 Isis and Osiris 1 1 (355CD), 67 (378A). 105 Ibid. and Gwyn Griffith's ed., 291 . 1 06 Plutarch, Isis and Osiris 6 7 (377EF). 99

1oo Ibid. 24 (367E-F). 16

=

=

=

=

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260

behind all the various religious symbols is a single reason (A6yoc;) and providence that orders and guides everything. The number symbolism Plutarch uses in all three texts work according to these principles. As Lamberton says, the Delphic dialogues emphasize the voyage to truth, not its attainment. But even in these dialogues there is an assumption Lamberton misses. That assumption is stated clearly only in Isis and Osiris. To engage piously with symbols is not just to pursue the truth but to contact it. That explains why number symbolism appears so frequently in Plutarch's writings. In The E at Delphi the reader is meant to engage piously with the number symbols, and thereby interact with divine truth. It may be only one aspect of truth, but it is nevertheless a genuine engagement. Number symbols, however, are not self evident, and they can be abused. There is superstitious number symbolism (the numbers surrounding the cat, for instance, and probably some of the number symbolism in Table Talk) and there is an atheistic treatment of numbers, where they lose all meaning. It is important to find the middle way, which is what Plutarch tries to do throughout the rest of his writings when he engages with numbers.l07 Plutarch's criterion for what constitutes appropriate number symbolism compares well with those of Irenaeus and Iamblichus. All three agree that numbers are important symbols, but they caution against abuse. For Plutarch the abuse comes from superstition, that is, an impious or unphilosophical approach to symbols. For Irenaeus it comes from starting outside the rule of faith. For Iamblichus it comes from reducing the meaning of the 1 07 Plutarch's number symbolism is extensive. For examples, see excursus B2. Of special note is his

Genesis of the Soul in the Timaeus, in which major theses are advanced about the relationship between the soul and number. The text is also vital for understanding the history of Platonist interpretations of number symbolism in the Timaeus.

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261

symbol to arbitrary, transient customs. For all three, identifying the source of error is important because to mishandle numbers is to mishandle the truth. Conversely, to handle numbers piously is to encounter the divine.

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10 Numeri ex Regula

In the late Roman Republic, Pythagoreanism arose from the dead. The symbolism of the mathematical sciences so fired the imagination of authors in late antiquity that Pythagoras was figuratively reincarnated and reintroduced to intellectual and religious life. In the two centuries after Nigidius Figulus, Pythagoreanism grew to become as important an intellectual influence as Stoicism and Platonism, albeit on paper. Arithmetic, geometry, music, and astronomy were taught as if Pythagoras founded them, and in later antiquity other related sciences and pseudo-sciences-most notably, prognostication by means of arithmetic, especially isopsephy - came under Pythagoras's wing. The gradual growth of Pythagoreanism explains the appearance of the theological systems of the Valentinians, Marcus, Basilides, the Barbelo-Gnostics, deutero-Simon, and

Marsanes, all of whom make Pythagorean number symbolism a central part of their worlds. They all arrange into an arithmetical array multiple beings initially projected by a Monad or Monad-Dyad pair, the source of all things. The imagery and terminology they use depend upon the fundamental structures of arithmetic as it was taught and understood in the second century. Some systems focus on the utter solitude of the Monad; others make the eternal relationship between Monad and Dyad central; still others mix the two metaphors,

262

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263 or develop models that fall somewhere along the monadic-dyadic spectrum. The variations are not contradictions, but complementary ideals on the origin of the numbers. Attractive to both Christians and non-Christians, this arithmetical theology seems to have first developed in the 160s, and lasted through the mid-third century. After this period the theology of arithmetic is less evident, at least in Christianity; Platonism continued to make numbers central to its divine structures. This historical peak in the late second and early third century coincides with the observation Markschies makes, that the 160s through the 180s mark a period of "classical," i.e., highly philosophical and well developed, gnosis. Marcus, whose writings form the epitome of the development of the theology of arithmetic, exemplifies how, in this era of classical gnosis, a Christian could tap into Pythagorean and semi-Pythagorean science and lore and fuse theology with the numbers and the alphabet. The general view many scholars take toward Valentinian and other gnostic protology is that the structures express the multiple characteristics of the one God. That is, Irenaeus and other heresiologists mischaracterize as polytheistic their fellow Christians, who were attempting to put in the language of philosophy the Christian message. Although there is much to commend in this perspective, it must be corrected by some of the themes I have presented in this study. In late antique mathematics, the progression from monad through dyad to the rest of the numbers was presented as a descent from absolute unity to plurality. The dyad, triad, tetrad, and so on, were not thought of as mere aspects of a single monad, but as entities that once lay potentially in the monad, but now exist separately, as "others" to the monad. Valentinians use the same mathematical language and models to describe the emanations of the aeons, a kind of cascade of multiplicity. They extend the analogy to explain the origins

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264 of the natural world and the organization of the human being. The mathematical symbolism they use emphasizes the otherness of the aeons. No doubt, the aeons in the Ogdoad reside potentially within the Monad or Monad-Dyad, but when they emerge, they exist apart from from their parents, and become separate entities. Some of the aeons have names that describe characteristics of the primordial entity, but this does not mean that they are meant to represent merely the characteristics of their source. The mathematically structured relationship of the aeons makes clear that the erstwhile characteristics have been reified and now have separate existence. This explains why Irenaeus and other orthodox writers treat Valentinianism as a form of polytheism: it makes divine multiplicity central to its system. The aeons have as real and as separate an existence as does the water that results from the tears of Wisdom. The Valentinian approach may be compared favorably to the Platonic systems presented in this study. For Marsanes, Theodore, and even Iamblichus, the great mystery to be pondered is the transition from absolute unity to multiplicity, an organic process that leads to multiple levels of reality, each of which is mathematically organized. Redemption from our fallen world involves an ascent through stages and levels that taper off in the ethereal purity of the Monad. In Spiritual Seed Thomassen has argued that the Valentinian myth depends upon and elaborates on the Pythagorean-influenced philosophy concerning the rupture of duality from monadic simplicity. My study confirms his thesis, and paints a fuller picture of how the Valentinians, as well as non-V alentinian systems like those of Mono"imus and the Paraphrase of the Apophasis Megale, depended upon arithmetic for their theology. For all of them arithmetic is the beginning, the end, and even the content of their doctrines of God.

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265 Did the Platonists influence the Valentinians or vice versa? The chronology of my sources might suggest that the Valentinians shaped Platonism, since Numenius and Theodore of A sine postdate the second century. But this appearance may be deceptive, since the vast bulk of literature from this period has perished. But deciding the cause-effect relationship has no bearing on the main point, that Platonists and Valentinians alike (and the other systems discussed in chapters 2 through 5) collectively participated in an intellectual culture that prized mathematics for offering coherent and cogent explanations of their metaphysics. This does not apply to Irenaeus and Clement's theology. Their writings reveal their commitment to the doctrines commonly held by all the churches spread across the Roman Empire. They separate themselves from the heretics' views of the godhead, of the Incarnation, and of salvation. Likewise, Clement and Irenaeus avoid or correct their theology of arithmetic. Aside from the symbolism of the number one, Clement and Irenaeus never apply arithmetical models to the godhead or divinity. Irenaeus is unambiguous in his commitment to God as three persons, Father, Son, and Holy Spirit. Clement champions a Christian monotheism where God is free of any mathematical models or constraints. For both, neither God nor the Christian tradition is subject to mathematics, but rather the converse. This is not to say that orthodox theology was completely unified in how arithmetic should be used in theology. Irenaeus, as we have seen, writes often about one Father and one Son. The oneness he emphasizes has less symbolic and philosophical overtones than Clement's emphasis on oneness, which derives from Platonic and Stoic descriptions of God. For Clement, God transcends any predicate, including that of the hen/one. Although God

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266 cannot be properly described as One, because of his transcendence, the analogy is fruitful. God is very much like a hen/one that stands above the hierarchy monad - hen. Clement is comfortable with such analogies. Irenaeus, however, never approaches such analogies, part of his reluctance to use the metaphors of Platonism or Pythagoreanism for theology. The distinction between gnostic and orthodox applies to the number symbolism found in their theological structures, but it does not apply to the way these various groups read and interpreted Scripture and the natural world. Everyone - Valentinians, Marcus, Mono"irnus, Pythago"imus, deutero-Sirnon, Irenaeus, and Clement- approaches numbers found in Scripture with well-developed ideas of number symbolism. They draw from and add to a centuries-old tradition of number symbolism - a tradition captured in arithrnological textbooks such as the Theology ofArithmetic-to press horne their exegetical points. When reading Scripture, Christians looked for numerical patterns that might help unlock the mysteries of the text. Those numbers could appear in the Bible in several forms. It could be stated directly, such as the reference to the ninety-nine in the parable of the lost sheep. It could be merely implied, such as story of the Transfiguration, which itemizes, but never states, the number of people present. Or it could be even more cleverly hidden, in letters or alphabetic numerals whose numerical value was considered significant, such as the psephic value of the word dove, or the mention of the numeral ten in the story of Gideon. In

all these cases, Christian exegetes latched onto the numbers they read, and they

interpreted them in light of some other part of their tradition. To understand the natural world Christians adopted the conventions of number symbolism common in the Greco-Roman world. There are seven planets, twelve hours,

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267 twelve signs of the zodiac, four winds, five senses, and so on. Some parts of the natural world were open to different kinds of numerical arrangements. Thus, human ages could be divided into four, five, or seven phases. The human being could be divided into three, seven, eight, or ten parts. The world, both physical and ideal, provided many number symbols, any of which could be used to explain myth, theology, or ethics. Plutarch's treatment of the rectilinear triangle of sides three, four, and five touches on all three explanations. The number symbolism collected by the Pythagorean Nicomachus of Gerasa and the Christian Anatolius of Laodicea, preserved in the Theology of Arithmetic, epitomizes the very wide varieties of number symbolism that Christians and philosophers used. Irenaeus accuses the Valentinians of having a faulty exegesis, particularly of the numbers that appear in Scripture. He champions the standards necessary for a correct interpretation. The most important of these is that number symbolism should be set squarely within the rule of faith. Scripture should be treated as a narrative, and the numbers that appear should be handled in the context of the entire narrative, not simply plucked from the page. Numbers should come from the rule of faith, not vice versa. Because he uses very much the same techniques as the Valentinians to interpret Scripture, Irenaeus may seem hypocritical, at least when it comes to interpreting the natural world. Both Irenaeus and the Valentinians appeal to the natural world to enhance and not justify their theology, to frost their cake and not to bake it, so to speak. Irenaeus accuses the Valentinians of drawing from the number symbolism of the natural world in an inconsistent or incomplete manner. But this weakness is evident in some of his analogies, too, particularly of the four winds representing the four Gospels.

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268 But Irenaeus' s critique is consistent in three major areas (which is not to suggest that the Valentinians were necessarily wrong). First, the exegesis Irenaeus criticizes really does not attend to the context of the Scriptures used to explain the Pleroma. The overtones of the language Irenaeus's Valentinians use suggest that they felt no need to do so, since the kind of knowledge they claimed was something that was hidden, and only cryptically alluded to in the Bible. The Bible did not justify their knowledge of the Pleroma; the Pleroma was seen in the Bible retrospectively, in passages hidden to everyone but those initiated in the mysteries of the system. Irenaeus, however, sees the Biblical text and, more generally, the apostolic rule of faith, as the standard by which such claims should be judged. Any fool with a half-baked idea could claim that Scripture secretly alludes to a system revealed only to the few around him or her. The Valentinians' method could be used to justify any system one wanted to invent. Irenaeus's complaint is almost exactly parallel to Iamblichus's criticism of the arbitrary methods and ideas of Theodore of Asine. Maybe the Valentinians and Theodore were truly guilty of these charges; maybe they weren't. In any case Irenaeus and Iamblichus argue successfully against the solipsistic interpretive methods that were as likely then as they are today. Second, Irenaeus argues against the Valentinians' dependence upon changeable, human conventions. Irenaeus criticizes Marcus for his psephy and dependence upon the Greek alphabet. This temptation seems to have been common in the ancient Mediterranean. Some of Plutarch's characters also appealed to changeable, human conventions of numeration to interpret the world. True, lrenaeus's interpretation of Gideon's ten men suggests that he found the technique attractive. But ultimately he stays away from psephy, most evident in his interpretation of the name of the Beast. Irenaeus warns that using the

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269 alphabet and its numbers to discover hidden truth can lead to grave error. The caution is echoed by Hippolytus, who criticizes Colarbasus' s numerology on similar grounds. Although Colarbasus's numerology cannot be tied to Valentinianism, the trajectory is clear: Marcus's experiments in gematria lay the foundation for such numerology. The orthodox Christian resistance to this trend resembles Iamblichus' s criticism of Theodore of Asine, who theologized on the soul using techniques also bound to human linguistic conventions. Third, Irenaeus insists that you must begin with the rule of faith, and derive any number symbolism from it, not the other way around. On their own the Valentinians had developed a notion of the Pleroma, without recourse to the Scriptures and the traditions of the Church. They had predetermined what numbers and symbolic numerical structures should be the key to reading the rest of the Christian tradition. Although there are many parallels to the Valentinian Pleroma in Christian and non-Christian literature in late antiquity, there is no single model that can be considered the prototype of Valentinianism. There is no evidence of Valentinian protology prior to the 160s. Presumably they invented their systems, either individually or in small groups. Their ethos encouraged creativity and the development of new models. This individualism, Irenaeus charges, motivated them to revise the apostolic rule of faith in the light of private, arbitrary opinion. It may be reasonably answered that Irenaeus is still ingenuous on this point, that the Valentinians were doing what he was doing, albeit from a different starting point. After all, they too cherished a rule - a rule that involved the Pleroma and the mythology of the fall of Wisdom- and from that rule had emerged a panoply of number symbols. Thus, the Valentinians also held to numeri ex regula, but the rule (regula) differed from Irenaeus's; it was one of a number of rules that existed in a pluralistic primitive Christianity.

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270 This response misunderstands Irenaeus's claim and charge. He does not advocate a general principle, that, given any rule, numbers should come out of it. No, Irenaeus is more specific. There is only one rule. Everything else is a shadow or a lie. That one rule, taught by Christ to the apostles, and entrusted by them to the churches around the world, is unswerving and unchanging from one region of the inhabited world to the next. As far as we can tell, Irenaeus is correct: there is no evidence that Valentinianism was shared by all the early churches in the Roman Empire. Irenaeus claims to uphold the apostolic rule of faith, the rule given by the apostles to all the churches in the world. Determining the truth of this claim is not important here. The claim explains his number symbolism, and in this he is consistent, since he always draws his number symbolism from the rule of faith. But the Valentinians relied on an idiosyncratic, changing system, thereby disqualifying themselves from any claim that they were preserving the Church's common rule of faith, a rule that was corporate, not private, property. Clement of Alexandria joins Irenaeus in this line of attack, as do other orthodox writers from the second and third century. In this respect Christians and Platonists part company. Although Platonists also had a highly developed tradition, they did not treat it as Christians treated their own. For Christians, the rule of faith was a revealed, unchanging gift of God to the Church. Platonists had no such view. For Christians, the Church, spread throughout the world, was witness and guard to the truth, a community of divine origins and purpose. Platonists had no such ecclesiology; if they had social structures, they must have been minimal, since we hear nothing about them.

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271 The orthodox tradition of number symbolism had a great deal of variation. Clement's arithmology differs from Irenaeus' s in key respects. Clement oftentimes ignores the context of a given passage and sees in a text a hidden reference to a theological symbol of one sort or another. The substantive theological points for which he argues are not d ifferent from Irenaeus's, but his technique is very similar to that of the Valentinians and Mono"imus. Irenaeus advocates principles of interpretation that he himself does not follow; Clement breaks those principles, but he also never champions them. He uses the same interpretive techniques that Marcus does, but in service to the orthodox, ecclesiastical tradition. Both Marcus and Clement use the episemon ogdoad as a key theological symbol, but Marcus uses it to depict the arithmetical composition of the Pleroma; Clement handles it as a symbol of the Incarnation. Irenaeus shows little interest in this kind of expansive, more speculative number symbolism.

We have not explored in any detail how subsequent Christian generations and writers developed these themes. A thorough portrait would require a separate study, but the outlines can be sketched. The formation of the theology of arithmetic in the late second and early third centuries extensively influenced subsequent generations. Just as Irenaeus and Clement handled numerical symbols differently, there was no single acceptable way to use number symbolism in later Christianity. Those inclined to mystical, speculative, or allegorical theology tended to embrace Clement's pattern; those more skeptical of such methods tended toward Irenaeus's, or omitted it altogether. All sides, however, agreed that there were forbidden uses of numbers, namely, when it subordinated God to arithmetic, or undermined the Christian teaching on the Trinity, or

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272 tried to predict the future. Each of these three prohibitions was challenged at various times in various places. In the scholastic era in the West, theologians began to write treatises that proved the undeniable logic of the Trinity by appealing to mathematical principles that logically preceded the godhead. During that same period, Jewish, then Christian, kabbalistic literature reintroduced the notions of arithmetically arranged emanations in the godhead. The third restriction was challenged at the outset: numerological prognostication blossomed and grew from the third century onwards throughout the Greek-speaking East, albeit without the Church's approval. Thus, the errors Irenaeus fought against either never went away or returned after a lengthy departure. But that story is to be told another time.

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Excursus A Pythagoreanism in Outline

Scholars in the last thirty years have come to a rough agreement on the shape and history of Pythagoras and his tradition.1 Pythagoras was born on the island of Samos, around the midsixth century BCE, a time when in nearby Miletus thinkers such as Anaximenes and

J

The attempt to find the historical Pythagoras has proved to be as captivating and elusive as parallel efforts to find the original Jesus or Hippolytus. For nineteenth- and early twentieth-century research on Pythagoras, see Burkert, Lore and Science, 1-4. In his study, still admired as one of the most important works on the subject, Burkert agreed with the skeptics, arguing that there was very little evidence to suggest that Pythagoras was a scientist or philosopher by ancient standards. Rather, the oldest testimonies (especially the akousmata) suggested that Pythagoras was a shaman! ike figure, a charismatic holy man. His assessment, although not universally adopted, is universally respected. Zhmud, Wissenschaft, Philosophie und Religion, and Kahn, Pythagoras and the Pythagoreans, have worked within the terms and framework set by Burkert, but are more optimistic in their assessment of Pythagoras, suggesting that he probably was involved in the science and philosophy of his day. More skeptical is Huffman, whose Philolaus of Croton and Archytas of Tarentum have reinforced a skepticism concerning Pythagoras's scientific accomplishments. For an extensive bibliography, see Navia, Pythagoras: An Annotated Bibliography. A stream of scholarship in the last ten years has amplified our picture of what "Pythagoreans" must have looked like in the age of Iamblichus. See Staab, Pythagoras in der Spiitantike; von Albrecht et al., Pythagoras: Legende, Lehre, Lebensgestaltung; Rappe, Reading Neoplatonism; Shaw, Theurgy and the Soul; Blumenthal and Clark, Divine lamblichus. Especially noteworthy are the recent attempts to describe the fresh endeavors in late antiquity to philosophize about the metaphysical status of number, an activity that seems to depend upon Pythagorean arithmology. See Bechtle and O'Meara, Philosophie des mathematiques. For more recent accounts of the history of Pythagoreanism see OCD, s.v.; Dillon, Middle Platonists, 338-41; Riedweg, Pythagoras: Leben, Lehre, Nachwirkung; Math�i, Pythagore et les pythagoriciens. A two-volume history of Pythagoreanism, by C. Joost-Gaugier, is in preparation.

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Xenophanes were active and a new system of numeration had been invented (see excursus B). According to the later tradition, Pythagoras left Samos and traveled to Egypt and Mesopotamia, acquiring religious and scientific knowledge along the way. Contradictions in the chronology and geography of these late accounts obscure any certain knowledged of his whereabouts before he settled in Croton, in southern Italy, around 530 BCE. There he founded a philosophical-religious community and became active in the political life of Croton, which won in 510 BCE a battle that secured for itself local economic and military hegemony, which lasted until about 450 BCE. Although Pythagoras probably helped in Croton's success, a wave of violence directed against the Pythagoreans there forced him to flee to Metapontum, where he died a refugee in the early fifth century. His followers, who were in positions of power across southern Italy, weathered the persecution and maintained a presence on the peninsula for a century and a half. Scholars generally regard Pythagoras as a charismatic sage, a religious teacher, and a politician. How much of a philosopher or scientist he was is disputed. The community he established was bound by a common life and cult. New members were expected to spend several years of probation in silence and, when fully inducted, to preserve the secret teachings of the society. Members swore to uphold the community's strong code of ethics, which included rules for conducting one's family, and dietary restrictions, which in its earliest phase probably did not include the vegetarianism for which Pythagoreanism later became famous. Pythagoras emphasized the immortality of the soul and metempsychosis. Our basis for reconstructing the life and character of the earliest Pythagorean communities depends largely upon the akousmata, early Pythagorean sayings preserved by Aristotle and others. These akousmata are cryptic, and display an interest in 274

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taboo prohibitions, especially in diet and dress. They show no interest in the mathematical arts, natural science, or philosophy, which suggests that the earliest Pythagorean community was not as scientifically inclined as later generations thought them to be. We know very few names of Pythagoreans who flourished after the death of the master. Hippasus of Metapontum (fl. early 5th c. BCE) is the earliest. He is remembered for being expelled by the Pythagoreans for publishing their mathematical secrets. Philolaus of Croton (or Tarentum; ca. 470 BCE-ca. 390 BCE), who is the earliest Pythagorean whose writings are still extant, wrote about astronomy, medicine, and the soul. In his metaphysics he argued for a mathematical harmony in the world, which was composed of unlimiteds and limiters.2 These two shadowy figures -Hippasus and Philolaus - are the earliest examples of scientifically inclined Pythagoreans. To account for the emergence of scientific interest in the Pythagorean community, scholars tum to the reports of early schisms. Some time after the death of the master, those who wanted to emphasize and retain the religious and ritualistic character of the community - the so-called aKOVGf.H:XnKo(- separated from those who began to engage in the philosophical and scientific currents of their age -the l-la.8YJ!-11AHKOL The former group is said to have treated the latter as if they were innovators, and to have denied them any right to claim to be Pythagoreans. As far as we know, the !-!CX8YJ!-11AHKOL did not return the favor. There may have been more than one split in the Pythagorean communities of the fifth century, but this rifts shows that early on it was disputed as to how to live the Pythagorean way of life.

2 See below, pp. 296-297.

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One of these !J.U8f]!J.UHKOL, Archytas of Tarentum (fl. ca. 400-350 BCE), provides an important link to the next major phase of Pythagoreanism. The few fragments we have depict him as a Pythagorean philosopher, mathematician, and politician. As general of his city, he rescued Plato (ca. 429-327) from Dionysius II of Syracuse (b. ca. 396) in 361, at which time the two became close associates. It is quite plausible that Timaeus, the sage in Plato's

Timaeus, represents Archytas. The later dialogues of Plato-notably the Timaeus, Phaedo, Philebus, and the Republic take up and develop Pythagorean themes, such as the etemality -

of the soul, metempsychosis, and the harmoniously mathematical construction of the world. Plato was not a Pythagorean, since in each of these dialogues he develops a philosophy that is uniquely and distinctly his own. But he nevertheless depends upon Pythagorean insights.

In the generation after Plato's death three competing interpretations of the Platonic and Pythagorean traditions emerged. The first is that of Aristotle (384-322 BCE), one of the few authors of the fourth century to distinguish between the Pythagoreans and Plato. Although the book Aristotle wrote on the Pythagoreans is lost, comments he makes in the rest of his corpus supply a great deal of insight into the pre-Platonic Pythagorean tradition. For this reason, scholars tend to give Pythagorean fragments found in Aristotle stronger weight than they do other testimonies, despite Aristotle's often critical tone. Aristotle's representation of the Pythagoreans did not prove to influence the subsequent tradition the way Plato's immediate followers did, the second strain of interpretation. Speusippus (407-339 BCE), the nephew of Plato, succeeded his uncle as head of the Academy from 347 to his death. Only fragments of his once-extensive literary corpus remain, but what we have shows that he recast Platonic doctrine in the image of Pythagoreanism. He claimed that the Timaeus was a Pythagorean dialogue, and he 276

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transformed Plato's forms into numbers, which, he argued, derived from the Pythagorean principles of the One and Plurality. Speusippus's successor, Xenocrates (fl. 339-314 BCE) continued to reshape Platonic doctrine to conform to the Pythagoreanism of the fourth century 1--!a eru..tanKoL A third interpretive tradition went further. Aristoxenus of Tarentum (b. ca. 370 BCE) - musician, philosopher, and one-time disciple of the Pythagorean Xenophilus ­ diverged considerably from the Pythagoreans in his music theory and philosophy. Despite his biting sarcasm of predecessors such as Plato and Socrates, Aristoxenus held Pythagoras in respect, avoiding superstitious descriptions of him. In praising Pythagoras, Aristoxenus credited him with inventing doctrines later embraced by Plato and Aristotle. His lost works on the Pythagoreans probably furnished material for writers in late antiquity, and they signaled a trend discemable in the pseudo-Pythagorean writings, of ascribing not just Plato's teachings to Pythagoras, but also Aristotelian and Stoic doctrines. Of these three reinterpretations, the second proved to be the most influential in the later tradition, which conflated Pythagoras, Plato, and the Pythagoreans. Plato was reinterpreted in the light of a Pythagorean tradition, itself radically transformed as Platonic science. This resulted in the Platonizing of Pythagoras: uniquely Platonic insights were regarded as Pythagorean. From Speusippus onwards, it has proved difficult to disentangle the two traditions. The fourth century was also a fertile period for biographies of Pythagoras. In addition to those writers already mentioned, Heraclides Ponticus (fl. 4th c. BCE) wrote about Pythagoras, casting him as a shamanistic holy man and crediting him for first using the term

philosophy. Dicaearchus of Messana (fl. ca. 320-300 BCE) also wrote a life of Pythagoras. Like 277

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his fellow Aristotelian Aristoxenus, Dicaearchus denied key Pythagorean doctrines, yet extolled Pythagoras as a model social reformer. The variety of images of Pythagoras - from shaman to politician - that were composed in the fourth century are all evident in the various lives of Pythagoras composed in late antiquity. This same period was important, too, for the transmission of Pythagorean number symbolism. Speusippus wrote a treatise, now lost, titled On Pythagorean Numbers, purportedly based on Philolaus' s works.3 Aristotle wrote two books on the Pythagoreans, and one on Archytas, and passages in his Metaphysics suggest that numerical lore was one of the major topics. Xenocrates, too, wrote On Numbers and Theory of Numbers, each a single book.4 Since he was interested in Pythagoreanisrn, it is likely that both these books discussed Pythagorean number symbolism. There is no evidence for a Pythagorean community after the fourth century. The Platonic tradition forged by Speusippus probably became home to whatever was left of the 1-llX8TJI...HXnKol, the scientific faction of Pythagoreans. What happened to the aKOVG !-HXHKOL is unclear. There is some similarity between them and the later Cynics, but no connection can be firmly established. At any rate, in the Hellenistic period, Pythagoreanism ceased to be a lived reality, and Pythagoras was revered, but only as a dim memory. Our earliest extant specimens of pseudepigraphal Pythagorean writings come from the third and second century BCE. Many of these texts treat philosophical themes then current in the Hellenistic period, and are written in an archaizing Doric Greek. The texts tend to focus on ethical and

3 Theology of Arithmetic 82.10-15. 4 Diogenes Laertius, Lives of the Philosophers 4.13.

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political themes, not mathematical or scientific ones, and they generally borrow the philosophy of the Academy and its successors. Nigidius Figulus (d. 45 BCE) is credited by Cicero ( 106-43 BCE) with the resurrection of Pythagoreanism. "Last but not least, it was [Figulus], in my judgment, who, following on those noble Pythagoreans, whose system of philosophy, after flourishing for a number of centuries in Italy and Sicily, was somehow extinguished, arose to revive it."5 That Figulus played a pivotal part in the reinvention of the philosophy is confirmed by Varro ( 1 1 6-27 BCE), who used Figulus's writings to compose his book Hebdomades (written after 32 BCE), which was full of Pythagorean lore. Other figures of the first century BCE are known for introducing or supporting Pythagorean doctrines. Eudorus of Alexandria (fl. ca. 25 BCE) wrote a commentary on the Timaeus, in which he opposed the Stoicized readings of Plato found in Antiochus of Ascalon (ca. 130-69/8 BCE) in favor of a transcendental Pythagorean reading. Eudorus may have been the single most important intellectual force for the renewed interest in Philolaus, Archytas, and the broader Pythagorean tradition.6 Juba II (ca. 45 BCE-ca. 23 CE), king of Mauretania, was known as an avid collector of Pythagorean books. Thrasyllus (fl. early 1st c. CE), a Platonist philosopher from Alexandria and astrologer to Tiberius, wrote about the principles of Pythagoreanism, which he considered as important as Platonism. The teacher of Plutarch, Ammonius (d. ca. 80 CE), also a Platonist, was an aficionado of Pythagorean number symbolism, which he probably taught to Plutarch. Even Alexander Polyhistor, who cannot be considered a Pythagorean, wrote a book on Pythagorean symbols (now lost). This mirrors the more Stoic Cicero, who decided to 5 Trans. Dillon, Middle Platonists 1 17.

6 Ibid. 114-20.

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translate into Latin the Timaeus, the most "Pythagorean" work by Plato. Thus, during the Republic and early Empire, Pythagorean themes had achieved a new kind of respectability in literate Roman society. Some of this respectability ran parallel to the successes enjoyed by astrology, then a relatively new science? In the first and second centuries CE authors of very different interests and backgrounds picked up Pythagorean themes. Moderatus of Gades (mid-1st c. CE) wrote ten or eleven books on Pythagorean teaching, attempting to show point by point how Plato derived his doctrines from Pythagoras. Apollonius of Tyana (fl. 1st c. CE) adopted the lifestyle of a Pythagorean holy man. His biography was embellished under the influence of later cultic reverence so we cannot say what episodes are genuine. But it seems that he styled himself as something of a successor to the Pythagoras depicted by Heracleides Ponticus. In the second century, Nicomachus of Gerasa, Numenius of Apamea, and Theon of Smyrna (fl. ca. 115-40 CE) all wrote mathematical and philosophical texts that depended upon Pythagorean lore. Nicomachus and Numenius are known to have written treatises devoted to Pythagorean number symbolism. Other authors from this period who ordinarily would not consider themselves Pythagorean nevertheless frequently appeal to Pythagoreanism, particularly in discussions regarding the sciences of the quadrivium (excursus B4). Those who reinvent a long-lost tradition inevitably omit key parts of the parent tradition, and introduce new ideas. The Pythagoreanism of the Roman Empire is no exception. Three major shifts are worth noting.

7 The connection is noted by Dornseiff, Alphabet in Mystik und Magie, 81 .

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1 . Astrology, magic, and divination. Nigidius Figulus was famous, not just for his Pythagorean writings on science and theology, but for his astrology and magic. Whether or not he was the father of neo-Pythagoreanism, he epitomized its new image. Although Pythagoras w as regarded from the earliest times as something of a wonderworker and shaman, he was not thought to have taught techniques in astrology, magk or divination. Indeed, astrology was still relatively new in Nigidius Figulus's day, since the practice entered Greek (and from there, Roman) culture only from around the third century BCE.8 But it was well-known that Pythagoras and his followers were interested in the sciences of the quadrivium, so it was natural to treat the Pythagoreans as if they were adept in using the diagnostic powers of those same sciences. Thus, there are many iatromathematical texts that are ascribed to Pythagoras or his circle. All date from late antiquity or after (see excursus D).

2. The loss of community. Up to the opening of the third c. BCE there were Pythagoreans who claimed to live, in unbroken succession, the Pythagorean way of life. When the movement was resurrected, there was no attempt as far as we know, to resurrect the communal life Pythagoras emphasized. The stories of holy men who championed Pythagoreanism, like Apollonius of Tyana and Alexander of Abonuteichos (fl. 2nd c. CE), show that the mysticat theurgic side of Pythagoreanism was something they took on individually. Their followers formed communities patterned on the religious groups of their own age, not sixth century Croton. Late antique Pythagoreanism was a literary ideat not a lived reality. This is not to exclude the possibility for a large following of Pythagoras in late antiquity, dependent upon oral lore, and not just written texts. But such an oral culture

s Barton, Ancient Astrology.

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w ould have been "literary": it had to either invent the past or reconstruct it from literary fragments. 3. Pervasive literary presence. Pythagorean themes extended into all gemes of literature. Ovid features Pythagoras in the last book of his Metamorphoses. Whereas the writings of Euclid (fl. late 4th/mid 3rd c. BCE), Apollonius of Perge (fl. 200 BCE), and other early Hellenistic scientists reveal no Pythagorean influence, late antique texts on the

mathemata, such as Ptolemy's (fl. ca. 146--c a. 1 70 CE) Harmonics and Nicomachus of Gerasa's Introduction to A rithmetic, do. The Jewish exegete Philo of Alexandria (fl. early 1 st c. CE) was termed by the later tradition a Pythagorean, in part because of his allegorical use of number symbolism, about which he wrote extensively.9 Hermippus of Berytus (fl. early 2d c. CE), a grammarian interested in dream interpretation, wrote an entire treatise devoted to the number seven. In Plutarch's ethical and philosophical treatises Pythagoreanism features often (see chapter 9). Iamblichus of Chalcis (ca. 245-ca. 325 CE) is a watershed figure in Pythagoreanism. Student of Porphyry (234-ca. 305 CE), who was himself a student of the great Platonist Plotinus (205-69/70 CE), Iamblichus wrote many of his works with Pythagoras as his model. His On the Pythagorean Way of Life was the first installment of a ten-book series meant to introduce students to a philosophical and theurgical approach to the quadrivium. lamblichus' s series was so attractive to the emperor Julian (331-63 CE) that he had it distributed in the Empire as part of his campaign to renew Hellenism. The literary image of

9 See Runia, "Philo 'the Pythagorean'." Philo's lost treatise On Numbers is reconstructed by Stahle, Zahlenmystik.

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Pythagoreanism developed after the fourth century CE.10 Beginning with the work of writers such as Damascius (fl. 4th/5th c. CE), Proclus (410/12-85 CE), and Macrobius (fl. 5th c. CE), the literary image of Pythagoreanism flourished in the ages of Islam and medieval Christianity, and into the age of Johannes Kepler (1571-1630).11

10 The best account of this transformation of late antique Platonism is O'Meara, Pythagoras Revived. 1 1 For Pythagoreanism in the modern age, see Kahn, Pythagoras and the Pythagoreans.

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Excursus B Themes in Pythagorean Number Symbolism

Despite appearances to the contrary, Pythagorean number symbolism has a history. Although Pythagoras was in all likelihood not a mathematician (see excursus A), he seems to have made numbers a central part of his philosophy. The number symbolism of the earliest Pythagoreans formed the core of an arithmological tradition that developed in the centuries that followed. In this excursus I outline the development of certain key themes in Pythagorean number symbolism, but only those themes that directly bear on the philosophical and theological debates relevant to this study. I cite the texts that are most important for showing the historical development of each theme to provide a starting point for future research. For the dates and Pythagorean background of the authors cited here, see excursus A.

1

ONE VERSUS ONE: THE HIERARCHY OF THE HEN AND THE MONAD

Theon of Smyrna begins his explanation of the different kinds of numbers by defining and describing the qualities of the number one.1 Initially, he uses the terms hen (i:v) and monad

1

Mathematics Useful for Reading Plato 18.3-21 .19.

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( f.WVa<;) indiscriminately.2 He defines number as a collection of monads, or, alternately, as the progression of a multitude, starting from a monad, and its regression, diminishing into a monad.3 This was a standard definition of number, one that made clear that the monad was the principle (cXQXTJ) and measure of number, but not itself a number.4 But, further into the passage, Theon explains the etymology of monad, and then the difference between monad and hen. He relates the terms to the difference between number (aQL8!J6<;) and numerable thing (aQL8 !1frr6v).5 In distinguishing number from numerables, Theon defines the former as "quantity in intelligibles," and not part of the material world.6 Numerables, on the other hand, are "quantity in sense perceptibles," and are predicated of beings? Numerables have bodies, but numbers are bodiless.8 As numbers are to numerables, Theon claims, so is the monad to the hen.9 The monad is the intelligible form of the hen, and is indivisible.1 0 Both the monad and the hen are principles: the monad, of numbers, and the hen, of numerables.11 The monad and the hen differ, too, in that only the hen may be divided infinitelyP Theon claims that more "recent" authors identified the monad and dyad simply as the principles of numbers, unlike the Pythagoreans, who claimed that all the idealized

2 Ibid. 1 8.5 vs. 18.11, 14; 19.6 vs. 1 9.7. 3 Ibid. 18.3-5: tXQL8p6c; ECJH mJO"TT)f-lCX powxbwv, 11 7TQ07TOCllO"f-lOc; rrAfJ8ovc; a no povaboc; tXQXOf-lEVOc;

KCXL avarrobLO"f-lOc; f ie; povaba KCXTaAfJywv. 4 Cf. Nicomachus, Introduction to Arithmetic 7.1 . 5 Theon of Smyrna, Mathematics Useful for Reading Plato 1 9.14. 6 Ibid. 19.15: aQt8poc; pi'v yaQ iun To iv VOTJTOic; nou6v. See also 21 .5. 7 Ibid. 19.17: tXQL8f-lTJTOV b[ TO iv aiu8TJTOic; nou6v. See also 21.6. s Ibid. 19.16, 20.5. 9 Ibid. 19.13-15. 10 Ibid. 19.19. 1 1 Ibid. 19.21-22. 1 2 Ibid. 19.22-20.4.

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numbers- monad, dyad, triad, tetrad, and so on -provided the principles for the numbers instantiated in the realm of sense perception -hen, duo, tria, tettares, and so onP A third, unnamed group claimed that the monad was the principle for all idealized numbers, and that the hen -not just the hen as a quality or point of differentiation, but the absolute hen - was the principle and measure of beings.14 Theon presents yet a fourth group, consisting of Archytas and Philolaus, who, he says, make no distinction between hen and monad.1 5 This is probably correct, since Aristotle, one of the more reliable sources for pre-Platonic Pythagoreanism, states that the Pythagoreans called nous both monad and hen.16 There is no evidence that Plato held to a distinction in the terms eitherP Theon, therefore, confirms that the distinction between the terms entered Pythagoreanism only after Plato. Theon presents other opinions on the monad. The "majority" - a fifth group that probably overlaps with some of the previous groups- distinguish the first monad from other monads. They call it "more frequent," "monad itself," and "hen" (understood to be the chief intelligible essence of the hen, since the first monad is responsible for furnishing to individual things the property of being one).18 For this group, something can be said to be "one" by virtue of its participation in the monad.19 Thus, this fifth group embraces the

1 3 Ibid. 20.5-11 . 14 Ibid. 20.12-19. 1 5 Ibid. 20.19-20 Archytas, test. 20 Philolaus, test. 1 0. 16 Aristotle, frag. 203, in Alexander of Aphrodisias, Commentary on the Metaphysics 39.15. 1 7 Note, for instance, the heavy dependence upon hen in the Parmenides, and the lack of any similar interest in monad as a technical term. Studies like Brumbaugh's (Plato on the One) focus exclusively on hen. 1 8 Theon of Smyrna, Mathematics Useful for Reading Plato 20.20-21.2. 1 9 Ibid. 21.2-3. =

=

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hierarchy monad - hen, where the arrow indicates not only metaphysical priority, but a transfer of properties. A sixth group distinguishes between hen and monad in a different m anner. To them, the hen is immutable in three ways. The hen is immutable in its essence, an immutability that cannot be ascribed to the monad or to the odd numbers.20 Second, the hen is immutable in its quality since it is a monad and is unlike many monads.21 The wording here is vague, but it may mean that many monads can be arranged in different shapes, but a single monad, never. Third, the hen is immutable in quantity since it cannot be added the way one monad is combined with another monad. Otherwise the hen would be many and no longer one.22 Theon has summarized the doctrines of this sixth group so tersely that the exact meaning is obscure. The main idea seems to be that in a collection of monads - the standard definition of number- the monads retain their identity. But countables' numerical identities change as the size of their group does. Thus, the three immutable aspects of this hen- essence, quality, and quantity - correspond to the first three of Aristotle's categories, probably no coincidence.23+ This sixth group also sees Plato's use of "henads" in Philebus l5a as referring to a category other than hen, a category that is a monad by virtue of its participation in the hen.24 But the hen itself is unchangeable and is limited by monads. The ultimate distinction

2o Ibid. 21.7-10.

21 Ibid. 21.10-1 1 . 22 Ibid. 21.11-13. 23 According to my reading of 21.8-13, the punctuation in Hiller's edition should be emended, converting the first comma in line 10 and the comma in line 1 1 to colons ( ) and the colon in line 12 to a comma. 24 Ibid. 21.14-16. "

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between hen and monad is that the former is defined and is a limit, whereas monads are limitless and indefinite. This group, then, seems to propose that the hen and monad hold the positions assigned by members of the Old Academy to the one (hen) and the indefinite dyad. This arrangement, hen - monad, reverses the schemes found in other groups Theon discusses. Theon's survey nicely summ arizes the variety of distinctions that could be made in the second century between hen and monad, and the amount of importance that could be assigned to the subject. The complexity of the sixth group's doctrine, and its position last in the doxography, suggests that it was the position advocated by Theon or his principal source, probably Moderatus.2s Theon's explanation of Archytas and Philolaus's positions shows that the distinction between hen and monad postdates Plato. Nevertheless, Plato did distinguish between ideal and mathematical numbers, a polarity that may have provided the foundation necessary for positing metaphysical levels to numbers.26 If they can be trusted, the fragments from Speusippus suggest an increased complexity of layers of numbers in the Old AcademyP It is more likely, however, that Platonists and Pythagoreans of the fourth century BCE and later (if there were any left) held to two levels to numbers, or none at all. Alexander Polyhistor,

2s On this, see below. 26 Aristotle, Metaphysics 1 .6.13.6. See Nikulin, Matter, Imagination, and Geometry, 73, and Dillon, Middle

Platonists, 6. 27 This kind of complexity is such a feature of late antique thought that it is tempting to believe that Iamblichus, the source for scholars' reconstruction of Speusippus' s philosophy of mathematics, depends upon a spurious writing or some other intermediary source much closer to the fourth c.CE. See Dillon, Middle Platonists, 14-15, who depends on Iamblichus, Common Mathematical Knowledge. Dillon (p. 430) defends the authenticity of these fragments against Tarim, Speusippus ofA thens, 86-107.

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who recounts the Pythagorean doctrine of the generation of numbers describes the monad begetting the dyad, which in tum generates other numbers. There is no supreme principle over the two sources -the monad and dyad - and Alexander's source, which postulates a monad and indefinite dyad in place of the hen and indefinite dyad, does not distinguish the terms for the number one.28 The earliest datable text to distinguish formally between hen and monad is a fragment of Eudorus of Alexandria, who held that there were two hens, one the source of everything, and the other, called a monad, paired with the indefinite dyad.29 Eudorus' s position is clearly related to the distinctions discussed by Theon, but it reverses the order of priority, placing the hen above the monad. Although this is the earliest attested order in the lateantique and medieval tradition, it is rare. Hippolytus reports a rather strange version of the hen � monad doctrine when he claims that the Pythagoreans held to the hierarchy number

seems to be associated with the level of "number," and the first monad is the principle of numbers "in their instantiation" (Ka8 ' un6a'ramv).31 All four levels are associated with the tetraktys, and are thought of as the four parts of the decad. It is also no coincidence that this series corresponds to the series point, line, plane, and solid. But this is only one of

2s Alexander Polyhistor, frag. 140 (ed. Muller, 3:240b), in Diogenes Laertius, Lives of the Philosophers 8.24-25. See also Dillon, Middle Platonists, 127. Alexander agrees with an undatable Pythagorean text ascribed to Xenocrates, who uses "first monad" in place of "hen." [pseudo-]Xenocrates, frag. 120.77, in Sextus Empiricus, Against the Physicians 2.262. For other late antique uses of monad instead of hen, see also idem, 10.276 and 282 and Aetius, Placita 281 .5. 29 Cited in Simplicius, Commentary on Aristotle's Physics 1 81 .27-30. Note the pair monad-indefinite dyad parallels the terminology of Alexander Polyhistor, discussed above. 30 Refutation ofAll Heresies 1 .2.9 4.51 .7. 31 ibid. 1 .2.6 4.51.4. =

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Hippolytus' s sources for Pythagoreanism.32 Elsewhere he slips into language that prioritizes the monad.33 Iamblichus witnesses to the order hen � monad when he describes the second, self-sufficient deity springing from the first as if a monad from the hen.34 There are possible vestiges of the system hen � monad in Clement of Alexandria and Plotinus.35 In any case, the choice of hen to describe the primary level of the number one probably derives from the Platonic tradition, which relied nearly exclusively on hen to describe the metaphysics of arithmetic.36 Of those who distinguish hen from monad, the great majority prefer the order monad � hen. We do not know for certain why. The sources suggest that grammar was an important reason. Monad, dyad, and so on, are abstract nouns, and they lend themselves well to descriptions of ideal numbers. Hen, duo, and so forth, although often used for abstractions, are nevertheless adjectives, and so tend to be attached to things that can be counted. This is Theon's rationaleP His source here is Moderatus, who himself probably depends upon earlier sources, such as Tiberius Claudius Thrasyllus - the court philosopher and astrologer to Tiberius - or the pseudo-Pythagorean treatises.38 Moderatus describes the 32 See above, p. 1 1 3 n. 38. 33 E.g., Refutation of All Heresies 1 .2.2, 6.23.1 .

Iamblichus, De mysteriis 8.2. 35 Clement: see p. 1 86, above. For Plotinus, see below. 36 See, for instance, Plato, Parmenides passim, and above, n. 17. 37 Theon of Smyrna, Mathematics Useful for Reading Plato 19.15-1 8. 38 Syrianus, Commentary on the Metaphysics 151.17-22. This passage attributes the distinction between hen and monad to two groups of writers, "older Pythagoreans" versus "more recent." The "older" here means Archytas, who says the hen and monad, "being of the same class, differ from each other." ( pseudo-Archytas in Thesleff ed., 47.27-48.2) The "more recent" are Moderatus and Nicomachus. The quote from Archytas is certainly spurious (and thus included by Thesleff, Introduction, 8 n. 4, and 10). Syrianus probably found it in one of the "more recent" Pythagoreans, namely, Moderatus or Nicomachus. Since Theon makes the same distinction between older and more recent Pythagorean 34

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monad as the source and endpoint for all numbers.39 He holds to the order monad --+ hen, describing it in the very terms later authors would.40 Even though Moderatus reports this distinction, it seems that he did not personally hold to this scheme, but preferred a more complex one, probably to be reconstructed upon the basis the views expressed in the sixth group outlined by Theon, and of those reported by Simplicius as belonging to Moderatus.41 In both passages Moderatus considers the term hen to be the more important. In the fragment preserved by Simplicius, Moderatus postulates three levels of hen, the first hen transcending being, the second hen consisting of the forms (described as "truly existent" and "intelligible"), the third hen (thought of as being "of the soul") participating in the first hen and the forms. When this is combined with Theon's sixth group, we learn what Moderatus considered to be the properties of the uppermost hen. This complex scheme

writers on this subject (Mathematics Useful for Reading Plato 20.6--7), and because Theon depends here on Moderatus ( frag. 2 : see n. 40, below), quite possibly Syrianus found the pseudo-Archytas quote in Moderatus. On the other hand, Nicomachus, whose quotations from Archytas and Philolaus are nearly certainly all spurious (see below on the quadrivium), makes the same distinction between older and more recent Pythagoreans. He may be Syrianus's source. If so, then the pseudo-Archytas fragment (inspired by Moderatus/Thrasyllus?) was in Nicomachus' s Theology of Arithmetic, since his Introduction to Arithmetic nowhere explicitly distinguishes between hen and monad. Thrasyllus' s connection to Moderatus is suggested by Dillon, Middle Platonists, 398. 39 Moderatus, frag. 1, in Stobaeus, Eclogae. 1 .2.8. 40 Moderatus, frag. 2. The standard text for Moderatus is Mullach, 2:48-50, who bases frag. 2 on Stobaeus, Eel. 1 .2.9, with no reference to Theon, who preserves the fragment at Mathematics Useful for Reading Plato 1 9.21-20.9. Probably the whole of Theon (18.3-20.19) depends, more or less verbatim, on Moderatus. The anonymous Life of Pythagoras epitomized by Photius, Biblioteca 249 (fol. 438r = Thesleff, Pythagorean Texts, 237.8ff.) also probably depends on Moderatus (but see Burkert, Lore and Science, 58 n. 30, who suggests Photius reports an altogether different scheme). Theon's explanation is more complete than Stobaeus' s, so is probably also closer to Moderatus' s text. Theon, at any rate, should be the basis for correcting any future edition of Moderatus' s frags. 1-2. 41 Simplicius, Commentary on Aristotle's Physics 1.7 (230.34-231 .24). =

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anticipates in many important respects Plotinus' s.42 It cannot be easily reconciled with the monad - hen doctrine, so it is likely that Moderatus merely had a strong interest in the Pythagorean tradition (especially evident in fragment 3), and so reported without embracing their distinction in terminology. It is difficult to say how old Moderatus' s source is, but in light of Eudorus' s testimony, it is not likely to be older than the first century BCE. It cannot postdate Philo, who uses the doctrine to make a theological point about Genesis 24.22.43 He points out that the monad is to the hen as the archetype is to the copy, and he does so in a way that presupposes that this analogy is common knowledge. Philo does not consistently hold to the scheme monad - hen, but here and elsewhere he shows that this doctrine was widely held.44 That the monad - hen doctrine was widespread by the first century seems clear, but this does not mean that the doctrine was universally held, even by Pythagoreans. Philo, we have seen, can be ambivalent on the matter. Nicomachus, moreover, is totally silent about it. If he had held to such a distinction, it would have been prominent in the Introduction to

42 See Tornau, "Prinzipienlehre"; Baltes, Platonismus in der Antike, 4:477-85; and Dodds, "Parmenides of

Plato." 43 Philo, Questions and Answers on Genesis 4.1 10.

Philo, at Who Is the Heir of Divine Things ? 1 87-90, describes the monad as source of numbers, but does not contrast it to the hen. In On Rewards and Punishments 41 he uses hen and monad as a pair, but it is unclear whether he is distinguishing or conflating the terms (cf. idem, On the Unchangeableness of God 1 1). At On the Creation of the World 98 he uses hen where monad might be expected; at On Abraham 122 he uses monad where hen might be called for. At Allegorical Interpretation 2 .3 he uses both terms together, but specifies that the "one God" (hen theon) supercedes the monad. This may be Philo's way of using the language of "one God," native to Judaism, to invert and thereby challenge the monad -+ hen doctrine so clearly stated at Questions and Answers on Genesis 4.1 10. Note the proximity of his thought to that of Clement, discussed above, p. 1 86. 44

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Arithmetic. It is not.45 Even if Nicomachus reported the doctrine in his Theology of Arithmetic, it seems not to have been central to his thought.46 Plutarch, too, for all his numerical lore, does not report the doctrine, but this may be the result of the loss of many of his worksF Also noteworthy is Plotinus, nearly every page of whose corpus uses hen far more frequently than monad. It is unclear whether Plotinus sharply differentiated the terms. Aside from his use of hen to describe the highest, ineffable, and transcendent realm, he formally defines neither hen nor monas, and occasionally he conflates them.48 In several places, however, he assumes the hierarchy hen - monad. In the same treatise in which Plotinus seems to conflate the terms, he claims that the hen in itself is not the same as the hen in the monad, dyad, and so forth.49 Elsewhere, he places the dyad over the number two, arranging them according to his established hierarchy of essential number over quantitative number.50 Thus, monad and dyad preside over numbers two, three, and so on. In the very last treatise of the Enneads Plotinus contrasts the hen to both the monad and the point, and suggests that the latter two have a different kind of unity than the hen has: the monad and point are the result of the soul's reducing a quantity or magnitude to its smallest element.51 Even though unified, such a monad or point is part of something divisible and part of some other object,

45 The appropriate place for such a discussion would have been 1 .7. On the other hand, there Nicomachus uses monad in a way that would be consistent with someone who distinguished between hen and monad. 46 See n. 38, above. 47 An extensive ancient list of Plutarch's writings, Lamprias' s Catalogue, is printed in the LCL edition of Plutarch, Moralia, vol. 15. 48 Ennead 6.2.9.16-18. See also Nikulin, Matter, Imagination, and Geometry, 77. 49 Ennead 6.2.11 .43-45. so Ibid. 6.6.14, Nikulin, Matter, Imagination, and Geometry, 77, 81. s1 Ennead 6.9.5.42-43.

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attributes that cannot be predicated of the hen.52 Thus, Plotinus appears on balance, not only to preserve Eudorus's hierarchy, hen -+ monad, but to add to this the lower hierarchy monad (with dyad) -+ hen (with duo, tria, and so forth).53 But the distinction appears seldom and does not play a critical role in his philosophy. Rather, as an interpreter of Plato, Plotinus defers to the language of the master, and therefore treats hen as the most fitting term for the highest level of his metaphysics. Despite its absence in Plutarch and Nicomachus, the doctrine was well established in the second century. In addition to the ample testimony of Theon, Sextus Empiricus adds details about the generation of the hen from the monad.54 His source held to the "first monad" and the "indefinite dyad" as the first principles.55 The hen derives from this first monad, whereas the number two emerges from the combination of the monad and indefinite dyad. Sextus goes on to discuss the generation of the geometrical shapes from the numbers, an idea found in Alexander Polyhistor. Since Alexander excludes the possibility of various levels for numbers, Sextus must be using a later source. From the second century CE onwards the doctrine monad -+ hen is widely reported.56 There are a number of variations on the theme, showing that the doctrine could 52 Ibid. 6.9.6. 53 Properly speaking, only the number two is part of this scheme, not the number one. Henads, too,

yet another kind of numbor for Plotinus, reside below the monad in this scheme. See Nikulin,Matter Imagination, and Geometry, 82-84. The implications of this complex scheme go beyond the boundaries of this short survey. 54 Sextus Empiricus, Against the Physicians 2.276. See also the parallel at ibid. 2.261 . 55 See above, p. 288. 56 E.g., Sextus Empiricus, Against the Physicians 2.261; pseudo-Pythagoras in pseudo-Justin Martyr (III), Exhortation to the Nations 1 9.2 (ed. Otto 1 8c); Favonius Eulogius, Disputation on the Dream of Scipio 3.1-31; John Lydus, On the months 2.6; Proclus, Commentary on the Timaeus 1 :16.27-29; Boethius, De unitate et de uno; Asclepius of Tralles, Commentary on Nicomachus of Gerasa 41. ,

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prove fertile for theological and philosophical ideas. The doctrine of a first and second god parallels that of monad -+ hen.57 The anonymous doctrine presented by Irenaeus of a fourfold panoply of ones develops the monad -+ hen doctrine in a bold new direction.58 Clement of Alexandria transforms the doctrine to suit better his theology, suggesting the hierarchy hen [theos] -+ monad -+ hen, an arrangement that resembles Plotinus's, but is probably inspired by Philo, discussed above.59 The doctrines hen -+ monad and monad -+ hen undoubtedly are the kernel for later, more complex philosophies of number discussed in the writings of Iamblichus and Proclus, who postulated numerous levels to numbers and unities. Very similar to the doctrine monad -+ hen is the earlier, and more widely attested doctrine of the monad (or hen) and indefinite dyad. I have not discussed it, mainly because it differs considerably from the doctrine monad -+ hen. Speculation on the one and indefinite dyad is tied with fifth and fourth century BCE interest in on the relationship among finitude/infinitude, numbers, and the world. Although the one takes precedence over the indefinite dyad, both are treated as coeval principles in the earliest sources. This scheme tends toward a kind of dualism, since the one and dyad are utterly different from each other and in a kind of pecking order, but on the same metaphysical plane. The later schemes hen -+ monad and monad -+ hen reflect Pythagorean and Platonic speculation on the levels of numbers in the world. Such a hierarchy ensures that the lower principle depends for its existence upon the higher. This dependence ensures a monistic philosophy

57 Dillon, Middle Platonists, 46. 58

Against Heresies 1 .1 1 .3, discussed above, pp. 39-40.

59 Clement, Paedagogue 1 .8.71, discussed above, p. 185.

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and theology since the two principles are not opposed to each other in the way the one and the indefinite dyad are.

2

ODD AND EVEN NUMBERS AS MALE AND FEMALE

Two of the oldest and best known concepts of Pythagorean arithmetic are (1) numbers are fundamentally of two types, odd and even, and (2) odd numbers are male, and even numbers are female. Both doctrines can be found in the earliest traces of Pythagorean thought. Aristotle mentions the first doctrine, that all numbers are fundamentally either even or odd. He summarizes at Metaphysics 986a1 3-21 the teaching of Philolaus:6° But the object of our review is that we may learn from these philosophers also what they suppose to be the principles and how these fall under the causes we have named. Evidently, then, these thinkers also consider that number is the principle both as matter for things and as forming both their modifications and their positions, and hold that the elements of number are the even and the odd, and that of these the latter is limited, and the former unlimited; and that the One exists from both of these (for it is both even and odd), and number from the One; and that the whole heaven, as has been said, [is] numbers.6 1

Thus, in Philolaus' s system, the abstractions even and odd preexist and generate numbers, via the One. Even and odd are thought of as species of the unlimiteds and limiters that form the basic principles of the universe.62 The One exists from a synthesis of both even 60 That in this passage Aristotle quotes from Philolaus in particular is argued, passim, in Huffman, Philolaus of Croton. 61 Trans Ross, with modifications. 62 Huffman, Philolaus of Croton, 39 and elsewhere, suggests that Aristotle misrepresents Philolaus's system when the former makes the latter's preferred plural form - unlimiteds and limiters- into an abstract singular, and merely equates the two. That may be true for a passage such as Aristotle,

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and odd, and is therefore both. All resultant numbers generated by the One are one or the other, either even or odd. At Physics 203a10-15 Aristotle contrasts the Pythagoreans, here probably meaning Philolaus, to Plato. The wording of the entire passage is quite obscure, but what clearly emerges is evidence of a Pythagorean doctrine that numbers are fundamentally odd or even, and that they reflect the difference between limiteds and limiters, the basic principles of the universe.63 Philolaus reaffirms this basic division of all numbers into odd and even or their combination in fragment 5: " Number, indeed, has two proper kinds, odd and even, and a third from both mixed together, the even-odd (aQ'UOITEQLT'Wv). Of each of the two kinds there are many forms of which each thing itself gives signs."64 In his commentary, Huffman analyzes the term cXQHOITEQLnov in this fragment and presents other evidence to support the traditional interpretation, that the term refers to the number one.65 Huffman's analysis shows that the Pythagoreans- Philolaus in particular- held to the fundamental numerical categories of odd and even, while holding to the number one as a combination of both.66

Physics 203a10-12, but not at Metaphysics 986a17-19: 'WV bi: lXQL8�-tOU CJTOLXEia TO TE aQTLOV K£XL TO ITEQLTTOV, TOVTWV bi: TO �-ti:V nEITEQ£XCJ�-tEVOV TO bi: anE LQOV. Here Aristotle specifies that the odd is limited and that the even is unlimited (nEnEQ£XCJ�-tivov and anELQOV are adjectives, not abstract neuters). I.e., odd and even are species of the genera unlimiteds and limiters. 63 The most sensible reconstruction of this passage is that of Burkert, Lore and Science, 33 n. 27. 64 Trans. Huffman. Frag. 5 derives from Stobaeus, Eclogae 1 .21 .7c (1:188.9 Wachsmuth). 6s Huffman, Philolaus of Croton, 186-90. 66 Huffman also suggests (ibid., 1 89-90) that Philolaus, in referring to the mixture of odd and even, might have meant not only the number one but harmonic ratios, which bring odd and even numbers in relation to each other. For example, 2 to 3, an even to an odd number, forms the ratio for the musical fifth.

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According to Theon of Smyrna, this fundamental distinction between even and odd was held by not only Philolaus but also Archytas.67 Theon attributes to Archytas a work, On

the Decad, in which the decad is presented as a perfecting agent, encompassing every nature within itself, both odd and even, both moved and unmoved, both good and evil. Earlier in his discussion, Theon reports Aristotle as claiming, in his lost work on Pythagorean doctrines, that the Pythagoreans held the One to participate in both natures, i.e., both odd and even.68 When appended to an even number, the number one makes it odd; when added to an odd it makes it even. According to this fragment, the Pythagoreans conclude that it would be impossible for this to happen if the One didn't participate in both natures, so it is called even-odd, cXQH07H�QL'f'rov.69 The fundamental distinction between odd and even numbers is epitomized in

cXQHOTIEQL'f'fOV, a term that describe the ability of a number to synthesize in itself two otherwise irreconcilable categories. Generally that honor is given to the number one, but in the later Pythagorean tradition it was applied to other numbers that seemed, in one respect or another, to reflect the same behavior. For instance, Philo calls the One cXQHOTIEQL'f'fOV. He then expands on this tradition by likening God's creation of the world in six days to the act of the first cXQHOTIEQL'f'fOV, which needed to be fashioned into a mixed number, namely six.

67 Mathematics Useful for Reading Plato 1 06.7-1 1 . 68 Aristotle, frag. 199 Archytas test. A21 = Theon of Smyrna, Mathematics Useful for Reading Plato =

22.5-9. This passage is attributed to Archytas because of Theon's comment at the end, "Archytas too concurs in these matters." But it is unclear whether the concurrence happens because Aristotle is already depending upon Archytas, or if Aristotle is using (an)other Pythagorean text(s) and Theon notes that Archytas also supports Aristotle's claim. 69 See parallel comments attributed to Aristotle in Alexander of Aphrodisias, Commentary on Aristotle's Metaphysics 40.18, 41 .12, 47.13.

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Philo claims that the number six is an image of the UQHOTH�Qrrrov (one) since it exists as both male and female inasmuch as it is fashioned by each power. That is, six is the product of two and three, both of which are the principles of even and odd, respectively ?0 Thus, for Philo the number six is even-odd because it provides an image of how the principles of odd and even are at work in the number one. Philo calls the number six even-odd elsewhere?1 Philo also calls the number five even-odd, probably because five is the sum of the first even and odd numbers (just as six is their product).72 Philo's application of the term to numbers other than one is paralleled in the Theology of Arithmetic.73 Nicomachus and mathematicians after him use the term cXQH011EQL'l'WV for a quite different reason, to subdivide the class of even numbers. In Nicomachus's classification of numbers, all even numbers are one of three types: evenly-even (d:QncXKLc; &Qnov), even-odd (d:QnOnEQLnov), and odd-even (m:: Q LaaaQnov). Evenly-even numbers are those that can be divided all the way down to the monad, which is indivisible. These are the numbers that constitute the set of powers of two, such as 2, 4, 8, 1 6, and 32?4 Even-odd numbers are even numbers that can be divided into whole numbers only once, such as 6, 1 0, and 14?5 The third and last class is odd-even numbers, which, like 24, 28, or 40, can be divided into half more than once, but cannot be reduced to monads like the evenly-even numbers?6 Thus, the

70 Philo, On the Creation of the World 13---1 4. This is a very difficult passage, and my paraphrase attempts to provide what a strict translation cannot. 71 Philo, On the Special Laws 2 .58.4, reiterated at Questions and Answers on Genesis 3.38a, 3.49b.2. 72 Philo, On the Decalogue 20. 73 One is even-odd at 1 .12; six, at 53.14-15. 74 Nicomachus, Introduction to Arithmetic 1 .8.4-14. 7s Ibid. 1 .9.1. 76 Ibid. 1 .10.1-2.

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class of odd-even numbers resembles and stands between the classes of evenly-even and even-odd numbers: odd-even numbers can be divided multiple times (just as evenly-even numbers can), and they cannot be altogether reduced to factors of ones and two (as is the case with even-odd numbers). This basic division in the kinds of even numbers becomes a central part of the tradition after Nicomachus?? Thus, there are two ways cXQHOITEQL'r'WV is used in ancient texts. The first is rooted in the early Pythagorean idea of the number one synthesizing in itself the opposites of odd and even, and male and female. Nicomachus or his immediate sources (probably to be dated to the Hellenistic period, post-Euclid) altered this definition to apply to a particular kind of even number, with no reference to gender symbolism. Both definitions of the term result from attempts to classify the most basic categories of number. Both definitions coexisted throughout late antiquity.

Philo's use of cXQHOITEQLnov illustrates the second doctrine relating to even and odd, that they are female and male, respectively. The earliest evidence for the Pythagorean association of odd numbers with masculinity and even numbers with femininity is provided by Aristotle at Metaphysics 986a22-26. Just prior to this section, Aristotle has discussed Philolaus' s teachings regarding limit, unlimited, even, odd, and one, already discussed above. He continues: Other members of this same school say there are ten principles, which they arrange and unlimited, limit in two rows77 Julius Pollux, Onomasticon 4.162; Alexander of Aphrodisias, Commentary on Metaphysics 769.12-

770.10, 818.26; and Theon of Smyrna, Mathematics Useful for Reading Plato 25.5-6, 25.19-26.4 (despite his using the term in the Pythagorean sense also).

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odd one right male resting straight light good square

and even, and plurality, and left, and female, and moving, and curved, and darkness, and bad, and oblong.78

The use of "other" in the first sentence of this passage shows that Aristotle is following not Philolaus but another Pythagorean author. Aristotle mentions immediately after this passage that Alcmaeon of Croton subscribed to this list of opposites too?9 But, after deliberation, Aristotle cannot determine who influenced whom, Alcmaeon or the unnamed Pythagorean of 986a22-26. In any case, it was a Pythagorean sentiment, whether it derived originally from Alcmaeon or from someone else. Aristotle elsewhere reaffirms this basic claim, that the Pythagoreans associated number with gender.80 The comparison of number to gender seems to have been popular with the Old Academy, if not earlier schools of philosophy. In Philolaus, fragment 20a, deemed by Huffman to postdate Plato, the dyad is called the consort of Kronos.81 The implication is that

78 Trans Ross, with modifications. 79 Aristotle, Metaphysics 986a17-b2. For another table of opposites, see Plutarch, Isis and Osiris 48 (370E) and commentary in Gwyn Griffith's ed., 484. 80 Frag. 203 (in Alexander of Aphrodisias, Commentary on Aristotle's Metaphysics 39.12-13). See further discussion in Burkert, Lore and Science, 30-37 and 432-38. s1 See Huffman, Philolaus of Croton, 351-52, and cross references there. In favor of this late date are striking parallels in Xenocrates, who assigns the monad to Zeus, and Speusippus. Huffman suggests in frag. 20a's reference to Rhea an implicit play on QEW, to flow, a trope seen in late sources, specifically the Theology ofArithmetic 14.6-9 and the context of fragment: Lydus On the Months 4.64 ( 1 14.20 Wunsch). Huffman could be right to doubt the authenticity of the fragment, but such a word play need not be implied here. Note, the monad is Kronos in Philolaus, but Zeus in Xenocrates;

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Kronos represents the number one. A comparable association may be at work in Philolaus, testimony 1 4, where the angle of a triangle is assigned to male gods, and the right angle is assigned to goddesses.82 Xenocrates, fragment 15, calls the monad and dyad gods.83 The monad is male and has the rank of a father reigning in heaven, and Xenocrates calls him "Zeus and odd and mind." This is his first god. The second is female, and is like the mother of the gods. Thus, in the fourth century BCE, Pythagoreans were associating odds and evens not only with the two genders but more specifically with male and female deities. Numerous sources from late antiquity call odds and evens male and female numbers.84 As suggested elsewhere in this study, particularly concerning Valentinian number symbolism, this association is used frequently in texts from late antiquity to express theological ideas. From this period derives a new meaning for GQGEv68f1Auc;.85 The term, generically meaning "androgynous," was now applied to theological or metaphysical schemes that had a strong arithmetical component. The word nicely parallels the compound

common to both is that mythology, not etymology, is applied to odd and even numbers. Compare the later tradition in which Pythagoras is said to liken the monad to Apollo and the dyad to Artemis. Moderatus, frag. 3; Plutarch, Isis and Osiris 10 (discussed in chap. 9). 82 The specific number and names of gods and goddesses assigned to each geometrical figure varies in the three different sources for this testimony, but all agree on the gender-specific arrangement. Plutarch, Isis and Osiris 30; Proclus, Commentary on the First Book of Euclid's Elements 130.8-14, 1 66.251 67.14, 173.1 1-13, 174.12-14; Damascius, Commentary on Parmenides 2.127.7-17. 83 Ed. Isnarde Parente, 213. This fragment derives from Aetius, Placita 304/Stobaeus, Eclogae 1 .1 .29b.44-57. 84 Dozens of sources could be cited. See, e.g., Hippolytus, Refutation of All Heresies 1 .2.6-7, 4.51 .4-5, 6.23; Jerome, Letter 48; and the anonymous treatise edited in Delatte, E tudes, 167-68. ss The word is first attested in the fifth century BCE, in Hellanicus (FGrH 1a, 4, F .87.10). The term seems to have been used with arithmetical overtones only after Philo. His explanation of odds and evens as male and female John Lydus, On the Months 2 . 1 1 .13-14, glosses with an explanation of Aphrodite (representing the number six; see below, excursus BS) as aQacv68T}i\vc;, crediting the term to other "theologians." John's sources tend to postdate Philo.

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d:QTLOITEQLnov, discussed above, but emphasizes the gendered aspects of number. The

Theology of Arithmetic, probably following Nicomachus, uses d:QaEv68Tji\uc; to d escribe the number one, the number six, and the number five, numbers also associated with d:QTLOITEQLnov and marriage.86 The gnostic literature cited by Irenaeus and Hippolytus uses the term, as do Hermetic texts, of a supreme being thought of as androgynous; the deity's androgyny, however, often mirrors arithmetical descriptions of the relationship between the one and the indefinite dyad. The term d:QaEv68Tji\uc; is frequently used in the subsequent arithmological tradition_87 Plutarch describes the genders of numbers with much more explicit sexual imagery.88 The number one potentially "belongs equally" (EmKoLv6c;) to both odd and even numbers.89 Therefore when the number one is added to an odd number it makes an even, and vice versa. The number five is produced by the "mingling" (f.HYVVf.!EVwv) of the first odd and even numbers.90 Even and odd numbers have a resemblance (Of.!OLO'rTjt;) to the genders, made apparent when you try to divide them. Any even number, when divided, leaves behind "a certain receptive principle and space in itself" (nva bEKTLKTjv aQxi]v otov [v i:av-rc}J Kai. XWQav). But when the same thing happens to an odd number, there is always a remainder needing distribution to one side or the other.91 Because of this remainder, odds

86 4.1, 43.5, 46.20. See below, excursus BS. 87 See e.g. Macrobius, Dream of Scipio 1 .6.7. 88 Plutarch, On the E at Delphi 388A-c. 89 For the sexual overtones to £mKotv6c; see LSJ, s.v. 90 Again, f.HyvVflEVoc; describes the consummation of the marriage between two and three. On the

number five as marriage, see excursus BS. 91 Plutarch's appeal, here, to anatomy of human sexual organs, has no ancient parallel, to my knowledge. Cf. Nicomachus, Introduction to Arithmetic 1 .7.3, with far less sexual terminology.

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are more fruitful (yovLflW'rEQ6c;) than evens, and when they mingle (the connotations of

fl LYVUflEVoc; suggest "copulate" is more accurate) the odd "always overpowers" (ad KQ£X'rci) the even, which is why an odd number is always produced.92 On the other hand, when even numbers are added to other even numbers, their sterility and incompleteness means they never produce an odd number or its properties. The third possibility is odd numbers mingling with each other, which "perfects many even numbers, because [odd numbers} are fruitful everywhere" (aQ'rtouc; noMovc; bllx 'rO mivnJ y6v LflOV ano'rEAoum)?3 In a different treatise, Plutarch says Zaratas called the dyad mother and the one father. Plutarch uses the example to show that the best numbers, the male ones, are those that resemble the monad.94 Numbers were capable of symbolizing gender, but the association was not automatic. For instance, Plutarch says the Pythagoreans assigned triangles to the gods Hades, Dionysius, and Ares, and squares to the goddesses Rhea, Aphrodite, Demeter, Hestia, and Hera.95 But in the same passage Zeus is assigned a dodecagon and Typhon, a fifty-six-sided polygon, without any suggestion that they are therefore female. Neither the twelve apostles, nor the twelve signs of the zodiac are, to my knowledge, interpreted by any

92 This appeals to common ancient opinion on the generation of the fetus. See, for instance, Aristotle, On the Generation ofAnimals. This passage is paralleled by the earlier, but less explicit, Moderatus, frag. 3. 93 Compare this account with the Plutarch fragment preserved in Stobaeus, Eclogae l .pref.IO, where Plutarch attributes to Pythagoras a similar set of arithmological principles. Also see Plutarch, Roman Questions 1 02 (288B12-E3), where in answer to the question, why are male children named on the ninth day and females on the eighth? he suggests, among other reasons, the Pythagorean one. Here too Plutarch uses human sexual anatomy to explain his position. 94 Plutarch, Genesis of the Soul in the Timaeus 2 (1012£4-7). 9s Isis and Osiris 30 (363A).

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ancient text as being feminine. To invoke the gender symbolism of numbers, authors needed to make the connection explicit.

3

THE TETRAKTYS

The Pythagoreans symbolized the number ten by a special term for the first four numbers, the tetraktys (Tet:QaKn)�).96 The term is probably of Doric origin, but it is unclear exactly how this unusual word was derived from a root meaningfour.97 The term is first attested in texts from the first century.98 The texts that refer to the tetraktys depend upon earlier Pythagorean texts that are not precisely datable. Some may go back to the mists of early Pythagoreanism, others may be part of the first-century reinvention of Pythagoreanism. The concept underlying the tetraktys has been shown to have preexisted Pythagoras in non-Greek societies.99 The tetraktys refers to the first four numbers, which were depicted in the Pythagorean tradition as four rows of pebbles arranged in the shape of an isosceles triangle: . <<·. The figure symbolizes, first, that the tetraktys, although a collection, is nevertheless a unity. Second, it illustrates that the sum of the first four numbers was ten, which itself was revered in Pythagoreanism for constituting the foundation for all numbers. Third, by

96 A number of studies have been published on the tetraktys. The most extensive and complete are Delatte, E tudes, 249-68 and Kucharski, Doctrine pythagoricienne. See also Apatow, "Tetraktys"; Sbordone, "Storia antica e recente"; Lampropoulou, "TIEQL nvwv Tiu8ayoQE iwv q)L.Aoao¢LKwv nQOTtJQWv"; Burkert, Lore and Science, passim; Haase, "Beitrag Platons." On the special use of the term in music see Karpati, "Musical Fragments of Philolaus." 97 See Burkert, Lore and Science, 222 n 24 and Delatte, E tudes, 253-54. Cf. Chalcidius, Commentary on the Timaeus 35 (84.9-11 ), who calls it the quadratura. 98 See below, n. 1 04. 99 See Burkert, Lore and Science, 474 n 50.

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depicting a harmonious arrangement of pebbles, the figure demonstrates the complementary character of arithmetic and geometry, one of the trademarks of the quadrivium (see below). This triangular figure was so well known, Lucian, in one of his satires on the philosophers, has Pythagoras instruct a prospective "buyer" of philosophy count to four. This four, says Pythagoras, "is ten, and a perfect triangle, and our oath."1 00 The oath in question is found in the so-called Golden Poem, attributed to Pythagoras and probably the oldest of the Pythagorean texts to mention the tetraktys:1 01

No, by the one who grants our head the tetraktys, Fount possessing roots of everlasting nature.1 02 100 Lucian, Vitarum auctio 4. Other explanations of the tetraktys as the summation of the first four numbers are found in Aetius, Placita 1 .3.8 ( Diels and Kranz 58b.15); Sextus Empiricus, Against the =

Logicians (= Against the Mathematicians 6-7) 1 .94; and Hippolytus, Refutation of All Heresies 1 .2.8, 4.51 .6, 6.23.2-5. 101 Delatte, E tudes, 249-53 traces this fragment of the poem to Timaeus, of the fourth c. BCE, and an anonymous treatise on arithmology of the second or third c. BCE. The tetraktys is also attested in the akousmata of the Pythagoreans in Iamblichus, The Pythagorean Way of Life 82.12 (Diels and Kranz 58c.4). Old, but later, Hellenistic Pythagorean texts that mention the tetraktys are "Lysis," frag. 4.4 ( Diels and Kranz 46.4) in Athenagoras, Legatio 6.1 and anonymous philosopher paraphrased by Photius, Bibliotheca 439a7-8 (Bekker). Thesleff tentatively dates these to the fourth and third c. BCE, respectively . Also to be mentioned is Philolaus, frag. 1 1 (found in Lucian, De lapsu in salutandum 5), of dubious date and authenticity. 1 02 Sextus Empiricus, Against the Logicians (= Against the Mathematicians 6-7) 1 .94. The two lines are reproduced with significant differences in other authors: pseudo-Pythagoras, Golden Poem 47-48; Aetius, Placita 282.3--7; Nicomachus of Gerasa, in Theology of Arithmetic 22.21-22; Sextus Empiricus, Against the Mathematicians 4.2; Theon of Smyrna, Mathematics Useful for Reading Plato 94.6-7; Hippolytus, Refutation of All Heresies 6.23.4; Porphyry, Life of Pythagoras 20.18-19; Iamblichus, The Pythagorean Way of Life 29.162.17-18; Julian, To the Untaught Dogs 15.34; Stobaeus, Eclogae 1 .10.12.7273; Hierocles, On the Golden Poem 20; Damascius, On the Parmenides 63.29; Proclus, On the Timaeus 2.53.6. For analysis of these differences, see Delatte, E tudes, 249-53. Possibly even Xenocrates (frags. 101-2, Isnarde Parente ed.), when he suggests that "the universe consists of the One and the =

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These two lines can be reasonably interpreted in light of the authentic fragments of Philolaus to suggest that the ancient Pythagoreans held that the first four numbers had been forged out of the principles of nature (in the case of Philolaus, these are limiters and unlimiteds) to provide a "spring" for the physical world. There is the intriguing possibility that the couplet comes from the same literary milieu as Philolaus' s lost work, On Nature.103 In the first and the second century, probably as a result of the revival and reinvention of Pythagoreanism, the tetraktys entered non-Pythagorean literary circles as a powerful metaphor.104 Because legend had it that the Pythagorean tradition was a secret one, and because the tetraktys was seen as the basis of their oath, the symbol took on special mystical significance that extended beyond its primary mathematical meaning. Like other Pythagorean symbols, it could connect disparate foursomes in the world. Theon of Smyrna

Everlasting" (cruVEUTUVCH TO miv i:K TOU EVOC, KC< L TOU a Evaov), uses the Pythagorean tetraktys as a symbol of matter. Such an ancient testimony does not help date the Golden Poem, but it does help establish the antiquity of the motif. See Dillon, Middle Platonists, 24. 1 03 The argument in outline is this. Philolaus is concerned with "nature," an important concept in the couplet. One way to read the second line is that the tetraktys is the root of eternal nature. But it is equally possible to read the genitives so that the roots producing the tetraktys derive from eternal nature. In this case, number is subordinate to and derived from eternal principles such as unlimiteds and limiters, as Huffman (Philolaus of Croton) has stressed to be the nature of Philolaus's philosophy. Further, the epithets for the tetraktys in the akousmata - the oracle at Delphi, harmony, and the location of the Sirens (Iamblichus, The Pythagorean Way of Life 82.12 [= DK 58c.4J) - are ancient, non­ mathematical, and (with the exception of harmony) non-philosophical. Does the couplet, then, derive from the mathematikoi faction of ancient Pythagoreanism (see excursus A)? If so, the question of origins remains. Did Philolaus write the couplet, was the couplet forged in light of Philolaus's book, did the couplet come from the older Pythagorean oral tradition, or are the couplet and Philolaus independent of each other but dependent upon a common tradition? 104 Search results from the TLG (E) are instructive on the popularity of the term. Discounting the statistics for the Hellenistic Pythagorean texts, tetraktys appears in no texts BCE, five times in the first century CE, forty-six in the second, twenty-six in the third, twenty-four in the fourth, and twenty-four in the fifth.

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collected eleven different quaternities found in the world, calling them tetrakyses.105 His examples range from the mathematical (point, line, plane, and solid) to anthropological (ages of human beings: child, teenager, adult, and elder). Another author, of unknown date, drew up a similar list of six tetraktyses, three of which have no parallels to Theon or other ancient authors.106 This reflects the popular, literary character of Pythagoreanism. An author could theoretically take any foursome, relate it to the tetraktys, and thereby show its Pythagorean character. Similarly, an author could postulate a foursome and describe its internal relations so as to invoke Pythagorean doctrines. By using Pythagorean imagery and terminology to describe the relations among four elements reinforced and supplemented the lore behind the tetraktys. In philosophy and theology in late antiquity this phenomenon is common. The internal structure of a philosophical or theological quatemity generally follows one of two patterns. In the first pattern, the first element of the quaternity begets the second, the second begets the third, and the third, the fourth. Examples of this kind of quaternity are the number series one, two, three, and four, or the geometrical series point, line, plane, and solid.1 07 In the second pattern the author conceives of the foursome as two complementary, hierarchical pairs. The pairs can be expressed in the relation A : B : : C : D, and they can be

105 Mathematics Useful for Reading Plato 94-99. 1 06 This very brief treatise, called TETpaKTvv n]v Ta mivTa DwuivovtJav Kai DwtpoiJO"av TE Tpaxi] ruivTa (The Tetraktys Suspending and Apportioning All Things Four-fold), is found in Paris gr. 1 1 85 suppl., f. 62v. and is published in Delatte, E tudes, 1 87. J 07 Cf. the examples provided by Alexander Polyhistor and Hippolytus, discussed above, pp. 288-289.

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imagined to represent the four comers of a square. Examples of this are Neoplatonic theories of epistemology or the quadrivium, on which see below .1 08 Setting polemic aside, the substance of the accusations of Irenaeus, Hippolytus, and other apologists, who charge the Valentinians and others of teaching the Pythagorean tetraktys in the guise of Christian doctrine, cannot be completely dismissed. The apologists' rhetoric oftentimes goes to the excesses expected in the genre. But they correctly recognize that certain doctrines, for example the Monotes-Henotes-Monas-Hen doctrine assigned to an unnamed Valentinian and Marcus, depend upon a Pythagorean model.I09 The history of the use of tetraktys in Christian literature reflects the early but transient suspicion the orthodox had of gnostic opponents. In the second and third century orthodox Christian authors use tetraktys in a disparaging manner, or at least one that does not embrace it as a Christian term.1 1 0 But in the fourth century, after Valentinianism waned, Christians freely let the tetraktys to symbolize Christian truths. They used it to portray the unity of the four Gospels or the fourfold character of Christian virtue.1 1 1

JOB

The clearest representative of this epistemology is Iamblichus, Common Mathematical Knowledge 8.

109 See my discussion above, pp. 39-40 and 93. 1 10 The warmest religious use is by Athenagoras, Legatio 6.1, who simply presents it as a part of the

philosophical apparatus that undermines polytheism. Other instances are found at Irenaeus, Against Heresies 1 .1 .1, 1 .1 .13, 1 .8.4-5, 1 .8.10, 1 . 1 1 .1-2; Clement of Alexandria, Stromateis 2.23.138.6; Hippolytus, Refutation of All Heresies 1 .2.9; 4.51 .7; 6.23.4-5; 6.24.1; 6.34.1; 6.44.1; 6.45.2; and Anatolius of Laodicea, On the Decad 5.11, 8.1, 15.20. 1 1 1 Eusebius of Caesarea, Church History 3.25.1; Theodoret of Cyrus, Letters 131 .112, 146.200; Evagrius of Pontus, On Prayer pref (PG 79.1 1 65D).

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4

THE QUADRIVIUM

For many ancient authors the symbolism of the number four is especially demonstrated by what was termed by Boethius the quadruvium (sic), the four mathematical disciplines that, with the trivium of grammar, dialectic, and rhetoric, formed the cornerstone of the curriculum in late antiquity and the middle ages.112 It was common in antiquity to think of the quadrivium -both the individual sciences that constituted it and the concept as a whole-as a Pythagorean invention, probably because of their ancient devotion to the tetraktys, and their alleged involvement in each of the four mathematical disciplines: arithmetic, geometry, music, and astronomy. There have been numerous modem claims that the quadrivium dates to Plato's time, if not before.113 Archytas, Plato's contemporary and associate, clearly teaches the fourfold unity of astronomy, geometry, arithmetic, and music (in that order), which he claimed to be sisters.11 4 The authorship of the fragment is questionable, but if it is authentic, it is the 1 1 2 The equivalent of quadrivium is TEGGa:Qcc; flc 86bm: Nicomachus of Gerasa, Introduction to

Arithmetic 1 .4.1 . Common to both Latin and Greek terms is the concept of a path: via and oboe;. Throughout this section I use the Latin term because of its elegance and familiarity. 1 1 3 The most extensive study on the history of the structure of the quadrivium is Kuhnert, Allgemeinbildung und Fachbildung. See also Hadot, Arts liberaux et philosophic; Sbordone, "Storia antica e recente"; Hellgardt, Zum Problem; Burkert, Lore and Science, 421-22; and Reindel, "Vom Beginn des Quadriviums." Other studies are listed in Radke, Theorie der Zahl, 9 n. 4. Many of these studies date the origin of the quadrivium to the classical period, although Hadot, Arts liberaux et philosophic, 991 00, suggests it emerges from Middle Platonic thought. Radke's book deserves special consideration, since all 885 pages are devoted to exploring the various liberal arts within the context of ancient Platonism. His analysis- philosophical rather than historical - of the quadrivium is essential for anyone wishing to go beyond the mere lists and historical sketch I provide and understand the content of the liberal arts in the ancient Platonic tradition. 1 14 Archytas, frag. 1 (Diels and Kranz 4 7B 1 ). Nicomachus's version of the fragment sets the order geometry, astronomy, spherics, and music; Porphyry's version, astronomy, geometry, arithmetic, and music. Huffman, "Authenticity of Archytas Fr. 1," and Bowen, "Foundations," argue persuasively in favor of Porphyry's version.

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earliest secure reference to the quadrivium.115 Burkert also takes Plato's accounts of Hippias to be an early witness to the quadrivium.11 6 At Protagoras 318DE, Hippias is said to teach

AoyLaf.tOUc; 'rE Kai. aaTQOVOfl LaV Kai. YEWflETQLaV Kai. flOUULKJlV, which would conform to .

the members of the quadrivium exactly, since at Hippias Minor 366c-368A AoyLaflOL are clearly arithmetical calculations. But this second passage also obscures Hippias' s curriculum, since it lists his areas of expertise, but omits any reference to music, and so presents Hippias as teaching only arithmetic, geometry, and astronomy. Plato does, however, mention the members of the quadrivium when discussing Theodore (Theaetetus 1 45A, 145c), although the two lists are slightly out of order, with geometry and astronomy first and second, but arithmetic and music in alternate orders. Thus, Plato's representation of his predecessors shows mixed evidence for the quadrivium, and also suggests that the order of the sciences was not settled. The same unevenness in the mathematical curriculum prior to Plato is evident in others. Note, for instance, that Xenophon portrays Socrates as teaching geometry, astronomy, AoyLaflol, and medicine.117 One of the authentic fragments of Philolaus states that geometry is the source and mother city of the other mathematical sciences (liQXJl Kai.

flYJTQ6noALc; . . -rwv aMwv f1lX8Yjf1(hwv). This suggests that he conceived of geometry, not .

arithmetic, as presiding over the mathematical sciences.1 18 If so, then Philolaus, unlike most

1 15 Huffman, "Authenticity of Archytas Fr. 1," argues for its authenticity. For reasons too extensive to

discuss here, I reject his argument, and believe there are good reasons for classifying it with the Pythagorean pseudepigrapha of the Hellenistic period. 1 1 6 Burkert, Lore and Science, 421 . 1 1 7 Xenophon, Memorabilia 4.7.2-9. Cf. Simplicius, Commentary on Aristotle's Physics 1 0.833.9-10. 1 1 8 On the authenticity of Philolaus, test. 7a, see Huffman, Philolaus of Croton, 1 93-99. Huffman too easily assumes, rather than argues for, a clearly defined set ofmathemata in the fifth century. There is

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ancient Greek philosophers, gave geometry the priority it was given by practicing mathematicians.1 1 9 At Epinomis 990c-991e (a Platonic pseudepigraphon written in the time of the Old Academy) there is a root triad of mathematical sciences - arithmetic, geometry, and stereometry - without reference to astronomy or music. Plato's own system of mathematical education is constructed quite differently from all these models, further showing that the content and order of the mathematical sciences was not standardized. At Republic 522E-528E, the four mathematical disciplines are outlined as arithmetic, geometry, stereometry (the study of solids), and astronomy, an order that follows the succession of studies of number, planar figures, solids, and solids in motion. Music is missing from this list, and there is no suggestion that it has been accidentally or intentionally omitted. On the contrary, given the logic put into constructing it, music would not fit. A similar list is found at Laws 747A, where five mathematical disciplines are outlined: the study of number in itself, planes, and solids, along with investigation of the sound and motion of the planets. Note that music is fourth in the list, but it is coupled with astronomy, and the pair is thought of as an outgrowth of a discrete trio: arithmetic, planar geometry, and solid geometry. This fivefold scheme in Laws appears to be Plato's most developed view, and the basis for handbooks of late antiquity. Theon of Smyrna lists five mathematical disciplines: arithmetic, music, and geometry, the last of which he subdivides into

no indication that Philolaus held mathematics to consist of three, four, five or some other number of subdisciplines. 1 1 9 Burkert, Lore and Science, 220 n 14, 249.

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stereometry and astronomy. Albinus presents the order arithmetic, geometry, stereometry, astronomy, and music.120 Aristotle, who categorizes and classifies anything he can, seems to some scholars to mention the quadrivium at Physics 194A8 or Metaphysics 1078Al4-1 7. But in these passages music and astronomy are associated not with arithmetic and geometry but with optics or mechanics, certainly not members of the quadrivium. Aristotle classifies music and astronomy as physical disciplines, sharply distinguishing them from the ideal sciences (arithmetic and geometry are here implied). If Aristotle knew the traditional quadrivium, then for some inexplicable reason he splits it up and augments each pair with sciences that lay outside the quadrivium, such as optics or mechanics. The system he offers is incompatible with the traditional presentation of the quadrivium as four disciplines that are mutually complementary and complete. Further, in Posterior Analytics 78B36-40 Aristotle states that the four physical sciences of optics, mechanics, harmonics, and phaenomena are each subordinate to, respectively, geometry, stereometry, arithmetic, and astronomy

(aaTQOAoytKijv).1 2 1 Here, if a quadrivium is to be found, it is in the last set of four, which resembles, in some respects, Plato's three- or fivefold arrangement of the mathematical sciences: music is excluded, and mathematics are conceived of as a progression from number to solids in motion. But this cannot be considered Aristotle's preferred arrangement. At Metaphysics 1 073b4-8 he mentions merely three mathematical sciences: astronomy, arithmetic, and geometry. All these things suggest that in the late fourth century

120 Theon of Smyrna, Mathematics Useful for Reading Plato 1 .1 6-1 7 and Albinus, Epitome of Platonic

Teaching 7.2--4 . Note, however, that Albinus changes the order later in his treatise. See below, n. 1 32. 1 21 See also Themistius, Analyticorum posteriorum paraphrasis, esp. 5.1 .29.7.

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BCE there was no standard quadrivium, and Aristotle tinkered around with different taxonomies of the sciences.122 Based on Presocratic, Platonic, and Aristotelian testimonies, I would suggest that mathematics was conceived of in the fifth and fourth centuries BCE as consisting of a number of elements, in a variety of orders. There were certainly schemes that set the number at four, but even these could differ as to what those four elements were, and in what (if any) order. There is no evidence that a fourfold arrangement of mathematics was dominant in the classical period. I am thus hesitant to suggest, for instance, that Plato's fivefold arrangement of mathematics is a tacit criticism of a Pythagorean quadrivium, as advanced by Huffman.123 It is much more likely that Plato's scheme draws from one of the many available in his day. It may seem to some that my arguments emphasize too much the order and division of the mathematical sciences, but it should be remembered that ancient Greek writers used the order and content of such lists to signal their allegiances and, ultimately, metaphysics.l24 The diversity in the number, order, and relationship of the mathematical sciences lasted well into late antiquity. Cicero treats music as preliminary to the three mathematical disciplines of arithmetic, geometry, and astronomy, which he presents as a threefold

122 For further details on Aristotle's views on the contents of the mathematical sciences, see the Routledge Encyclopedia of Philosophy, 1 :154-55. 123 "Authenticity of Archytas Fr. 1." 1 24 For a parallel discussion of the taxonomy of philosophy, see Dillon, Middle Platonists, index, s.v. "philosophy, divisions of," and Baltes, Platonismus in der Antike, 4:2-21, 205-31. See also above, p. 114 n. 41, and Dillon, Middle Platonists, 133--35 and 348 on the order of Aristotle's categories.

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unity.1 25 He treats music apart from mathematics, much in line with Aristotle's models. Varro's nine books on the liberal arts (now lost) may have provided some order to the liberal arts, but this cannot be reconstructed with certainty.1 2 6 Sometimes, authors from the late Republic and early Empire offer no schema, even when one would be appropriate. For example, Vitruvius attempts to place architecture among the various sciences, and he mentions the various mathematical disciplines, but his presentation of them shows no evidence of a standardized number or pattem.1 27 In fact, some ancient authors discussing the mathematical disciplines propose models that contradict the fourfold scheme. When Galen situates medicine in relation to the other intellectual disciplines he, unlike Vitruvius, provides an order. But he lists nine disciplines, in groups of three, probably to allude to the nine muses: medicine, rhetoric, and music; geometry, arithmetic, and logic; astronomy, grammar, and law .1 28 In one of Plutarch's after-dinner conversations, his brother, who quotes Hesiod, also frames the various sciences in groups of three, in recognition of the three (not nine!) muses of antiquity. He says that there are only three mathematical disciplines: music, arithmetic, and geometry; he treats astronomy as a proper subset of 125 For references in Cicero and a chart of comparison, see Kuhnert, Allgemeinbildung und Fachbildung, 26-29. 1 26 Ibid. 58-63, and Hadot, Arts liberaux et philosophie, 156-90, effectively refute Ritschl's reconstruction of the order of Varro's work. Kuhnert argues for the more Ciceronian order to Varro's work, but this is doubtful since Kuhnert assumes, along with Ritschl, that Varro necessarily assigned to each book one discipline (see NP 2:72 for references and discussion), and that in the first c. BCE mathematics necessarily came as a fourfold set (note my discussion below and Kuhnert's own chart at p. 62, both of which show the wide variety of schemes in late antiquity). Hadot's caution against reconstructing Varro's books from later sources is wise, but this does not undermine the soundness of claim that Varro ordered some of the liberal arts. The particulars are lost. 1 27 De arcitectura 1 . 1 . 128 Galen, Protreptic to Medicine 14.24-25. Earlier i n the same work (5.5-6) h e lists the order geometry, arithmetic, astronomy, mixed with other sciences.

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geometry.1 29 There are many other late antique authors who list only two or three of the mathematical disciplines.l3° A fivefold arrangement of mathematics was also still an option in late antiquity. We have already mentioned Theon, who conceives of five mathematical disciplines. This is striking, considering that a list of four disciplines would have fit well into his long list of tetraktyses.131 (In contrast, the tetraktys and the quadrivium are loosely associated by the Theology of Arithmetic 20.15-22.22, based on texts probably drawn from Nicomachus of Gerasa.) For nearly any order there is a textual witness.132 Some lists are clearly incomplete, and some lists are inconsistent within the same author.133

1 29 Plutarch, Table Talk 7440-F. 13° For the purposes of this section, Ar = arithmetic, G = geometry, M = music, and As = astronomy.

The following are attestations of trios of the mathematical disciplines: G-Ar-As: Heron in Pappus of Alexandria, Synagoge 8.1022.15-16; Galen, Protreptic to Medicine 5.5-6 (mixed with other sciences); Basil of Caesarea, Hexaemeron 1 .3.22-24. G-M-As: Origen, Letter to Gregory Thaumaturgus 1 ; Lactantius, Divine Institutes 3.25.9; Jerome, Letter 5 3 (Origen's and Jerome's lists are mixed with other non-mathematical disciplines). As-G-Ar: Gregory of Nazianzus, Oration 43.23.5; John Chrysostom, Homilies on John 63.3 (PG 59:352.21-22; curiously, John seems to substitute mathematics for music here); Ammonius of Alexandria, On Porphyry's Eisagoge 7.3-4. Ar-G-As: Anatolius of Laodicea in both Eusebius, Church History 7.32.6 and Jerome, De viris illustribus 73; pseudo-Theodosius of Alexandria, On Grammar 52.17-18; Theodoret of Cyrus Church History 269.20-21 . Ar-G-M: Maximus of Tyre, Dialexeis 37.3. G-As-M: Philo, On the Preliminary Studies 11 (mixed with other rhetorical disciplines). In the same work (15-18) Philo lists music and geometry together, and elsewhere (On the Special Laws 1 .335) merely arithmetic and music. For lists of only two mathemata see references to Augustine in n. 133, below, and Apuleius, Flor. 20: G-M. 131 See above, p. 307. 1 32 The orders attested are as follows (Ar-G-M-As and Ar-M-G-As, which became more conventional, are discussed later): References Order Ar-As-G-M Chalcidius, Commentary on the Timaeus 58.6-7 Theon of Alexandria, Commentary on Ptolemy's Almagest 321 .12-13; John G-Ar-M-As Philoponos, Commentary on Aristotle's De anima 15.124.17-18 Themistius, In Aristotelis libros de anima paraphrasis 5/3.1 14.26-30. Structural G-Ar-As-M arrangement of the books in: Varro, Nine Books of Disciplines, Sextus Empiricus, Against the Mathematicians, and Martianus Capella, On the Marriage of Philologia and Mercury.

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This is the strongest argument against a settled Pythagorean quadrivium dominant (or even standardized) in Plato's time. If there had been such a settled order, then it must be explained, how, when, and why mathematics went from such a neat arrangement and order in the classical period to such a bewildering variety of arrangements in the subsequent. Despite this seeming disarray in late antiquity, in the same period there was a concerted effort to provide a coherent content and order to the mathematical sciences, and this became the foundation for the standardized content and order of the medieval quadrivium. The first clear evidence for a systematically ordered mathematical quadrivium is found in Nicomachus. He argues that mathematical science treats objects that participate either in multitude (rrAfi8oc;) or in size (!-1EYE8oc;). Multitudes or quantities are either properties (e.g., the four infour horses) or relations (e.g., the musical octave, with the relationship two to one). Arithmetic deals with things that have the property of quantity, whereas music treats of quantities in relation. On the other hand, objects that partake of size are either stationary or in motion. All stationary sizes are handled by geometry; those in Pinax of [Kebes]; Irenaeus, Against Heresies 2.32.2; Clement of Alexandria, Stromateis 6.80.1 Porphyry in Eusebius, Preparation of the Gospel 14.10.10 As-Ar-G-M Alcinous Epitome of Platonic Teaching 28.4.7-8 M-Ar-As-G Chalcidius, Commentary on the Timaeus 346.6 G-M-Ar-As Socrates Scholasticus, Church History 7.27.15-16; Boethius, Institution ofMusic 2.21 G-As-Ar-M Seneca, Letter 88 M-G-Ar-As Theodoret of Cyrus, On Providence 5 (PG 83:624.29-31) As-G-Ar-M As-M-Ar-G Ptolemy, Harmonics 3.3.74-82 1 33 Syrianus, Commentary on Aristotle's Metaphysics has G-Ar-M (Kroll 4.9-10), G-As-Ar (et al.) (21 .19-20; 54.19), G-Ar-M (58.3-5), Ar-C-As-mechanics (61 .25-27), and Ar-G-M (101 .33). Augustine lists various schemes: G-Ar (Retractions 1 .5 .6), M-G-As (De ordine 2.35-42), M-G-Ar-As (De quantitate animae 33.72), M-Ar (Confessions 4.30), and M-G-As-Ar (De ordine 2.14). M-Ar-G-As

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motion, by astronomy. Thus, Nicomachus presents the mathematical sciences (£ maTfl!-lm) in two orders: (1) arithmetic and music, geometry and spherics (= astronomy) - an order guided by conceptual pairing- and (2) arithmetic, geometry, music, and spherics I astronomy.1 34 The two orders are not contradictory. Rather they both reflect a conception of the quadrivium as two complementary pairs of disciplines. To support his arrangement of the mathematical sciences, Nicomachus quotes several Pythagoreans. We have already mentioned the fragment of Archytas, which Nicomachus cites in his Introduction to Arithmetic. In the identifiable fragments of his

Theology of Arithmetic Nicomachus quotes from the treatise On the Gods (or Holy Discourse) attributed to Pythagoras, who lists the disciplines as arithmetic, music, geometry, and

(J(j:>CUQlKU, cr.' W y' b' Tncr.yl-l£vcu).l35 Nicomachus also quotes from a text attributed to Kleinias, where the preserved order is arithmetic, geometry, music, and astronomy (Tcr.i:ncr.

UQ!-lOVLav Kcr.i. aGTQOV0!-1Lcr.v).1 36 Neither of these Pythagorean texts can be dated with any certainty, but they are clearly part of the archaizing Doric Pythagorean pseudepigrapha of the Hellenistic or Roman periods.137 Even if they are not from the fifth century BCE, the texts

1 34 Nicomachus of Gerasa, Introduction to Arithmetic 1 .3.1-2, 1 .3.7. His explicit mention of spherics and

astronomy in the second reference seems to me to attempt to make explicit how the five mathematical disciplines mentioned by Plato fit in a fourfold scheme. 1 35 Theology of Arithmetic 21 .8-1 0. Concerning how much of this is drawn from Nicomachus's treatise of the same name, see Delatte, E tudes, 140-41, and Taran, Speusippus of A thens, 291-98. 1 36 Theology of Arithmetic 21.10-13. m The composition of Pythagorean literature in ancient Doric dialects in Hellenistic and Roman eras is treated by Thesleff, Introduction, 83-96, who identifies inconsistencies in many of the texts, thus

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obviously antedate Nicomachus. This means that the formal attempt to provide a Pythagorean order to the mathematical sciences began in the era of the Pythagorean pseudepigrapha; Nicomachus drew from this tradition, in his day probably only a couple of centuries old, and epitomized it. Whether or not he was the first to provide Pythagorean coherence to mathematics, Nicomachus was the most influential. The later stand ardization of the quadrivium in the curriculum of the Roman world depended, ultimately, on his

Introduction to Arithmetic. Almost two centuries later Iamblichus embraced the Nicomachean tradition when he structured his magnum opus, On Pythagoreanism, an introduction to the mathematical sciences in ten books. Books four through seven are devoted to arithmetic, and books eight through ten, to each of the remaining members of the quadrivium, in the Nicomachean order: geometry, music, and astronomy.138 In the third book of On Pythagoreanism Iamblichus streamlines Nicomachus' s terminology for the theory of the mathematical sciences as antithetical pairs of property and relation.139 Multitude ( ni\f]8oc;) corresponds to investigations of discrete quantity (n6aoc;), and its natural complement is size (f.1EYE8oc;), which corresponds to investigations of greatness or largeness ( nr'JALKoc;).1 40 The first is governed by arithmetic; the second, by geometry. Each of these can be subdivided between absolute (Ka8 ' t:av'r6v) and relative (nQ6s n). Arithmetic and geometry are the

showing them to be forgeries. Also see Cassio, "Nicomachus of Gerasa," 135-39, and Uguzzoni, "Note sulla lingua." 1 38 On the general plan and outline of Iamblichus' s ten books of On Pythagorean ism, see O'Meara, Pythagoras Revived, 32-35. 1 39 Common Mathematical Knowledge 7. 1 40 This terminology and the distinction it describes derives from Euclid, if not earlier. See Nikulin, Matter, Imagination, and Geometry, 91-92.

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mathematical sciences investigating quantity and size absolutely; music and astronomy treat them relatively. Iamblichus's description, based on Nicomachus's account, lends itself to depicting the quadrivium in a square:

TYPE OF NUMBER Continuous (extent) Discrete (quantity) !-1EYE8oc;/ m1ALKoc; 11Af)8oc;/ 116aoc; IJ...

0 Cl 0 >-< :r:: o f-< ::>

j:.l..J f-< � (/)

Absolute Ka8 ' i:au'l6v Relative TIQ6c; n

arithmetic cXQL8!-lfJHKTJ

y EW!-1E'lQL£X

music !-10UGLKTJ

astronomy a¢mQLKTJ

geometry

A square like this can be read left to right, then down, or top to bottom, then right, or in several other ways. This is the reason why authors who clearly follow Nicomachus and Iamblichus' s presentation of the quadrivium render the list in different orders, just as Nicomachus himself did. The standard orders are arithmetic, geometry, music, and astronomy and arithmetic, music, geometry, and astronomy.141 The same authors freely use different orders because the quadrivium was conceived not as a sequence but as an ordered

1 41 Ar-G-M-As: Clement of Alexandria, Stromateis 6.84-90; Albinous, Epitome of Platonic Teaching 7.24; Proclus, Commentary on Plato's Republic 35 (2.36.3-4); Boethius lnstitution of Arithmetic 1 .1; Cassiodorus, Institutions 2.pref.4; George Pachymeres, Quadrivium. Ar-M-G-As: Porphyry, in John Tzetzes Chiliades 1 1 .377, lines 529-30; Augustine, De ordine 2.12.35-2.15.42; Proclus, Commentary on the First Book of Euclid's Elements 35.21-36.3; Cassiodorus, Institutions 2.21; CCA G 7.58 (= cod. Berlin 1 73 [XV c.], f. 137v); John of Damascus, Philosophical Chapters 66.18; Isidore of Seville, Etymologies 1 .2; the structure of books 2-5 of the anonymous Logica et Quadrivium. ,

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matrix.142 Even some of the authors who seem to give an order quite different from the Nicomachean nevertheless show that they are thinking in his terms and arrangement.143 Thus, the quadrivium of the medieval period owes its origin to the Pythagorean reorganization of the mathematical disciplines in the Hellenistic period and late antiquity, and its dominance to the epitomizers and the encyclopedia and textbook writers who found in Nicomachus's synthesis a coherent worldview.

5

THE NUMBER FIVE: MARRIAGE

The epithet ya1-1oc; for the number five is quite old, attested by Aristotle. At Metaphysics 1 078B23 he mentions the Pythagorean habit of attaching words to numbers, and specifically mentions "opportunity," "the just," and "marriage" (KmQoc; � TO blKmov � ya1-1oc;).144 Traditionally, these three epithets are attached to seven, four, and five, respectively .145 Aristotle does not state what numbers symbolized them, probably because he had already written two books on the Pythagoreans, and in these he would have discussed such matters. If his fragment 203 is authentic, then we have clear evidence that this Pythagorean epithet

1 42 Compare, for instance, Ammonius of Alexandria's Commentary on Porphyry's Isagoge 13.11, 14.126, which, in its summary, breaks down the mathematical sciences according to Iamblichus' s scheme, but discusses them in the order G-As-M-Ar. 1 43 The language used in the order presented by several of the authors listed above, n. 132 suggest that they were working off the Pythagorean order. See especially Ammonius of Alexandria, On Porphyry's Eisagoge 13.11, where the four are listed as G-As-M-Ar, but are expounded in Nicomachean terms in the order Ar-G-M-As. 1 44 The Pythagorean habit of attaching names to numbers is also attested by Aristoxenus, frag.23. 1 45 But note Syrianus, Commentary on Aristotle's Metaphysics 1 04.24-27, who assigns them to seven, five, and six, respectively. Moderatus, frag. 3, says Pythagoras assigned to opportunity and marriage (the just is omitted) seven and six.

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had a long, and consistent, history.146 In the fragment, seven is compared with Athena, who is " motherless" and "ever virgin," just as the number seven is neither the product of, nor produces, any of the other numbers in the decad. In contrast, the Pythagoreans call five

marriage because marriage is the bringing together of male and female, which correspond to odd and even. Five is the first number to derive its existence from the first even number, two, and the first odd number, three. This Pythagorean explanation is repeated, sometimes with variants, throughout Greek literature.147 After explaining the connection between five and marriage, Plutarch elaborates further by comparing five and six to the act of generation.148 Any other number when multiplied by itself produces numbers that end in a different digit. For instance, four times four is sixteen, which has a six in the units place. Five, however, multiplied by itself yields twenty-five; six squared yields thirty-six. The units place retains the original multiplicand, five or six.149 Furthermore, the analogy applies to five more than it does to six, since any number multiplied with five results in a number ending in five, or in the decad. In this way, Plutarch says, the number five imitates the adornment of the universe, since five begets either itself or perfection. This harmonizes with Heraclitus's description of the fashioning of the universe.15o

1 46 In Alexander, Commentary on Aristotle's Metaphysics 39.8-13. 1 47 Plutarch, Roman Questions 2 (264A); Theology of Arithmetic 13.17-19; the anonymous On Numbers. 1 48 Plutarch, On the E at Delphi 388CD. 1 49 Plutarch does not give the example of the number one probably for two reasons. First, one was

technically not a number. Second, the number one, no matter how many times multiplied against itself, never "grows." The analogy Plutarch offers is based on generation and growth. l SO On the number ten as a sign of perfection, see above, p. 50 n. 1 25 .

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Plutarch provides his most colorful Pythagorean explanation of the number five as marriage when he compares the trio Osiris, Isis, and Horus to the orthogonal triangle of three, four, and five sides.151 The side of length three is to be likened to the male, the base of four to the female, and the hypotenuse to their offspring. Osiris is the source (d:Qxr)), Isis the receptacle (unoboxr)), and Horus the completion (anorr£Ma1-1a). The number symbolism follows the same pattern: three (Osiris) is the first odd number and is perfect; four (Isis) is a square with sides of the (first) even number two; and five (Horus) is likened to both its father (three) and mother (two). In this allegory, five symbolizes not only marital union but the perfect offspring of that union.1 52 There were non-Pythagorean reasons for associating five with marriage. Plutarch considers the question why exactly five torches were used in wedding ceremonies, and he entertains without completely embracing several possible explanations, only one of which (the longest) is Pythagorean.153 Occasionally the epithet is applied, not to five, but to six, either for its association with the product of two and three, or for its mythological associations with Aphrodite.154

1 51 Plutarch, On Isis and Osiris 56 (373f-374a). 1 52 Cf. Philo, On the Contemplative Life 65-66, which makes the point that the number five is "the most natural" (cpvmK6TctToc;) number because it is drawn from the orthogonal triangle that is the "source of generation of the universe" (UQXTJ Tile; TWV oA.wv yrviaEwc;). For another extended application of the orthogonal triangle to generation and copulation (but without direct reference to five as marriage), see Scholia on Homer, set D, 19.119. There, the triangle is used to explain why infants are viable in the seventh and ninth months, but not in the eighth, a common belief in the ancient world. 1 53 Plutarch, Roman Questions 2 (263f-264b). 1 54 Product of two and three: Philo, On the Special Laws 2 .58; idem, Questions and Answers on Genesis 3.38A, 3.49B; pseudo-Plutarch, On Music 1 139F5-1 140A7; Theology of Arithmetic 43.5-7. This passage also likens to marriage because it equals the sum of its factors (1, 2, 3), and the goal of marriage is to create offspring similar to its parents. Aphrodite: Moderatus, frag. 3; Plutarch, in Stobaeus,Eclogae

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Even the number three is called marriage.155 These variations should not been seen as contradictions as much as evidence for the wide variety of meanings available in ancient number symbolism.

1 .pref.1 0; John Lydus, On the Months 2.1 1 .14-16. The epithet is given without explanation in Clement of Alexandria, Stromateis 5.14.93.4 and Syrianus, Commentary on the Metaphysics 1 04.27. 1 55 Theology ofArithmetic 1 9.20 and Nicomachus of Gerasa, Theology of Arithmetic in Photius, Bibliotheca §187 (144A1 ).

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Excursus C The Elements and History of Psephy (Gematria)

The basic principles of isopsephy are well known, but its history and the purposes for which it was used have not been adequately stated or studied. The most complete exploration of the phenomenon to date is that of Franz Domseif£.1 Although Domseiff adequately discusses the various uses of isopsephy, he does not apply the historical rigor necessary to discern the shape of the tradition. As a result, modem studies tend to repeat his errors or mistaken assumptions. What follows here is a brief outline of the principles, history, and purpose of isopsephy, a basic outline for future research.

PRINCIPLES Isopsephy, better known today as gematria, is the literary device whereby the letters of the alphabet are assigned numerical values. Letters, words, or entire sentences are C
1 Das Alphabet in Mystik und Magie, 91-1 18.

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isopsephy. It was developed in Greek, and provided the basis for imitative systems in Hebrew or Aramaic. In traditional Greek isopsephy, each of the twenty-four letters of the Greek alphabet, plus three archaic forms, are assigned values of units, tens, and hundreds as follows:

a

f3 y b E c; [, f)

8

1 2 3 4 5 6 7 8 9

l

K A f.l v l; 0 n 9

10 20 30 40 50 60 70 80 90

Q a '[ u

cp X ljJ w ?1

1 00 200 300 400 500 600 700 800 900

One thousand to nine thousand were represented by a through 8, marked by a stroke or loop to the left. Numbers larger than ten thousand were broken up into blocks of ten thousands (myriads, signified by M), so that large strings of numbers were grouped in sets of four, much as commas today divide separate the thousands, millions, billions, and so on, of very large numbers. The digits were written normally in descending order, with the units on the right, marked by a stroke to indicate it was a numeral, not a word. For example: KE'= 25; aE' = 205;

,f3E' = 2005; ,b?1 l;f3' = 4962; avb' M ,ywL[,' = 2,543,817?

2 The M could also be placed directly beneath the numbers it modified. See P. Cairo, Inv. 65445,

reprinted in Neugebauer, Exact Science in Antiquity, pl. 5.

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In a few cases, a number rendered in this notation doubled as an acronym. For instance, X!-!Y' ( 643) appears in papyrus records from the early fourth century CE, and is likely a number read as a Christian acronym for X(E LQL) 1-l(ov) y(EYQ£X!-1!-1Evov), X(QLGT6s) (£K) M(aQLas) y(EVVYJ8 ds), or X(QLGT6s), f(a�QLr)A), M( Lxar)A). Its original meaning is debated.3 In a sixth-century inscription in modem-day Syria the number ,�v1-1y' [2443], has a dual role, to indicate the psephic value of each poetic line and to mark the acrostic for the refrain, either �(or)8 L) Y(LI':) M(ovo) y(Evr)c;) ("Help me, Only-Begotten Son!") or �(or) 8L) Y(LI':) [ EK] M(aQl£Xc;) y(EVVYJ8 dc;) ("Help me, Son born of Mary!").4 More famous is the 318 of pseudo-Barnabas, Epistle 9.7-9, discussed below. Most important, any Greek word could be read as a string of numbers. For instance, Koa1-1oc;

=

20 + 70 + 200 + 40+ 70 + 200

=

600. Thus, for some, the numerical value of K6a1-1os

confirmed the well-ordered character of the universe.5

HISTORY It is frequently thought that isopsephy is as old as the Bible. This impression has gained ground mainly because of an often-cited inscription ascribed to Sargon II, where the length of the wall at Khorsabad is said to be "16,283 cubits, the numeral of my name." The inscription, however, never explains the relationship between the number and Sargon' s 3 A synopsis of the debate and a select bibliography are provided by Derda, "Some Remarks," who

argues that the issue probably cannot be resolved. See more recently, but less completely, Llewelyn, "Christian Symbol XMG?" Scholars agree that the symbol came to represent several things after it was introduced -both an isopsephism and an acrostic-but its original (single?) meaning is unknown. 4 See also MacCoull, "Isopsephistic Encomium," discussing a sixth-century poem, the isopsephic value of whose lines probably indicates the year when the saint was martyred. 5 Theology ofArithmetic 48.18-20.

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name. In fact, the inscription does not even suggest that the number derives from Sargon' s name, just that it is "the numeral of my name." It is often assumed that gematria is at work in the Sargon II inscription because of certain close relationships between numbers and syllables in cuneiform, where words-cumnumerals are attested as early as ca. 2700 BCE. Because certain numbers were homophonic to certain phonemes, when those phonemes were written, the numbers were also used. Thus, certain numbers could be used to depict syllables and words, and likewise, some words were consciously depicted as numbers.6 There are a set of number-syllabary texts that date from the late first millennium, well into the Seleucid period. The authors of these texts associate gods, numbers, and syllables with each other? This literary phenomenon, however, is imperfectly understood. We do not know why certain gods are associated with certain numbers and syllables. There is no intrinsic phonological or pictographic logic to the associations. And we cannot tell if a comprehensive system was at work. Our best guess is that in these texts, late for cuneiform, the scribes were using a tradition that associated deities with round numbers.8 It is uncertain whether this tradition has anything to do with the Sargon II inscription. The operating principles, although still somewhat mysterious, are clearly quite different from those found in Greek isopsephy, so a genetic connection between the two can

6 For examples of Sumerian and Akkadian numeration practices, see Lieberman, "Mesopotamian

Background," 186-87, and Ifrah, From One to Zero, 1 70-99. 7 For discussion and analysis, see Pearce, "Number-Syllabary Texts." s Pearce (ibid.) argues for the innovative character of the number-syllabary texts. See Lieberman,

"Mesopotamian Background," 198-200 for examples of round numbers assigned to gods, and explanations as to why "one must carefully distinguish the numerological interpretation of texts based on the number values of words or letters from special meanings assigned to numbers."

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be safely ruled out. For lack of an alphabet, cuneiform's "isopsephy" is incidental in character. Only a few, not all, syllables were represented numerically, and not all numbers could represent phonemes. Cuneiform does not have an alphabet, and the phonemes have no order. The languages that employed cuneiform, then, could never supply the basic building blocks needed for a complete system of isopsephy. Sargon' s name was depicted as a number, probably not because of its value in gematria, but for reasons as yet unknown? Isopsephy did not emerge ex nihilo. It depended upon well-defined and long-used customs of numeration. Any successful literary device requires a shared culture that allows the author to play off customs already well known and accepted. For example, in own day we encounter messages that depend upon the association of letters with phone numbers, and vice versa. All this depends upon a shared social convention, the assignment of letters to the numbers on the dial of telephones in the early twentieth century. Suppose someone had, before the advent of the telephone, developed a system that assigned two to A-C, three to D-F, and so on. Any word plays that person published would be incomprehensible since the convention was a private one. Unfortunately, some scholars have tended to assume the existence of psephic techniques everywhere and at all times in the ancient world, and used that assumption to find the earliest examples. Few ask when and how the technique, as a whole, could have arisen and made sense to a given culture. Biblical scholars today persist in looking for instances of gematria in the Hebrew Scriptures, without investigating the requisite

9 For the most recent analysis of Sargon II's "isopsephy," see Fouts, "Large Numbers," esp. 207-8.

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background in habits of numeration.1 0 This is a critical omission, since in the era when most of the Hebrew Bible was composed, gematria was not an option. It is as if we have been finding instances of telephone-letter word plays in the nineteenth century. Just as in the telephone analogy, psephy depends upon shared conventions for numeration. Letters used as numerals must be widespread enough for the gematria to be understood. The first known instance of this convention in the ancient world is in the socalled "Miles ian" or " alphabetic" system of numeration.n This system seems to have emerged in the last quarter of the seventh century BCE, and probably no earlier, from somewhere like Naukratis, an Ionian trading outpost in the western Nile deltaP In that region of Egypt, and among the native Egyptian population, numbers were assigned to thirty-six individual characters-the units, tens, hundreds, and thousands. These characters were nonlinguistic signs that were merely shorthand renditions of hieratic and hieroglyphic numerals. The Egyptian practice seems to have inspired the Greeks living in the area to develop their own version, one based on the alphabet. By substituting Phoenician-cumGreek letters for the non-linguistic Egyptian characters, the inventor(s) created a system just as original as their Egyptian model. From Ionian ports in Egypt the practice traveled to the Ionian islands. 10 Heinzerling, "Bileams Ratsel"; Smit Sibinga, "Composition of 1 Cor 9" (and other articles by Smit Sibinga); Labuschagne, "De numerieke structuuranalyse" (and other articles by Labuschagne). The "New method projects," sponsored by the Berkeley Institute of Biblical Archaeology and Literature (BIBAL), analyzes the entire Hebrew Bible using gematria-inspired logotechnical analysis. It suffers from the same methodological error. 1 1 It is called "Milesian" because the earliest evidence is found in colonies of Miletus, although not in Miletus itself. 1 2 This, and the Demotic Egyptian origin of alphabetic numeration is argued by Chrisomalis, "Egyptian Origin."

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Of the original twenty-two letters of the ancient Phoenician alphabet, all but one (the san )

were retained in the Ionian alphabet. To these Phoenician letters were added the v (an

augmented waw), ¢, x, ¢,

w

(itself an Ionian invention), and the somewhat-mysterious

sampi.13 Even at the time it was devised for numeration this twenty-seven letter alphabet was probably somewhat artificial, since three of the letters-waw, qoppa, and sampi - are found rarely, and then only in archaic poetry.14 But the invention of an ordered, twentyseven element alphabet lent itself to an elegant system of numeration.15 Milesian letterforms gained ground across the Greek-speaking world: in 403, during the archonship of Euclides Athens officially adopted their form of the alphabet, but without accepting the Milesian system of numeration, which remained a minority system in the Greek speaking world, probably centered in northern Egypt. By and large, most Greek citystates used the base-five/ten system today termed the "decimal," "acrophonic," or "Attic."16 In this family of number-notation, each of the numbers 1, 5, 10, 50, 1 00, 500, 1000, 5000, 1 0,000, and 50,000 were represented by a particular character. The most common representation was: I, r (a n for ntvu with a shortened right leg), � (for bEKcx), P, H (for

1 3 The term sampi dates from the 1 7th c. CE. Since the letter san had been rendered obsolete, having been assimilated to the Greek sigma, the letterform was possibly reintroduced at the end of the alphabet to accommodate the Milesian system of numeration. See LSJ, "M," s.v. 1 4 The waw was later called either digamma - a description of the letterform's resemblance to two gammas (F) - or stigma-a conflation of sigma and tau, reflecting its hybrid letterform (c;). See above, pp. 91 and 213. 1 5 See Jeffery, Local Scripts of Archaic Greece, 327, for a summary of the evidence of the Milesian system of notation, with references to pottery from after 550 BCE. See also Chrisomalis, "Egyptian Origin." 1 6 Unlike Milesian numeration, "Attic" numeration is so called because of the prestige Athens had, not because of the system's provenance, which is unknown. The association is not modern: pseudo­ Herodian, On the Numbers (TLG 87.42; probably 2nd c. CE), relates the system to the laws Solon wrote for Athens.

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EKa'l6v), J11 , X (for XiALoL), P:, M (for f.lUQLOL), and JM. Any number could be represented by one or more of these characters placed in a sequence. Thus, for instance, 47,296 would be represented MMMMP:XXHH.P����ri .17 These two systems of numeration - the alphabetic and the Attic systems - should be sharply distinguished from the use of letter labels, since the latter is often confused as a third method of numeration. When writers use letter labels, they use single letters to identify objects in a series. In the Iliad, the Odyssey, and Aristotle's Metaphysics, letters mark the sequence of books. In texts dealing with geometry, authors identify points and angles with letters, a convention still used today. Letter labels differ from alphabetic and Attic systems of numeration in several important respects. First, in letter labels the ordinality of the letters -not their numerical value -is key. Book Cl> of the Iliad was thought of no more of as being "twenty-first" than, for us, "Q Street" is thought of as being seventeenth. Second, letter labels were never composed of, applied to, or inferred from strings of letters. Thus, a word was never interpreted in light of its letter-label value. Third, letter labels were generally applied to small, discrete series of objects. When a set of objects ran out of oneletter labels, the sequence continued with AA, BB, etc. It was inconvenient to use letter labels for sets larger than fifty elements. Sometimes the letter-label and Milesian systems of numeration are indistinguishable. Occasionally we find the letters a through

E

used as numbers in coins or other artifacts, but

it is unclear which of the two systems are being used.1 8 1 7 For more examples and variant systems, see Ifrah, From One to Zero, 225-27 and Tod, Ancient Greek

Numerical Systems, passim. 18 See H0yrup, "Mathematics, Algebra, and Geometry," and Lieberman, "Mesopotamian Background," 1 93-94.

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There is no evidence that letter labels were used for Greek isopsephy. In Latin it was used rarely, probably because the full Latin alphabet was never used for numeration.l9 Although each of the twenty-four Greek letters could potentially be assigned the numbers one through twenty-four (and not just a certain rank in the order of the alphabet), there is no explicit evidence that they ever were. The same is true of the twenty-two letters of various Semitic languages. It should then come as no surprise that there is no explicit evidence of a system of ancient gematria that uses this sequential system until the Middle Ages, when kabbalists stretched and expanded the methods of gematria.

Milesian notation was a minority system and it was little known outside of Ionia in the fifth century.20 How it emerged from relative obscurity to become the dominant system of numeration is unclear. Chrisomalis argues that alphabetic numerals were used mainly by the Ionians, and when their power and influence was eclipsed by Athens and later by Macedonia, the numerals fell out of use. The revival of alphabetic numerals in the Hellenistic period may have come because of the continued, isolated use of Greek alphabetic

19

See Domseiff, Alphabet in Mystik und Magie, 1 01, citing a fifth-c. text that mistakenly identifyies the Latin psephic value of ANTICHRISTUS as 154 (actually 1 55) so as to show gaiseric is the antichrist. See below, n. 26. 20 See JG 12.760, p. 222, cited by Tod, Ancient Greek Numerical Systems, 96, as the one Attic instance of the Milesian system. His observations are based upon over fifteen thousand inscriptions he studied. The inscription, a calendral table of some sort, antedates the Peloponnesian War. I am not convinced, however, that this inscription provides incontrovertible evidence for Attic knowledge of the entire Milesian system, since the only numbers that are incontestably represented by letters are the units, indicated by a through 8 (including the waw). A kind of letter-label system could be in play here. This inscription needs to be investigated further.

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numerals in lower Egypt, and the coincidental rise of Alexandria as a major political and economic power. Habits of numeration are slow to change. Chrisomalis' s hypothesis would explain, first, why the shift to alphabetic numerals seems to happen so suddenly in the third century

BCE. The shift is illusory: alphabetic numerals were presumably used by a minority of Greeks in Egypt for several centuries before the rise of their political and cultural fortunes. And since habits of numeration are slow to change, neither Hebrew nor Aramaic developed a comparable system for centuries. Specimens of shorthand numbers in these languages, even through the first century CE, show the tendency of their linguistic group to rely upon age-old systems of numeration. That is, in Hebrew and Aramaic the base-10 stroke-style system of numeration was used (see below). Imitations of the Greek alphabetic system were to emerge much later (see below). It is no surprise, then, that our earliest examples of isopsephy derive from the late Hellenistic period, only after alphabetic numeration was well established and widespread . Our first examples come from the first century CE, when isopsephy probably first originated. Of authors from the first century, Philo is one of the most attuned to numbers. In the hundreds of instances of number symbolism in his large literary corpus, there is only one example that approaches psephy, an innocuous reference to the change of Sara's name to Sarra (Questions and Answers on Genesis 3.53). Against those who might consider the name change in Genesis 1 7. 15 trivial, Philo argues that it represents the change, not of a single letter, but of a hundred of them, since that was the numerical value of the rho. Philo, however, does not consider the association of rho with one hundred of intrinsic significance. He favors instead an explanation based on the definitions of Sara and Sarra in Hebrew. This 334

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passage does not even imply Philo's awareness of or use of isopsephy, just his knowledge of the Milesian system of notation. That this is the only Philonic reference to anything remotely close to isopsephy is telling. It seems that if there were any author of the first century who would latch onto isopsephy it would be Philo, because of his propensity to employ speculative, allegorical exegesis. I infer from this that in Philo's day isopsephy had not yet won its place as a fully acceptable literary device. Litterateurs of less-lofty aspiration were more accepting of the technique. In the graffiti of Pompeii are three specimens of isopsephy quite similar to each other. One states, "I love her whose number is [??]1." Another: "I love her whose number is 545." Yet another: "Without care, he commemorated Harmony, his own lady, the number of whose good name was 1 035."21 These graffiti, probably from the first century, before the volcanic destruction of the city in 79 CE, show that isopsephic games were well known in the city. In religion, the name A�Qam:X<'; was early on associated with the solar year because the name's value is 365. The name may have been devised for this very purpose. It first appears in the first century CE tabulae defixionae of North Africa, and frequently recurs in the magical papyri and in early Christian texts, orthodox and otherwise. Most often, the name is ascribed to a deity associated with the year or the heavens.22 CIL 4.12*:
=

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We can date the active use of isopsephy in respectable literature no later than the reign of Nero, when Leonides of Alexandria flourished. Once an astrologer, Leonides turned to epigrams, where the psephic value of the couplets or individual lines are equal. He apparently wrote several books of these epigrams, some of which were birthday presents for Roman emperors.23 It is also to Leonides we can credit the first instances of the basic phrasing that led to the terms psephy and isopsephy, the earliest terminology for the technique:

Eic; nQoc; [va ¢TjcpOLmv imxl:;nm, ov bvo bOLmc; ov yaQ EH a'tEQYW 'tTJV boALXOYQ£XcpLT)V. One [line] equals one line in tallies, not two in couplets, For I no longer cherish prolix writing.24

Thus, to make the value of the letters in lines of poetry is "to make equal in count."

'Ia6¢11¢oc; is attested in the second century, and cognates such as ¢TJcpLl:;av were commonly used thereafter.25

if either of the fragments of Apollonius where Abrasax is called the "archon of birds" or "mountains" is genuine, it raises doubts as to whether the god was associated with the zodiac, as Janssens claims. Nevertheless, his suggestion that isopsephism emerged in literary circles due to the patronage of Nero remains a strong possibility, especially in light of Leonides, discussed below. 23 Page's wry assessment and commentary in his edition of the forty-two epigrams rescues the poet from his many careless critics and establishes important re-readings of the text. 24 Anthologia Graeca 6.327. For a similar construction, see 9.356. 25 See Aulus Cellius, A ttic Nights 14.6.4, and below, excursus D.

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JEWISH ISOPSEPHY There is little evidence for a first-century culture of isopsephy in other written languages of the Mediterranean, such as Latin or Coptic.26 Nevertheless, isopsephy appears early in Aramaic Jewish sources, possibly in the first century CE, more probably in the second. It quickly became an important device in Jewish and Samaritan exegesis in late antiquity. In ancient Hebrew when authors

used shorthand notation for numbers, they used a

decimal-based system, in imitation of Demotic Egyptian conventionsP There is plentiful evidence for a continuity of this practice from the tenth century BCE to the first CE, in both Hebrew and Aramaic. Calendral material from the Qumran material and pendants from Masada use this Egyptian-style stroke system.28 There is evidence that Hebrew letters were used as numbers as early as 79 BCE, during the reign of Alexander Jannaeus (103-76 BCE), who minted coins that read �J for the 25 years of his reign.29 How much earlier this practice

26

In Latin, there may be exceptions. Schmidt, "Ratselzahl 666 in Offb 13:18," argues that the 666 of Rev 13.18 refers to Roman numerals discernible in the name of the Emperor Claudius. William McCarthy has noted (pers. comm .. ) that Martial, Epigram 1 .23 possibly exhibits an isopsephic character similar to that found in Leonidas of Alexandria. See also the fifth-c. example mentioned above, n. 19. The exceptions, in my opinion, prove the rule. In subsequent ages, any Latin author's mention of Greek isopsephy is attached with an explanation of how it worked since there was nothing like it in Latin. Even Odo of Morimond ( 1 1 1 6-1 1 61 ), attempting to fill the lacuna by assigning numbers to Latin letters, did not attempt to replicate the Milesian system in Greek. Instead, he rather arbitrarily assigned 900 to A, 300 to B, 250 to E, etc. See Beaujouan, "Symbolisme des nombres," 1 63. Compare also the Catalan system devised at Lucas, Astrology and Numerology, 96-97. Even though Coptic used the Greek alphabet and added a few letters of their own, Coptic scribes tended to use only Greek letters for shorthand numeration. Thus, the earliest isopsephisms in Coptic draw wholesale from Greek practice. 27 For examples that show the dependence of ancient Hebrew conventions upon Egyptian ones see Ifrah, 244--48 . 28 See Talmon et a!., Qumran Cave 4 . XVI, 137 at 4Q326 line 2. Note 15 there summarizes the evidence and provides a current bibliography. 29 See Lieberman, Mesopotamian Background," 1 93-94.

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can be dated is difficult to tell, but I suspect not much further back. All other earlier instances of Hebrew letters used as numbers appears to draw on a letter-label system, not psephy.30 The balance of evidence shows that the decimal system of numeration was the preferred system in Hebrew and Aramaic first century BCE to the first century CE, but that an alphabetic system was intelligible and (probably) gaining ground.31 Even after the introduction of alphabetic system, the decimal system lingered on for some time.32 The twenty-two letters of the Hebrew alphabet are five short of the number needed to build a complete model, like the Milesian system. When required to write numbers greater than four hundred, Hebrew writers combined characters, thus jury-rigging their alphabet so as to function like the Greek.33 This is the system used: � p 100 � 1 10 1 200 J. 20 J. 2 ' 30 iD 300 � 3 n 400 1 4 rJ 40 J 50 pn 500 i1 5 D 60 1n 600 6 T 7 � 70 tDn 700 n 8 :J 80 nn 800 y 90 pnn 900 � 9 30 See Hoyrup, "Mathematics, Algebra, and Geometry," and Lieberman, "Mesopotamian

Background," 193-97. 31 Lieberman, "Mesopotamian Background," 198, claims that "the date when the Hebrew letters were first used to write numbers cannot be determined," so as to safeguard the possibility that Hebrew isopsephy antedated the Second Temple period. But the evidence he discusses 1 93-98 seems to necessitate the opposite conclusion. After all, the Alexander Jannaeus coin is the one and only example he gives of Hebrew alphabetic numerals before their more regular occurrence after 66CE. Lieberman's conclusion - "we must admit that it possible that such techniques were employed in biblical texts" - does not follow. 32 See Ifrah, From One to Zero, 279-81 for examples of decimal notation in the fifth century cE in Syriac, an Aramaic dialect. Alphabetic numerals in Syriac seems to be a rather late development, well after their introduction into Hebrew and other dialects of Aramaic. 33 See Ifrah, From One to Zero, 251-59 for examples.

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In much later (Kabbalistic) usage, the final forms of five letters (kaph, mim, nun, pe, and tsade) were introduced to replace doubled letters in the hundreds column, thereby making the system more elegant. Shortly after Greek isopsephy became a widespread literary phenomenon in the Mediterranean world, Rabbinic Jews picked up on the practice and began to use the Hebrew version of it in their Biblical exegesis. Possibly the earliest example of explicit Hebrew isopsephy is found, oddly enough, in Revelation 13.18, the infamous number of the beast. In variations of the Greek text, 616, rather than 666, is given as the number, which leads to an elegant solution, that both versions describe the name Nero Caesar as written in Hebrew. For 666 we have 10p

i 1 1 J (200 + 60 + 1 00, 50 + 6 + 200 + 50); for 616 the final nun is dropped, a

standard option in Hebrew for rendering foreign names.34 If this interpretation of the number of the beast is correct, it implies that Christians were active participants in the earliest days of Hebrew and Aramaic isopsephy. The earliest explicit examples of Rabbinic Jewish gematria come from secondcentury tannaim. Rabbi Yehudah (fl. mid 2d c. CE, in Galilee), interpreting Jeremiah 9.10, concludes that "no one passed through Judea for fifty-two years" because of the numerical value of the word Behemah (beast). Rabbi Nathan (fl. 2d-3d c. CE, in Palestine) suggests that the gematria of "These are the words" in Exodus 35.1 hints at the thirty-nine categories of

34 If this is the solution to Rev 13.18, it should be noted that it attests to the lateness of the system of

Hebrew gematria that employed the final form of five letters for the values five to nine hundred. Under this later, Kabbalistic system the final nun would have given Nero Caesar the value 956. On the number 616 see above, p. 1 71 .

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work forbidden on the Sabbath.35 The most famous example of Rabbinic isopsephy deals with Genesis 14.14 and the three hundred eighteen servants of Abraham, a tradition transmitted under the name of Bar Qappara' (2d-3d c., son of R. Eliezer).36 Noting that the name of Abraham's servant, Eliezer, also adds up to three hundred eighteen, Qappara' claims that the text meant simply that Abraham took only his servant to rescue LotF In a tradition dating back no earlier than the ninth century CE, Rabbi Eliezer (2d c., in Palestine) is said to have devised thirty-two rules of Biblical interpretation, of which the twenty-ninth concerns gematria.38 Genesis 14.14 is cited as a prime example. Although this tradition is much later than the second-century rabbi upon whom it is projected, it confirms the observation that the second century proved to be a fertile period for the development of Jewish techniques of isopsephy in Hebrew and Aramaic. Throughout the period covered by the Talmud, Jewish teachers used the term

gema�ria (� � 1tJD �

)

or i1 � � 1tJD ) ) to describe any number of methods of interpretation that

use grammatical analysis. The term is built upon a Greek word, probably YQLX.f.lf.lLX.TEta., not

YEWf.lETQLCX., as often cited.39 Somewhere around the time the Talmud was compiled, probably the sixth century, the term came to be used more narrowly, of the procedure we 35 Shab. 70a . 36

Ned. 32a, Gen. R. 43.2.

37 This is to be compared with ps.-Barnabas, Epistle 9.7-9, who suggest that the 318 servants is a

prophecy of Christ. After all, written in Greek (nfl'), the number stands for the Cross ('r) and the first two letters of Jesus's name (tT]). For the relationship between second century Christian and Jewish exegeses of Gen 14.14 see Ferguson, "Was Barnabas a Chiliast?"; Hvalvik, "Barnabas 9,7-9"; Leiberman, "Mesopotamian Background," 1 68 n. 47; and Gevirtz, "Abram's 31 8." 38 Lieberman, "Mesopotamian Background," 159. 39 Sambursky, "Gematria," is the authority most often cited. He attempts to show that gematria derives from a sixth century instance of yc:wflETQLKOV LXQL8f16V in Iamblichus (cited in Proclus, Jn Timaeum 2.278), which I treat above, p. 241 n. 45.

34 0

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have been discussing. Thus, whereas Greek used isopsephy, the term still used in modem Greek, Hebrew Aramaic used gematria, the term most familiar in modem western languages.40

In summary, psephy seems to have first emerged in the early- to mid-first century CE,

after alphabetic numeration was already well-known and well established. The date is

not hard and fast, but the phenomenon could not occurred without the cultural and political rise of Alexandria in the third century BCE. Psephy emerged first with Greek writers, and was later used in Hebrew. In dozens of early examples we find the phenomenon on both a popular and literary level. It occurs in poetry, riddles, theological systems, and divinatory techniques. It gained enough popularity that tables were composed, juxtaposing interesting and ironic isopsephisms, possibly an aid to party-goers who, after dinner, would often entertain themselves with "puzzles and riddles and sets of names in numbers."41 Isopsephy rose shortly after Pythagoreanism was resurrected (see excursus A). The idea that arithmetic could be applied to names so as to lay bare the secrets of the universe meant that psephy soon began to be seen as Pythagorean. Hippolytus saw the isopsephic exercises of Colarbasus and others as a Pythagoreanizing (i.e., corruption) of Christianity (see chapter 6). Iatromathematical texts that depend upon a close reading of the isopsephy of a patient's name and the lunar day are regularly linked to Pythagoras in the manuscript tradition (see excursus D). Isopsephy started as an arithmological tradition independent of 40 Isopsephy was very popular in Arabic, and was known as h_isiib al-jummal or, in an Iranian sect,

h.urufi. 41 Plutarch, Table Talk S.pref (673AB): aiviyf.laTa Kat yQiq>ouc; Kat 8£anc; OVOf.lUTWV i:v UQL8f.1oic;. For a table of amusing psephisms from the early second century see Skeat, "Table of Isopsephisms."

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Pythagorean number symbolism, the two were often (but not always) conflated from at least the second century onwards.

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Excursus 0 Types of Greek Numerology

Greek numerology was first developed in the first or second century CE. Cicero, in his De

divinatione, outlines all the major forms of divination, including astrology (then relatively new), but numerology is not included, even when discussing Pythagoras.1 By the fourth century, numerology was so prominent that Iamblichus has Pythagoras teach Abaris "instead of divination by the entrails of sacrificed animals . . . fore-knowledge through numbers, believing this to be purer, more divine, and more suitable to the heavenly number of the gods."2 Artemidorus, who discusses rules for the psephic interpretation of dreams, is the earliest datable text. (The system upon which he bases his advice, however, was either his own invention or a minority tradition: Artemidorus' s principles are replicated in none of the manuscripts I have so far investigated, and they contradict more standard techniques.) Vettius Valens, also from the late second century, may allude to isopsephic numerology when he mentions the technique of "reckoning the moon" (1VfJcJ:>tl:w 'rTJV crEAT]vf}v).3 Hippolytus' s Refutation of All Heresies is the next earliest datable text to report numerology, and the technique he describes is one we find scattered throughout Byzantine manuscripts. 1 1 .3.5; 2.58.1 19. 2 Pythagorean Way of Life 19.93 (Dillon trans., 117) . Cf. Iamblichus, Common Mathematical Knowledge 23. 3 Anthologies 1 .24.6; cf. 1 .23 (Bara ed., 220.2).

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Thus, numerology was well established in the early third century, and blossomed from there. After reviewing an extensive part of the catalog entries for the relevant manuscript tradition I have identified two major and four minor forms of Greek numerological prognostication, as well as numerous hybrids. The distinction between major and minor reflects the frequency with which these techniques appear in the manuscripts. I present below these types of Greek numerology. For each technique, I explain the procedure, discuss the variations, and list the relevant manuscripts, based on my examination of various catalogs, principally but not exclusively the CCAG. After introducing the main types I include two more areas of special relevance to Greek numerology. First, I list texts that explain auspicious days, since these texts have important bearing on the diagrams known as

The Circle of Petosiris. Second, I note other forms of Greek prognostication that depend upon or draw significantly from numerology or number symbolism. This is a preliminary attempt to classify a family of texts that have not been studied adequately. Catalog editors occasionally do not understand the numerological technique at play in a given text, and so allow errors to creep in their entries. None of these texts have been critically edited. The article by Neugebauer and Saliba ("On Greek Numerology") is the most extensive scholarly discussion of Greek numerology, but because the manuscript tradition is far more extensive than the dozen manuscripts they studied, their findings must be considered merely a prelude to further work. This excursus provides the next step. My taxonomy is provisional. Further work on the manuscripts could very well show that a "variant" is really an earlier stage of that particular form of numerology. The same applies to the titles I have given to each type of numerology -I have merely attempted to 344

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replicate the form of the title that appears most frequently in the manuscripts. If there is no author or title listed, as frequently happens in variations, I have supplied one. I am aware of more than thirty other works in manuscript form, whose catalog entries, although vaguely worded, suggest that numerology - often unclassifiable, based on the catalog entry alone -is at play. I have not included them in this excursus. I have also not attempted to discuss evidence from other languages of ancient numerological traditions that depend, in part or whole, on the Greek tradition.4

1 . PYTHAGORAS TO TELA UGES, OR THE LITTLE PYTHAGOREAN PLINTH In the pseudepigraphal letter often attached, Pythagoras promises Telauges that this method allows one to find out, given two combatants, which will defeat the other. The letter plays on the tradition that claims that Pythagoras wrote, or Telauges compiled, a treatise titled On Gods (or Sacred Discourse), a treatise inspired by Orphic number symbolism and number mysticism.5 The names of the author and recipient of this numerological letter occasionally vary .6 Although the method is intended primarily for predicting the outcome of contests, it can be employed for other purposes as well, such as determining the suitability of a marriage, the prospects of a journey, the outcome of a new job, or the chance of catching a

4 On an Armenian form of numerology see Russell, "Six Thousand." 5 Iamblichus, The Pythagorean Way of Life 18.145-47. 6 The recipient is also called Lais (Paris gr. 2009, f. 1 r; London cod. Add. 36753, f. 217v), Augia (Madrid 4631, f. 158), Iliades (Florence LXXXVI, 14, f. 37; Cambridge R.15.36, f. 17v; Bononiensis 3632, f. 274r; Florence LXXXVI, 14, f. 38r). In Oxford cod. Baroccianus 95, f. 307, the letter is said to be from Thrasyllos to Ammon, king of Egypt. But confusing syntax in the MS epigraph may obscure its original attribution to Pythagoras.

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runaway slave. The manuscripts provide ways the method can be suitably applied to d ozens of situations. Oftentimes one or several charts, called plinths, are attached, to help the user know, at a glance, who will vanquish whom. Michael Psellos distinguishes this technique, which he calls "the little Pythagorean plinth" (n) Tiu8a.yoQLKOV bf. nALv8 tbLov), from the technique assigned to Petosiris's letter to Nechepso, on which see below? The Technique First, find the psephic value of each contestant's name. Reduce each number mod 9 (divide by nine until there is a remainder; if there is no remainder, then use the number 9). The residue is then checked against a chart. If one number is odd and the other even, the larger number wins. If both are odd, or both are even, the smaller number wins.8 If both numbers are equal and odd (i.e., 1, 3, 5, 7, and 9), then the challenger wins, because odd numbers are male and therefore aggressive. If both numbers are equal and even, the challenged will win, again for reasons associated with gender. Variations

Mod 7: All rules apply, except reduce the numbers by mod 7, not mod 9. Attested: Hippolytus, Refu tation of All Heresies 4.14.8-10.

Mod 7, vowels only: All rules apply, except only the vowels in a name are used. Reduce psephic sums by mod 7, not mod 9. Attested: Hippolytus, Refu tation of All Heresies 4.14.19. 7 Tannery, Diophantus, 2:41; CCAG 8.1 :131 . s Paris gr. 2426 reports the exact opposite assessment.

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Coun t doubled letters only once: All rules apply, but if a letter appears twice, and only twice, count it only once. Attested: Hippolytus, Refutation of All Heresies 4.14.12. See my discussion at chapter 6.

Separate classes of letters: All rules apply, but first separate the vowels, semivowels, and consonants in each name. The procedure is applied to the psephic values of each of the three classes of letters. The best of three wins. Attested: Hippolytus, Refutation of All Heresies 4.14.19, Paris gr. 2426. In the Paris MS the procedure is likened to the letter Y.9 Its stem represents the innocence of childhood; its branches, the good and evil spirits that accompany a p erson throughout life. Upon this Y is depicted the three classes of letters: vowels on the good branch, semivowels on the morally neutral stem, and consonants on the evil branch.

Value reassignment: All rules apply, but different numerical values are assigned (arbitrarily?) to each letter. Attested: Hippolytus, Refutation of All Heresies 4.14.20.

Rematches: All rules apply, but first determine how many times the contestants have already met in combat. If this is their second match, drop the first letter of each name; if their third, drop the first two letters. Attested: Hippolytus, Refutation ofAll Heresies 4.14.20.

Coun t isodynamic letters once: All rules apply, but if the name has two letters with the same root value (e.g.,

w

[= 800] and fJ [= 8], which have the same root, eight), count only one

of them. Attested: Hippolytus, Refutation of All Heresies 4.14.14. See my discussion above, chapter 6.

9 On medieval and renaissance Pythagorean symbolism of the letter upsilon see, e.g., Harms,

"Pythagoreische Y," and Dornseiff, Alphabet in Mystik und Magie, 24. See also p . 348.

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Survival in marriage: All rules apply, but to the names of husband and wife. Add the psephic value of their two names together. If the result is even, the husband will die first; if odd, the wife. Attested: Madrid BN 4616, fol. 83v. In the same MS see also the scholium by Constantine Lascaris, who suggests a variation can be used to determine the gender of a firstborn child.

Detailed plinth for marital harmony: All rules apply to the two names of the couple, taken separately. But the resultant two numbers reduced mod 9 are used to find the correct entry in a list of forty-five items-the number of unordered pairs that can be formed from two series of elements. Each appropriate entry in the list explains how harmonious the marriage will be. The list does not display any obvious arithmetical pattern that might determine whether a given combination will be harmonious or not. Attested: Madrid BN 461 6, fols. 48v-86r; Athens, 211, fols. 46r-48v.

The elder wins: All rules apply, but if there is a tie, the decision is made with regard to who is older, not who was the challenger. Attested: Florence LXXXVI, 14, fol. 37r.

Simple marital harmony: Take the psephic values of both names of the couple, add, and reduce mod 9. The result is checked against a nine-item list that explains what is to be expected. Attested: Athens, 1265, fol. 61r; Athens, 1275, fol. 49v.

Patient versus the stars: Follow all rules, but let the two names be those of the patient and the name of the star of the day when he fell ill. If the patient wins, he or she will live; if the star, then death will occur. Attested: Athens, 1506, fol. 26r.

Psephic value of days: There exists a chart "of the days of the week" that lists the numbers one through nine spelled out in one column and the psephic value of the name of the number in a second. These charts resemble those that accompany the Circle of Petosiris 348

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(on which see below). It is unclear how these charts were to be used, but it does not seem coincidental that the list presents nine, and not seven, "days of the week," and that Pythagoras to Telauges uses mostly mod-9 operations. Possibly the two are related, but further work on the manuscripts is needed to determine this. Attested: Paris gr. 2419, fol. 33r. Manuscripts In the manuscript tables in this chapter any entry described as containing assorted or

multiple techniques refers to a MS whose entry in the CCAG is so abbreviated it cannot be determined precisely what techniques are discussed. The MS in question may also contain techniques I classify separately. Other listed MSS may have multiple techniques at play, too, but the CCAG, compiled with astrology as its primary focus, does not specify the contents.

CCAG City Rome Oxford Athens Athens Athens Athens Athens Athos Athos Berlin Bonn Cambridge Cambridge Cambridge Erlangen Florence

Codex Angelicus 17 (C.5, 4) Holkhamicus 292 1265 1275 1350 1506

Foliis 327v-328v

voL 5.1

1 92v-194r 61r

9.2 10 10 10 10

23 25 27 32

10

50

7 4

61 41 41

49v 2r 26r-v

46r-48v 211 Esphimenou 267 unstated Panteleemon 787 134r 1 73v-175r 1 73 274r-278r 3632 BibL Univ. Gg. 1 .2 29r-30v 15v CoiL S. Trinit. R.15.36 CoiL S. Trinit. R.15.36 Univ. ms. 93

LXXXVI, 14

9.2 9.2

page 3 73-74

Comments Assorted techniques, the circle of Petosiris, and the plinth. Assorted techniques. Ed. Delatte, Anecdota, 1 :151 Ed. Delatte, Anecdota, 1 :101 Ed. Delatte, Anecdota, 1 :142-44. Ed. Delatte, Anecdota, 1 :133-35 Lampros, KaTailoyo£;, 1:195, no. 2280 Lampros, KaTailoyo£;, 2:433, no. 6294

Multiple techniques.

49-50

1 7v-18v

9.2

50

l lv-12v

7

75 Described in Bandini, Catalogus, 3:338ff. See Desrousseaux, "Sur quelques manuscripts d'Italie."

37

349

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

CCAG Foliis

Florence

Codex LXXXVI, 14

37r-39v

Jerusalem

Patr. libr.

1 v-2v

City

vol. 4

Comments

page 75

Papadopoulos-Kerameus,

'lEpoaoi\Vf.I!TLK� �c�i\ w8r]KT), 4:189, no. 220 London London Madrid Madrid Madrid Madrid

Meteoron

32 14-15

Add. 36753 Harl. 5596 BN 461 6

217v 5v-6r 82v-83v

9.2 9.2 1 1 .2

59

Ed. CCAG 1 1 .2:139-42

BN 4616 BN 4616

83v-84v 84v-86r 158-159v

59-60 60 72-73

Ed. CCAG 1 1 .2:142-44 Ed. CCAG 1 1 .2:145-47

BN 4631

1 1 .2 1 1 .2 1 1 .2

Mon. Barlaam 204

Ed. CCAG 1 1 .2:139-40 n. 1 See Iriarte, Regiae bibliothecae matritensis codices graeci mss, 438-39 See Bees, Manuscrits des Meteores,

1 82v-185v

2:323. Fols. 184v-185v includes a list of personal names and their reduction mod 9. Modena Moscow

85 (III, C, 6) Mus. Hist. Mos.

77r-v 78rv

4 12

31 75

gr. 415 ( Vladim. 509) 287

1 34v-135v

II.C.33 (olim 34)

237r

7 4

Naples Oxford Oxford Oxford

II.C.33 (olim 34) Auct. F.4.14 Auct. T.V.8 Barocc. 95

44r-v 304r-305r 248 307r-308r

4 9.1 9.1 9.1

94 14

Oxford Oxford Oxford Paris

Cromw. 12 Misc. gr. f.2 Misc. gr. f.2 Supp. gr. 464

1 213r-v 72v-75r 76v-77r 8v-10v

9.1 9.1 9.1

50 57-58 58

Paris

gr. 2009

1 r-2v

8.3

=

Munich Naples

Paris Paris Paris

gr. 2256 gr. 2419 gr. 2419

Paris Paris Paris Paris Paris Paris

gr. 2426 gr. 322 Supp. gr. 1 148 Supp. gr. 2244 Supp. gr. 2256 Supp. gr. 2316

Paris Paris Paris

Supp. gr. 2426 Supp. gr. 637 Supp. gr. 696

593v 32r-33r 33r 16 1 4v 1 82r-184v 319v 593v-594r 335r-v 1 6r 58r-v 64r-66r

21 54-55

Ed. Hardt, Catalogus, 3:204-5. For Cumont's a<w>TQc; read m[au]Q[6)c;.

53 75 Example given is that of Zeno, not Hector.

Hippolytus, Refu tation of All Heresies 4.13-15, ed. Marcovich =

11

8.3 8.1 8.1

23 26-27 26

8.3 8.4 8.3 8.3 8.3 8.3

62 95 86 21 23 36 62 76 86-87

8.3 8.3 8.4

Ed. Tannery, "Notice," 248-52; Sti.idele, Briefe des Pythagoras, 357-58 Ed. Tannery, "Notice," 248-52 Ed. Tannery, "Notice," 255-60 Chart of the nine days of the week. Ed. Tannery, "Notice," 248-52.

Multiple techniques

Multiple techniques

Multiple techniques

350

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CCAG City Rome

Codex Palatinus Vat. 312

Foliis 1v-2r

vol. 5.4

72

page

Comments Multiple techniques

Rome Rome

Palatinus Vat. 73 Vat. gr. 952 (olim 740)

2r 1 68v

5.4 5.4

67 10

Only the plinths mentioned.

Rome

Vat. gr. 952 (olim 740)

1 69r

5.4

10

Specimen o f the variant Patient

Rome

Vat. gr. 952 (olim

1 70r-174v

5.4

1 0-1 1

Includes chart of men's names, reduced mod 9. Some entries may be reclassified based on a more secure reading, esp. of fol. 1 74. Multiple techniques

versus the stars?

740)

St. Petersburg St. Petersburg St. Petersburg Turin Vienna

Bibl. Publicae gr. 575

1 1 8r-122v

12

33-34

Bibl. Publicae gr. 576

11

12

55

Bibl. Publicae gr. 576 C, VII, 15 (c, I, 43) phil. gr. 108

26v

12

56-57

39v-39bisv

4

pinax chap. 7

6

5 2

Pasini, 283 Title only

An Arabic form of this technique is discussed by Bouche-Leclercq, Histoire de la Divination, 1 :263.

2. PETOSIRIS TO NECHEPSO The prognostic text of Petosiris, named after the pseudepigraphal letter often prefaced, purports to predict primarily whether a sick person will recover or not.10 Hippolytus, mentioning the use of psephisms to tell whether or not a doctor will heal someone easily, possibly refers to this technique when he mentions "the wisdom of the Egyptians."1 1 If so, 10 The letter is also ascribed to others. In Vat. gr. 432, f. 138v; Vat. gr. 509, f. 31 lv; and Vat. gr. 578, f. 176r-v it is said to be written by a priest Florentinos to Ptolemy. Par. gr. 985, f. 316r assigns it to Pythagoras. 11 Refutation of All Heresies 4.44.3: liMa Ked i.a-rQ6c; < nc;> Of10L0 ¢T]cjx,u CxQQWmovc; 8 t:Qamun· t:i. bE. ivavTLa � lJnlcj>oc;, ov 8t:Qamun (>qblwc;. TOUTOLc; TOLe; CxQL8f10Lc; nQOa!:'XOVTEc;, oaa OflOLa lJ i\oy(i:.;ovnn Ka-ra -r6vbt: -rov vouv, o< i.> flEV Ka-ra cj>wvf]t:v-ra f16va, oi bE. Ka-ra m:Xv-ra -rov CxQL8f16v. TOLaUTll Kat r'] Ai.yurn(wv aocj>(a, bt' Tic; TO 8 t:iov boE_ai:.;ov-rt:c; ytvwGKnv VOfl Ll;ovmv. Marcovich

351

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then this is the earliest securely dated reference (early third century) we have to this technique.

The Technique The method of Petosiris lends itself to predicting the capture of slaves, the outcome of one-on-one matches, and so forth. To begin, find the psephic value of the patient's name, preferably his proper name. Next, find the lunar date on which he or she fell ill. Look up the lunar date on a chart to get a second, larger number (see "The Lunar Chart," below). Now add the psephic value of the patient's name to the appropriate number for the lunar date. Reduce mod 29 (division charts occasionally accompany the text, to simplify the procedure). The remainder is then checked against a chart, often in the shape of a wheel with eight spokes- The Circle of Petosiris (on which, see below). Michael Psellos distinguishes this technique, which he calls "the matters babbled by Petosiris to Nechepso concerning life and death" (Orr6aa b[ T4J TinoaLQEL TIQOC:: NEXE'l\Jw

rrEcj:>AV£XQ11TaL TIEQL (wf]c:; Kat 8avaTou), from the technique ascribed to the Pythagoreans (see above).12

added ntc;> in imitation of the previous sentence, concerning the medical application of plants whose names' have auspicious psephic values. But his emendation suggests an unparalleled practice, the choice of a particular physician based on his name's psephic value (see Marcovich's ed., 129 at line 1 1 ). I think it more likely that the original text was something like Ctl\Aa Kai. iaTQoc; (sc. i\oyta8ivTac;, as in 4.44.3.13) 6!-LOLVW �f]¢cv liQQWaTovc; 8EQann)n, which makes the practice one of prognostication, instead of folk medicine. 1 z Ed. Tannery, Diophantus 2:41; CCAG 8.1:131 .

352

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The Lunar Chart In the procedure, one factors in not the numeral of the lunar date but a psephic value of the lunar date, spelled out. The lunar chart lists the psephic values of all thirty days in the lunar month. There is considerable variation across the MSS. Neugebauer and Saliba have successfully analyzed much of the rhyme and reason behind the way the charts assign various numbers to different lunar dates.13 For instance, Lun 1 = 7TQW'r1J [ sc. iJftEQt:;t] = 1288. ..

Thus, if a person falls ill on the first of the lunar month, the psephic value of his or her name will be added to 1288 (not 1 ) . Neugebauer and Saliba, however, d o not mention additional rules that were used to develop these tables. They have already noted that the psephic value of aE;\:r1VYJ (200 + 5 + 30 + 8 + 50 + 8

=

301) is to be added to the psephic value of the spelled-out numeral to achieve

the number indicated on the charts.14 In addition, KOLAtJ, which has the psephic value of 138, probably underlies the frequent variant where all dates of the lunar month (normally from the 16th to the 30th) are 138 greater than the psephism of the ordinary numeral words. Also, one variation makes the first element in a compound number take on its adverbial form. Thus, 'rQL'rlJ KctL bEKlhlJ (= 1 088) is to be read 'rQLc; KctL bEKthlJ (= 979). This is explained in Madrid BN 4616, fol. 87r, despite serious scribal errors. The method is employed in Neugebauer and Saliba's 1<2, F, and H.15 The authors state that 1<2, representing "the backbone of the whole numerical system," spells out word by word the numbers used

1 3 "On Greek Numerology." 1 4 Ibid., 200, 206 n 3. 1 s Ibid., 201 .

353

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to construct the table, but they do not provide the Greek. An edition of Vat. gr. 852, fol. 1 86 remains a desideratum. The Circle of Petosiris The manuscripts attribute this diagram to Petosiris, although occasionally the Circle is attributed to someone else.l6 In its most elaborate form, the Circle consists of eight radial spokes, evenly distributed across the arc. The diagram is labeled in various parts by the numbers one through twenty-nine or thirty. The sectors of the circle are also labeled. The upper half is assigned to "life"; the lower, to "death." Each half is divided in three parts, and "great," "medium," or "small" are assigned to each part. The location of the number within the circle indicates the subject's fate, and its degree of intensity. The Circle has been simplified in other manuscripts. Sometimes the numbers are listed on two lines. The numbers in the upper row are associated with life, and those associated with death are placed in the lower row. Other diagrams take the form of a cross designed so that the upper quadrants represent life; the lower, death. Neugebauer and Saliba reproduced one figure and four charts, showing the location of each number on the scheme of life versus death. For instance Madrid BN 4616, fol. 87r and Naples, II C33, fol. 310r give the following: 1 3 4 7 9 10 1 1 13 14 1 6 17 2 5 6 8 12 15 18 21 24 25 27

19 29

20 30

22

23

26

28 life death

Observing the variations in the MSS, Neugebauer and Saliba did not attempt to assign priority. They also noted that there is no obvious rhyme or reason to the distribution

16 In PGM 1 2.351-64 it is called the Sphere of Democritus.

354

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of the numbers. Although they suggested there might be astrological motivations, they left the problem open. Hopefully this list of manuscripts will assist in an eventual solution to the problem, which, I suggest, cannot be answered without investigating all variations. This is also why I discuss the auspicious days of the month, below. Variations

Mod 30: Follow all rules, but use mod 30 instead of mod 29. Attested: Madrid 4616, fol. 87r; Vienna, med. VIII, fol. 295v-296r (second method).

Otherfactors: Take the psephic value of the name, add ten, the hour of the moon, and the number of the day. The result, mod 30, is checked on the two-line chart for victory. Attested: Madrid 4616, fol. 87r(a).

Analyze separately lunar date and name: Perform the procedure separately on the lunar date and the name of the subject. If the lunar number is "subterranean" (unoydcp) on the

Circle but the number of the name (reduced mod 29) is "above ground" (ypergio) the subject will be in danger but eventually escape. If vice versa, then despite the appearance of good things, misfortune will occur. If both numbers are above ground all will be well, but if both are subterranean, misfortune is predicted. Attested: Florence Viet. pl. 38 cod. 24, fol. 174v.

Include name of mother: Follow all rules, but also add the psephic value of the subject's mother's name. Attested: Angelicus 1 7, fol. 327r.

Calculate by the week: Follow all rules, but use psephic values attached, not to the spelled-out lunar date, but to the spelling of the name of the day of the week. A chart is attached, listing the psephic values for each day of the week, as well as the name of the god ruling the feria. According to the abbreviated information in catalog entries, certain texts (in this variation and, more broadly, across the numerological tradition) require the user to 355

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know and incorporate the name of the god ruling the day. Attested: Madrid, BN 4616, fol. 75v; Cambridge, Bibl. Univ. Gg. 1 .2, fol. 30; Cambridge, Coli. S. Trin. R.15.36, fol. 23r. Manuscripts CCAG Codex

page

1 350

Foliis 1 08v-109r

vol. 10

30

Athens Athens

1501 1 906

19 1 13v

10

31

Berlin

1 73

81v--82r

7

53

Bonn

Univers. 3632

270r

4

40

Cambridge

CoiL S. Trinit. R.l 5.36

19r

9.2

50

Cambridge

CoiL S. Trinit. R.15.36 CoiL S. Trinit. R.l5.36 CoiL S. Trinit. R.15.36

23r

9.2

50

86r

9.2

53

87r-88r

9.2

53

77r-80r

9.2

47

30

9.2

41

City Athens

Comments Could b e Pythagoras to Te/auges. Polites, LV/17Ii\T)pW}llXTLKoi, 29. Title: 'l'fJ<jJoc; nu8ay6Qnoc; Cwf]c; Kai 8ava'wv. May be a hybrid Table of psephic values of stars and days. Also, assignment of vowels to

planets Ed. Delatte, Anecdota, 1 :573. Technique uses mod 30

Cambridge Cambridge

Florence

CoiL S. Trinit. 0.7.39 Bib!. Univ. Gg. 1 .2 LXXXVI, 14

Florence

Plut. 28 cod. 14

Florence

Plut. 28 cod . 14

Florence

Viet. pl. 38 cod. 24 Plut. 28 cod. 34 Plut. 28 cod. 34

Cambridge Cambridge

Florence Florence

95v-96v

4

pinax chap. 241 pinax chap. 243 1 74v

1

76 25

Title only

1

25

Title only

21 23r-v

1 1

61 61-62

98r-v

6

57

9.2

94

bib!. univ. 2526 F.F.VI, 5

Lei den

Vossianus gr. fol. 279v 59 P.Lugd.Bat. J 384 lines 351-64 (V) 50r Regius 16 C.II BN 4616 75v

London Madrid

Riess, "Nechepsonis et Petosiridis fragmenta magica," 382-83 no. 37

Krakow

Lei den

Cf. "Arch. Pembr. sc. [70] 18. 4to.," which depends on this MS.

Three charts for finding reductions mod 29, mod 30, and mod 36 Gollob, 24

PGM 12.351-64. Called the Sphere of Democritus 9.2 1 1 .2

26 58

Ed. CCAG 1 1 .2:125

356

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CCAG Madrid

Madrid

Foliis

Codex

City

BN 461 6

BN 4616

86v-87r(bis)

89r-90r

vol. 1 1 .2

1 1 .2

page 60-61

Comments Ed. CCAG 1 1 .2:148-49. Riess,

61

"Nechepsonis et Petosiridis fragmenta magica," 386-87 no. 40 Ed. CCAG 1 1 .2:152-53 Iriarte, 338-39; Riess, "Nechepsonis et Petosiridis fragmenta magica," 385-86 no. 39

Madrid

BN 4616

130r-131v

1 1 .2

Madrid

BN 4631 H 2 inf.

159v 246v-249v

1 1 .2

73

3

15

Neugebauer & Saliba, 190 (Text F) Ed. CCAG 1 1 .2:163--64. Biblical example given Iriarte, 438-39 Two methods listed

Modena

H 2 in£. 85 (= III, C, 6) 1 74 (II.F.9)

252rv 78r-v 262r-263v

3 4 4

15 31 34-35

ed. CCAG 4:120-21

Munich

287

136r

7

21

Naples

II.C.33 (olim 34) II.C.33 (olim 34)

1 7r 308r-309v

4

Oxford Oxford Oxford Oxford

II.C.33 (olim 34) Barocdanus 70 Baroccianus 1 1 1 Baroccianus 1 66 Cromw. 1 2 (olim

310nr 379r-380v 21 1 v 1 63v-164r 1214r-1216v

9.1 9.1 9.1 9.1

51 55-56 56 4 15 19 50-51

Oxford

297) Cromw. 1 2 (olim

9.1

46--47

297)

457 (pinax to chap. 128)

Epistle of Petosiris to Nechepso, title only, preserved in the Syntagma of Hephaiston.

supp. gr. 446

43v--44r

8.3

75-76

Example used is that of David and Goliath

Paris

supp. gr. 637

59r-v

8.3

76

Paris Paris Paris Paris Paris

gr. 985 supp. gr. 1 148 gr. 1405 gr. 1405 gr. 1405

316r 77v 65v 67v-68v 81r

8.4 8.3 8.3 8.3 8.3

5-6 83 6 6 6

Paris Paris Paris

gr. 1 991 gr. 1991 gr. 2009

48rv 50r-51r 2r

8.1 8.1 8.3

4 4 11

Paris Paris

gr. 2139 gr. 2139

1 15r-1 18r 90r-92r

8.3 8.3

12 12

Paris Paris

gr. 2184 gr. 2316

211r-v 332r

8.4 8.3

12 34-35

Milan Milan Modena

Naples Naples

Paris

4 4

69-70

Neugebauer & Saliba, 190 (Text H; corrects the CCAG)

ed. Hardt, 206. Neugebauer & Saliba, 190 (Text E). Technique mod 30, plus 10, and chart in form of cross Neugebauer & Saliba, 121 (Text L ) Neugebauer & Saliba, 121 (Text L)

Two examples of the technique preserved.

Attributed to Pythagoras

Tannery, 9:25. Neugebauer & Saliba, 1 90 (Text D)

357

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CCAG City Paris

Codex gr. 2419

Foliis 155v-156r

vol.

page 47--48

8.1

Comments Ed. Berthelot, Introduction, 89-90), Bouche-Leclerq, L 'astrologie grecque, 540, fig. 45 (Neugebauer & Saliba note [ 1 90): "with incorrect emendation" ). See also Riess, "Nechepsonis et Petosiridis fragmenta magica," 387 no. 42,

Paris

gr. 2419

32r

26

8.1

Neugebauer & Saliba, 1 90 (Text B) Ed. Berthelot, Introduction, 87-88),

Bouche-Leclerq, L'astrologie grecque, 539, fig. 44. See also Tannery, 9:42-

Paris

gr. 2419

33r

8.1

26

Paris

gr. 2426

16r

8.3

62

Paris Paris

gr. 2426 gr. 2509

6r 120

8.3 8.4

60 68

Paris Paris Paris Paris Rome

2847 2847

1 69rv 1 70v-172v 1 r-2r 372r-373r 7r-8r

8.4 8.4 8.4 8.4 5.4

72 72 73 73-74 35

5.4

36

gr. 2892 gr. 2992 Barberinianus

5.4

72

Rome

Vat. 1 14 Barberinianus 9r Vat. 1 14 l r, 2r Palatinus Vat. 312 Vat. gr. 285 ( olim 301v

5.4

5-6

Rome

224) Vat. gr. 509 ( olim 31 1v

5.4

7

Rome Rome

338) Vat. gr. 915 Rossianus Vat.

47v 388v-389r

5.4 5.4

8 108

Rome

986 (olim XI 136) Vat. gr. 578 ( olim

1 76rv

5.4

7-8

Rome

610) Vat. gr. 432 (olim

138v

5.4

6-7

Rome

931) Vat. gr. 1379

1 1 1r-112v

5.3

71-72

137v-138r

5.4

8

Rome Rome

Rome

Vat. gr. 952 ( olim 740)

50; Riess, "Nechepsonis et Petosiridis fragmenta magica," 387 no. 41; Neugebauer & Saliba, 1 90 (Text A) Tannery, 9:47 no. 9; N eugebauer & Saliba, 190 (Text G) Tannery, Memoires Scientifiques, 9:4043, photo opp. 29; Neugebauer & Saliba, 190 (Text C ' ) Neugebauer & Saliba, 1 90 (Text C) Epistle of Petosiris to Nechepso, title only, preserved in the Syntagma of Hephaiston.

Said to be by a priest, ¢lAWQ£VTivoc;, to Ptolemy.

Said to be by a priest, G>AwQEVTivoc;, to Ptolemy. Said to be by a priest, G>AwQEVTivoc;, to Ptolemy.

358

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CCAG City Rome Rome

Foliis

Codex

vol.

page

Comments

Vat. gr. 952 ( olim

1 68v-169v

5.4

10

Circle ofPetosiris. Neugebauer &

740) Vat. gr. 952 ( olim 740)

1 75r-176r

5.4

11

Saliba, 121 (Text K1) Epistle from TinwoUQT]c; to king

Bcxvt/Jw. Neugebauer & Saliba, 1 21 (Text K1)

Rome

Vat. gr. 952 (olim

184v-186v

5.4

1 1-12

Neugebauer & Saliba, 121 (Text Kz)

197r

5.4

14

Only chart of psephic value for days of the week and the associated god's name. CCAG cites the psephic value of Kg6vou as .<j>' (sic), a scribal or editorial error for tji'. Title: Tou ainov [= Leo the Wise] tjifJcj:>oc; bwywuonKI'l (
740) Rome

Vat. gr. 1077 (olim 770)

St. Petersburg

Bib!. Acad. Scient. XX Aa-8

65v

12

6

St. Petersburg Uppsala

Bib!. Publ. gr. 576 gr. 5

26r

12

56

1 1 7v (new =

9.2

1 08

120v) 380

2

70

8avcnov

Venice

Venice Vienna Vienna Vienna

Vienna Vienna

Marcianus 335

Marcianus 336 Nessel. 7 cod. med. VIII med. gr. 8 philos. gr. 37

phil. gr. 108 phil. gr. 1 79

259r 294r-296v

2

294r-v 288-90

6 6

pinax chap. 6 122v

72

Epistle of Petosiris to Nechepso, title only, preserved in the Syntagma of Hephaiston. Two methods outlined

56 50

2

6 6

35

Hunger & Kresten, Katalog 50 Epistle of Petosiris to Nechepso, collected in the Syntagma of Hephaiston. Unlike other three specimens, entire text is preserved. Title only Technique mod 30. Hunger, Katalog, 287

Latin versions are found in pseudo-Bede, De divinatione mortis et vitae (PL 90:963-66), and John of Mirfeld, Aldridge's trans., 71 . The Catalan tradition is discussed by Lucas, Astrology

and Numerology, 50-56.

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3. METHOD OF CHALETH (CHAETH/CHAEL) OR METHOD OF LEO THE WISE (BIBLICAL NUMERICAL PROGNOSTICATION) It is well known that many early Christians randomly selected portions of the Bible to help interpret their circumstances or tell the future. The famous example is Augustine, who used this method while he sat in the garden at Milan to contemplate whether or not he should become a ChristianP Less well known is that there were formalized techniques for doing so. The Method of Chaleth combines the finding of a random passage with numerological calculation. The text is sometimes called a revelation to Chaleth (said in some texts to be one of the seventy-two translators of the Septuagint) and sometimes ascribed to Leo the Wise, the ninth century emperor and litterateur. The method is used to determine whether a specified course of action should be pursued or not. The Technique My description of the method follows Delatte's edition of Athens, 210, fols. 20r-26v, the best edition of the text so far. After praying to the Trinity and the Theotokos the inquirer is to take the Gospels or the Psalter and pick a line at random. Take the first four letters of the line as the answer, which is deciphered in the following manner. All letters are classified as single or double, based on their value as alphabetic numerals. Single letters are a, y, �

(.uya) letters are �, b, TJ,

L, K, !J.,

E,,

'

E,

n a,

(., 8, A, v, o, Q, 1:, ¢, l[J and double (literally "yoked" : u, x, w . Note that the letters in th e first series have

numerical values that are odd when reduced mod 10; those in the second series, even values. (The assignment of the episemon to the single letters is strange for three reasons: 1 7 See his defense of this decision at his Letter 55.20.37.

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neither the qoppa nor the sampi are included; the episemon is out of order; and its value of six would suggest it belongs in the second list.) Take the four randomly drawn letters and convert them to a sequence of singles and doubles based on their classification as single or double. Since there are four letters drawn, there are sixteen possible combinations. The inquirer then consults a sixteen-item list and finds the one assigned to his or her combination of singles and doubles. This is the interpretation of the question. Each item in the list is assigned a descriptive name often associated with astrology. For example, a combination of four single letters is called Path (6b6c;), and it implies a beneficial outcome to the matter in question. A combination of four double letters is called People (Aa6c;) and Summation (auvaQL8!-16s), and it implies strife and a detrimental outcome to the matter in question. The list is of the same type as those used in geomancy (on which, see below). There is probably a genetic connection between the two prognostic techniques, but scholarly investigation into the matter has slowed after the work of Tannery and Delatte.18 Manuscripts CCAG City Paris

Codex gr. 2419

Foliis 226v-241v

Athens Berlin Florence

Hist. Soc. 210

20r-25v

75 LXXXVI.14

l r--4v 28v-29v

vol.

page

8.1

49-53

10 7 4

46 33 74

Comments Delatte and Delatte, "Un traite byzantin de geomancie." Ed. Delatte, A necdota, 1 :1 05-10 Attr. to Leo the Wise Attr. to Leo the Wise

J s Tannery, "Rabolion"; Delatte, Anecdota, passim; Delatte and Delatte, "Traite byzantin." Tannery has

a chart detailing the descriptive names of the items in the list. For an assessment of scholarship since then, and prospects for determining the relations between the various forms of geomancy, see van Binsbergen, "Astrological Origin," and Charmasson, "Lectura Geomantiae."

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CCAG Codex

City Jerusalem

Patriarch. Libr.

Comments

page

vol.

Foliis 272r-275v

Papadopoulos-Kerameus,

1Epoaoi\Vf1LTLKT) {3tf3i\w8r)K1J, 1 :455

502

Attr. to Chaleth London

Brit. Mus. cod. Harleianus 5596

1v-3r

9.2

14

Madrid

Scor. II. <:1>.14 II.C.33 (olim 34)

44r-45r 43

1 1 .1

111 53

B aroccianus 111 Baroccianus 1 1 1

205v-21 1 r

N aples Oxford Oxford Paris Paris Paris

4

15 16 4

Attr. to Chaleth

8.3

20 64

Attr. to Charouth To Chael/Chaleth. Ed. Delatte,

8.3 8.4

87 77

Anecdota, 1 :557-61 . Attr. to Chaeth/Chaleth Ed. Drexl, 332, as app. crit. to Delatte, Anecdota, 1 :557-61.

8.4 8.4 8.4 8.4 5.4

78 85

9 9.1

gr. 1043 gr. 2406

216r-219r 73v 81r

8.3 8.4

gr. 2494

58v-60r

Paris Paris

supp. gr. 1 191

33r-34v

supp. gr. 223

Br-Dr

Paris Paris

supp. gr. 338 supp. gr. 696

185v 30v

Paris Paris Rome

supp. gr. 696 supp. gr. 696 Vat. gr. 952 (olim 740)

55v 62v 1 65v-166v

Torino

C.VII.lO (B.VI.12) 4r-v

Ed. Delatte, Anecdota, 1 :388-91

85 86 9

Attributed to Nikolaos Chartophylax, metropolitan of Thessalonike

4

5

4. TECHNIQUE OF HERMES (DECAN PROGNOSTICATION) This tedmique is most similar to Petosiris to Nechepso, but it employs conventions of the Egyptian calendar, and the resultant chart is based on predictable arithmetical patterns. The method is used to determine whether and how a patient will recover from sickness. The manuscripts often attribute the technique to Hermes Trismegistos.

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The Technique Take the day upon which the subject fell ill and count the number of days it comes after 25 Epifi. Add 870.19 Reduce the sum mod 36. The result is checked against a table of outcomes, specifying life or death, or stipulating the kind of recovery. Usually the table consists merely of three lines with all numbers 1 through 36 distributed evenly: 1, 4, 7, . . . ; 2, 5, 8, . . . ; 3, 6, 9, . . .. Variation

Coun t from the vernal equinox: All rules apply, but start counting the number of days from May 18.20 Nothing is specified about reckoning the subject's name, adding 870, or other psephic elements. Apply mod 36 to this sum and consult the 36-element chart. Attested: St. Petersburg, Acad. Mus. Palaeogr., fol. 1 1 7; Paris, gr. 2419, fol. 33r; Athens, cod. 1275, fol. 46.; B erlin, 173, fols. 1 19v-120r. Manuscripts CCAG City Athens Berlin Bonn Cambridge Florence

Foliis

Codex 1275 1 73 Univ. 3632 Bibl. Univ. Gg. 1 .2 Plut. 28, cod. 13

46 1 19v-120r 270

vol. 10 7

30v

4 9.2

239v

1

page 25 55 40

Comments Ed. Delatte, Anecdota, 1 :151 Ed. CCAG 7:191 Ed. Delatte, Anecdota, 1 :572-73

41 20

1 9 Neugebauer and Saliba ("On Greek Numerology," 196) suggest that 870 is a psephism, but do not

attempt to suggest the word or phrase that underlies the sum. 20 This date is signifies either the vernal equinox at the time this text was composed, or the reputed

day of Creation. If the former, then the technique would be date approximately to the sixth or seventh century, when the equinox would be observed three days earlier than its date on the calendar. If the latter, then the text cannot be dated precisely, but its circle of origination might be identified.

363

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CCAG Codex

vol.

page

Florence

Plut. 28, cod. 14

Foliis pinax, chap.

Florence

Plut. 28, cod. 34

240 20r

1

61

Madrid Munich

BN 4616 gr. 287

87v 135v

1 1 .2 6

61 21

Naples

II.C.33 (olim 34) supp. gr. 1148 gr. 1405

3 l l r-312r 92v-93v

4

56 84 6 12

City

Comments

1

25

Title only Ed. CCAG 1 :1 28. The three lines are labeled ( K, and 8 for (wTJ, KLVDUVQS, and eavaToc;

8.3

Paris Paris Paris Paris

gr. 2139 gr. 2327

67v 87v 293

8.3 8.3

Paris Rome

gr. 2419 Barb. Vat. 127

33r 203v

8.1 5.4

26-27

184v

5.4

11

117

12

24

126

12

7

122v

6

35

(olim 340) Vat. gr. 952 ( olim 740) Acad. Mus.

Rome St. Petersburg St. Petersburg Vienna

Palaeogr. Bib!. Acad. Scient. XX Aa-8 phil. gr. 179

Ed. CCAG 1 1 .2:149-50 Hardt, 205

Described in Berthelot, Origenes, 35 Tannery, 259 no. 1 1

57

Hunger, 287

5. APPROVED PSEPHOS CONCERNING THE SICK (MEDICAL PROGNOSIS, USING THE FERIA) The title I have assigned to this brief technique comes from the Greek, Wf]¢oc; TrEQL

tXQQWCJ'rouvrwv b6KLf..toc; (Paris, gr. 1991, fol. 49v). The method allows one to learn the chances of the recovery of a patient, according to the d ay of the week of the start of the illness. If the patient is to die, one can use the same technique to learn the day of the week of the impending death. The Technique Take the psephic value of the subject's name, and reduce mod 3. Find out the day on which the patient fell ill. If on a Sund ay or Wednesday, and if the remainder is 1, he or she

364

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lives; if 2, has a long sickness; and if 3, dies. If the patient fell ill on Monday or Thursday, and if the remainder is 1, he or she dies; if 2, gets healthy; if 3, will be sick for a long time. The other three days are also listed. If the subject is expected to die, then take the psephic value of the patient's name and reduce mod 3. If the remainder is 1, expected death on Tuesday, Friday, or Saturday; if 2, Monday or Thursday; if 3, Sunday or Wednesday. Manuscripts CCAG City Bonn Florence Modena

Codex Univers. 3632 Plut. 28 cod. 34 1 74 (= II.F.9) gr. 1405 gr. 1 991 gr. 231 6 gr. 2847 Barb. Vat. 1 14 Barb. Vat. 127 Palatinus Vat. 73

Paris Paris Paris Paris Rome Rome Rome Rome Vienna

Vat. gr. 952 philos. gr. 1 79

vol.

270v

4

22v 263r

1 4

67r 49v

8.3 8.1

page 40 61 34-35 6 4

333r 1 70r 8v

8.3 8.4 5.4

35 72 36

204r 2 1 86r 122v

5.4

57 66-67 12 35

Foliis

5.4 5.4 6

Comments Ed. Delatte, Anecdota, 1 :573

Chart only Hunger, Katalog, 288

6. ZODIACAL ISOPSEPHY This technique is a preliminary step to an astrological calculation. It is used to discover the house under which the subject was born, presumably for cases where the birthday is unknown. The Technique Instead of determining dates and times of birth, psephic calculations are made on the subject(s) and their kin. To discover a person's planet of birth, find the psephic value of his or her name and his or her parents. Reduce this mod 7. The result is the planet under which 365

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he or she was born. The same technique may apply to find a zodiacal sign for a couple: add the psephic value of the names of the groom and his mother, then do the same for the bride and her father. Reduce both numbers mod 1 2. The results are assigned to a house of the zodiac and its appropriate element (earth, water, air, or fire), then the compatibility of the couple is assessed by consulting the values in a table. Manuscripts CCAG City Athens Athens Athens Athens Berlin Paris

Codex 355 1265 1265 1265 1 73 supp. gr. 1 148

Foliis 92v 28v 49 50v-51r 1 1 9v 92v

vol. 10 10 10 10 7 8.3

page 4 15 21 21 55 84

Comments Ed. CCAG 10:57 E d . Delatte, A necdota, 1 :68 Ed. CCA G 10:98-99 E d . CCAG 10:99-100 Ed. CCAG 7:191

7. HYBRID TECHNIQUES Greek numerology is effusive and diverse. There are many texts that blend or adapt the better-known techniques. What follows are some of the most interesting hybrids. 1 . To learn the outcome of a prospective job, investigate the day i t starts, and add to this number the letters of the inquirer's name by assigning one to alpha, nine to beta, and so on.21 Add the name of the planet for the day, and the name of the city. The sum, reduced mod 12, yields the number of days, weeks, months, or years the job will take. The success of the job is determined by the sum of the names of the boss, of the planet, and of the city. If

21 What numbers were assigned to what letters is not extant, and is assumed to be known to the reader. Compare the variation "Value Reassignment" under "Pythagoras to Telauges," above.

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this sum, reduced mod 9, is even it will be unlucky; if odd, lucky. Attested: Madrid, BN 4616, fol. 86v (CCAG 1 1 .2:60; ed. CCAG 1 1 .2:148). 2. Take 301 (the psephic value of crEi\.ftvll) and add to it the number of feet in your shadow at the time of inquiry. Reduce this sum mod 8. If the result is even, expect misfortune; if odd, fortune. Attested: Madrid, BN 4616, fol. 86v (CCAG 1 1 .2:60; ed. CCAG 1 1 .2:148). 3. Find the psephic value of the patient's name, and reduce this mod 3. The result is checked on a table of seven lines, one for each day of the week, representing the day upon which the patient fell ill. The appropriate entry states whether the patient will live, die, or remain sick for a long time. Compare the three-line table used in the Technique of Hermes, discussed above. Attested: Madrid, BN 4616, fol. 87v (CCAG 1 1 .2:61; ed. CCAG 1 1 .2:150). 4. The psephic value of the patient's name, after reduction mod 3, indicates the day of the week upon which he or she will die. Attested: Madrid, BN 4616, fol. 88r (CCAG 1 1 .2:61; ed. CCAG 1 1 .2:150); Oxford, Baroccianus 1 1 1, fol. 123 (CCAG 9.1:14-15); Leiden, Vossianus gr. Fol. 59, fol. 284r (CCAG 9.2:95). 5. The number of syllables in the names of a married couple are counted and checked against the list of zodiacal signs to determine who will outlive whom. Attested: Athens, 21 1, fol. 48v (CCAG 1 0:50; ed. CCAG 1 0:243). 6. In Paris, gr. 2419, fols. 143v-144r (CCAG 8.1 :45-46; ed. Delatte, Anecdota, 1 :45155) a whole litany of uncommon numerological procedures appear in Book 2, chap. 89 of a miscellany attributed to George Mitiales. The instructions are tersely worded, which suggests that the reader should already know the preliminary steps necessary to determine

367

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the required number before reduction mod x. The individual methods, in their MS order, are as follows: •

Add together the psephic values of the subject's name, the name of the planet ruling the day (to find this consult the table), and the "chapters of things inquired of" (presumably the number of an item in a long list of topics, similar to lists as employed in the Sortes Astrampsych1). Reduce this sum mod 8. The result indicates the subject matter to be inquired of. (The numbers one through eight are assigned to different topics of inquiry.)

•

To find something lost. If reduction mod 2 equals 1, it will not be found; if 2, it will. Reduce mod 7 to learn the kind of place where it will be found. (Numbers 1 through 7 are assigned to various things and places.)

•

To know the sex of an expected child. If reduction mod 2 equals 1, it is a male; if 2, a female.

•

To know if he will take the woman he wants. If reduction mod 2 equals 1, he will not take her; if 2, he will.

•

To know if the woman is bad. If reduction mod 3 equals 1, she is bad; if 2 or 3, she is good.

•

To know if the woman is a virgin. If reduction mod 3 equals 1, then she is not; if 2, she is; if 3, she is not, but because of a slave.

•

To know if she loves you. If reduction mod 4 equals 1, then she does not love you; if 2 or 4, she does; if 3, she is indifferent.

•

To discern recovery of health. If reduction mod 3 equals 1, then death is expected; if 2, then life; if 3, then a long sickness. 368

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•

Concerning soldiery (aTQan:lac;). If reduction mod 2 equals 1, he doesn't go; if 2, he goes.

•

To know if the path is good. If reduction mod 3 equals 1, it is bad; if 2, good; if 3, difficult.

•

Concerning av8EV'tla and life. Reduce mod 7 and check the result against chart. (Included is a seven-item list detailing what is to be expected.)

•

To know about the recovery of a theft. If reduction mod 12 equals 1, 3, 4, 6, 9, 10, or 12 expect discovery; if 2, 5, 7, 8, or 1 1, then do not.

•

To know the whereabouts of a slave or runaway animal. Reduce mod 12. Check against the list. (Included is a twelve-item list detailing locales.)

•

To know what will happen in a regnal year. Reduce mod 7 and check the result against chart. (Included is a seven-item list detailing what is to be expected.)

•

To know the whereabouts of a runaway. Reduce mod 12. Check against the list. (Included is a fragmentary twelve-item list detailing locales.)

•

To know the whereabouts of a hidden thing. Reduce mod 12. Check against the list. (Included is a twelve-item list detailing locales.)

•

Regarding fear. If reduction mod 2 equals 1, have no fear; if 2, have fear.

•

To know about the fate of a traveler. If reduction mod 3 equals 1, the traveler is delayed but will eventually return; if 2, there will be a quick return; if 3, the traveler died.

•

To know if he died. If reduction mod 3 equals 1, yes; if 2, he is sick; if 3, he is not well (KaK6c;).

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•

Concerning war. If reduction mod 4 equals 1, your enemy wins; if 2, you win; if 3, there will be peace; if 4, war.

•

To find out where a thief is from. If reduction mod 3 equals 1, he is a neighbor; if 2, he is of your household; if 3, he is a stranger.

•

Concerning color. If reduction mod 5 equals 1, then black; if 2, white; if 3, red; if 4, yellow; if 5, dappled.

•

To know if runaways will be retrieved. If reduction mod 2 equals 1, he will not be found; if 2, he will.

•

Concerning living together. If reduction mod 2 equals 1, it will be bad; if 2, good.

•

To know if the missing thing is in that place or not. If mod 2 equals 1, then yes; if 2, then it is elsewhere.

•

To know where the lost thing is. Reduce mod 7 and check against the list. (Included is a seven-item list detailing locales.)

7. Add together the following: 3, the lunar day, and the psephic value of the name of the subject who saw the dream. Reduce this sum mod 8. Refer to Psalm 1-8. The number of Psalm matching the remainder holds the key to the interpretation of the dream. Attested: Paris, gr. 251 1, fols. 26v-27r (CCAG 8.4:70; ed. Delatte, Anecdota, 1 :526). 8. Add together the following: the quantity of the lunar day; the day of the month on which the dream was seen; the number of syllables of the name of the subject who saw the dream; the four evangelists and the prophet Daniel (this instruction is not explained further); and the day, whatever it may be. Reduce the sum (by an unspecified denominator) to find the right Psalm, which explains the dream. Attested: Paris, gr. 2315, fol. 239r (CCAG 8.3:28; ed. Delatte, Anecdota, 1 :546-47). 370

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9. Take a couple, and count the number of syllables in each name. Starting from Aries, move that number of houses across the Zodiac. If the number is exhausted by the time you get to Leo, the man will die before the woman. If the number goes to Virgo or beyond, the man will outlive the woman. Attested: Athens, 241, fols. 48v-49r (CCAG 1 0:50; ed. CCAG 1 0:243). 10. Add together the following: the psephic value of the subject's name, the day on which he or she inquires, the seven vowels (this instruction is not explained further), and the number of lunar days. Take the sum and reduce mod 3. If the result is 1, expect good; if 2, neither good nor bad; if 3, bad. Attested: Berlin, 173, fol. 120r (CCAG 7:55; ed. CCAG 7:191); Paris, supp. gr. 1 148, fol. 93r (CCAG 8.3:84).

8. AUSPICIOUS DAYS OF THE MONTH A number of charts list, day-by-day through the lunar month, which days are auspicious for what activities, or stipulate what conditions will determine whether a patient who gets sick on that day will recover or die. These texts seem related to the Hippocratic tradition, which considered different days to be critical for the outcome of a sickness, and The Circle of

Petosiris. It is likely that some numerological or astrological principle helps determine whether a given day is full of life or death (and how much), or how long or troubled the recovery will be. Neugebauer and Saliba attempted to determine this principle based on their study of a handful of manuscripts, but failed to find anything satisfactory, and left the problem open. If the problem is to be solved, then all the relevant texts must be studied. The list below will hopefully assist in this effort.

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The manuscripts cover several distinct texts or text types, both pagan and Christian. One pagan model assigns to each day a Greek god. In Christian usage, this type is converted into a revelation from God to Esdras, and each day of the month is assigned to a biblical figure or event, from Adam up through Samuel. Some lists help determine whether a dream is auspicious or not, depending upon which lunar day it is dreamt. Other lists simply list in two rows the "lit" and "unlit" days of the month, similar to the greatly simplified Circle of

Petosiris, discussed above. Not all texts that purport to be "selenodromia" are also "auspicious days" texts, but many of them are labeled as such.22 It is worth noting that there is a variant of these "auspicious days" lists, one that itemizes the auspicious hours of the days of the week (e.g., Harleianus 6295, fol. 142r [CCAG 9.2:23]), or auspicious hours of the lunar month. I have chosen to include in the table only auspicious days of the month because of their affinity to the texts of Petosiris to Telauges. Further research, however, may show distinct numerological patterns in all these lists. None of these manuscripts have been studied in detail. Rather than attempting to separate the types based on CCAG entries that are sometimes too incomplete for full identification I have incorporated all discemable auspicious-days texts into a single table, without differentiating the various types that are no doubt present. Manuscripts CCAG City Athens Athens

Codex 1 005 1275

Foliis 96r-97r 105r

vol. 10 10

page 7-8 30

Comments Esdras Selenodromion. Ed. Delatte,

Anecdota, 1 :204-5 22

For further discussion, see Cumont, "Presages lunaires," which discusses pagan archetype and Christian revision.

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CCAG City Athens

Athens

1 275

Follis 22r-25v

10

23

1 275

26r

10

23

Biblical characters. Selenodromion of David and Solomon. Ed. CCAG 10:1 22-26 Ed. Delatte, Anecdota, 1 :1 82-83

Codex

vol.

page

Comments

Athens

1 275

44v

10

25

Selenodromion (David and Solomon) Esdras. Ed. CCAG 10:136-37

Athens

46v--47r 47v--48r 48v--49r

10

Athens Athens

1 275 1 275 1 275

10 10

25 25 25

Ed. CCAG 10:137-38 Ed. CCAG 10:138-39 Attributed to BouKOUQ£aT[ou. Ed.

Athens

1 350

79v

10

29

Biblical characters. Ed. CCAG

Athens

1506 1506 462 879 Bib!. Sen. Athen. 84

26v-27r

10

Biblical characters/Esdras

28r 185v 274v 69r

10 10 10

32 32 4

CCAG 10:139 10:1 96-200 Athens Athens Athens Athens Athens Athens Athens Athos

Bib!. Soc. hist. 21 1 Iveron 1 74

57v-58r 38r-39r 49v-56v 25v-28v

Athos

Iveron 174

35r--40r

Athos Athos Berlin

130r-131v Docheiarios 243 Koutloumousios 177 67r-69v llv 1 68

Berlin Berlin Berlin Berlin

1 73 1 73 1 73 1 73 314

150r-152r 177r-1 80v 182r 83r 291v

3632 Coli. S. Trin. R.15.36

333v 122v 257r-262r

Berlin Bonn Cambridge Dresden

Bib!. Soc. hist. 210 Bib!. Soc. hist. 211

Bib!. reg. pub!. Da

Florence Florence Leiden London London London

33 6r-1 0v Univ. Ms. 93 242r-245 Antinori Chartae. 121 r-v LXXXVI, 14 Vossianus gr. fol. 59 280v-282r p.Lond. 121 49v Regius 16 C.II Soc. Medic. Lond. 14 44r--46r

Madrid Madrid Madrid

BN 461 6 BN 4616 BN 461 6

Erlangen

88r-v 91r(bis) 92r-95r

10 10 10 10

7 47

Esdras Esdras

47 50 50

Esdras Ed. CCAG 10:243--47 Selenodromion of David. Lampros, KaTaAoyo<;, 2:46, no. 4294 Selenodromion of David. Lampros,

KaTaAoyo<;, 2:204, no. 4809

7

43

7

59 62 62 53 65

7 7 7 7 4

44

9.2 7

54 70

7

75 74

1 4 9.2

76 94

9.2 9.2 1 1 .2 1 1 .2 1 1 .2

26 33 61 61-62 62

Lampros, Kaux,ioyo<;, 1 :260, no. 2917 Lampros, KaTaAoyo<;, 1 :291, no. 3250 Selenodromion attributed to patriarch Nikephoros Diagnostic device of lunar days Selenodromion/Biblical characters Lit/unlit days Lit/unlit days Selenodromion

Selenodromion Biblical characters Includes lit/unlit days

PGM 7.1 55-67 Esdras Ed. CCAG 1 1 .2:151-52 Ed. CCAG 1 1 .2:154-56 Ed. CCAG 1 1 .2:157-62

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CCAG Codex

City Madrid

Scorialensis I.R.14

Follis 153r-157r

Meteoron

(erat III. 1"1.5; IV.I.l ) Mon. Barlaam 204

1 62r-170r

vol. 10

page 9

Comments Ed. CCAG 1 0:134-44 Melampous. Bees, Manuscrits des

Meteores, 2 :322 Milan Milan Milan

A 45 supp. E16 sup. E 1 6 sup.

20r-21v 39v-46v 47r

3 3 3

E16 sup.

47v

3

Milan

H2 infer. H2 infer.

Naples Naples

II.C.33 (olim 34)

242v-243r 243r-245r 237v

II.C.33 (olim 34)

396r-397v

3 3 4 4

Baroccianus 1 1 1

212r

9.1

Baroccianus 1 1 1 Baroccianus 166 Baroccianus 206 Baroccianus 224

214r-v 164v-165r

9.1 9.1 9.1

Milan Milan

Oxford Oxford Oxford Oxford Oxford Oxford Oxford Oxford Oxford

Baroccianus 27 CoiL Line. gr. 7 Dorvillianus 1 1 0 Dorvillianus 1 1 0

3 12 12 12 15 15 55 58

130r-v 1 321v

9.1 9.1

193r-v 105v 1 06r-v

9.1 9.1 9.1

15 15 19 22 24 3 96 52 52

107r-1 12v 78r-v

52 58 58 1 2-13 10 8-9

Oxford Oxford

Dorvillianus 1 1 0 Misc. gr. f.2 Misc. gr. f.2

Paris Paris Paris

gr. 1612 gr. 1630 gr. 1884

82v-85v 79r 1 1 2r-v 139v-140r

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gr. 1884

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Paris Paris

gr. 2149 gr. 2184

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gr. 2184 gr. 2184

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gr. 22

21 1 r-212r 212v 277r

13 15 1 2-13

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13 3

Paris Paris

gr. 2243 gr. 2243

648v-649r 650v-654r

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17 17

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gr. 2286

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26

Oxford

Biblical characters E d . CCAG 3:32-39 Selenodromion. Ed. CCAG 3:39-40 Ed. CCAG 3:40 Ed. Delatte, Anecdota, 1 :631-32 Selenodromion Ed. CCAG 4:142-45

Biblical characters To Sedrach Melampous (6 i\a flnov�) Text called Curse of Solomon Two methods: lit and unlit days; Melampous Biblical characters

Two lists Two methods attributed to Melampous. Ed. CCAG 8.4:103-4 Descriptive paragraphs for each number of the day. Selenodromion. Ed. CCAG 8 .4:105-7 To Esdras. Two lists Two lists, both to Esdras Days of the week

To Esdras. Partial trans. in Nau, "Analyse de deux opuscules astrologiques," 14-15

To Esdras. Two lists "Aristotle's" interpretation. No Biblical characters. Partial trans. in Nau, "Analyse de deux opuscules astrologiques," 1 6 Variation: days of the week. Still directed to Esdras. Partial trans. in Nau, "Analyse de deux opuscules astrologiques," 15-16

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CCAG City Paris

Codex gr. 2286

Follis 56r-57r

vol. 8.3

Comments

page 23-24

Several charts; Esdras. Ed. Boissanade, "Traite alimentaire du medicin Hierophile," 187

gr. 2294

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17

gr. 2313

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gr. 2315

239r

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28

Paris

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Paris Paris Paris

gr. 2292 gr. 2294

Paris Paris

12 74 17

Esdras

12-13 Selenodromion. Ed. Delatte,

Anecdota, 1 :546--47 Paris Paris

gr. 2316 gr. 2316

Paris

gr. 2316 gr. 2316

329v-331v 331r

8.3 8.3

34 34 35 41

331rv

8.3

gr. 2316 gr. 2316 gr. 2317 gr. 2317

332v 428v 438rv 13r 14r

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Paris Paris

gr. 2381 gr. 2494

77r 63v

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53

Paris

gr. 2511

26r

8.4

70

Paris Paris

supp. gr. 1 148 supp. gr. 1 148

144r-147r 189r-1 95r

8.3 8.3

85 86

Paris Paris

supp. gr. 1 148 supp. gr. 1 191

79v 59v--64v

8.3 8.3

83 88

Paris Paris Rome

supp. gr. 636

134r-136r

8.4

80

supp. gr. 684 (Reginensis) Pii II

35r 256v

8.3 5.4

80 1 06

Rome Rome

Vat. 39 Barb. Vat. 344 Palatinus Vat. 1 99

360r 476v

5.4 5.4

61 69

Rome Rome Rome Rome Rome Rome

Palatinus Vat. 220 Palatinus Vat. 312 Palatinus Vat. 363 Rossianus Vat. 986 Vat. 299 (olim 235) Vat. 342 (olim 902)

8v 207r 379v 389r 129r 280r

5.4 5.4 5.4 5.4 5.4 5.4

Rome Rome

Vat. 573 ( olim 607) Vat. 952 (olim 740)

214r 168v

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69 95 101 1 08-9 6 6 7

Paris Paris Paris Paris Paris

8.3

Several lists

34

42 17 17 64

10

Biblical characters Selenodromion Days of the week Lit/unlit days Lit/unlit days Esdras. Two lists. Partial trans. in Nau, "Analyse de deux opuscules astrologiques," 14-15 Selenodromion. Ed . Delatte, Anecdota, 1 :525-26 Selenodromion/Biblical characters. Partial trans. in Nau, "Analyse de deux opuscules astrologiques," 1 621 Lit/unlit days Partially translated in Nau, 16. Prognostic device of lunar days. Esdras Several methods; two to Esdras

Esdras Esdras Lit/unlit days Biblical characters Biblical characters

Lit/unlit days

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CCAG Foliis

Codex

City

18v-20v

Vat. gr. 1 753

Rome

page 23

vol. 5.4

Comments To Esdras. Numbers rather insignificant in this version. Ed.

CCAG 5.4:155-63 1 1 7v 23 16v

12 12

23 24

2

38

1 1 9r

6

56

Esdras. Hunger and Kresten, Katolog,

57 51

75 Selenodromion Melampous/Esdras. Hunger, Katolog,

Acad. Mus. Palaeog.

1 1 6r

Venice

Acad. Mus. Palaeog. Panepistemiou 87 Marcianus 335

Vienna

med. gr. 27

St. Petersburg St. Petersburg Thessalonike

med. gr. 49 philos. gr. 190

Vienna Vienna

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6

73r-v

6

Polites, Kcm:H oyo<;:, 82--83 Esdras

299

A Latin version is preserved in pseudo-Bede, De minutione sanguinis, sive, De phlebotomia (PL 90:959-62). Sample of Arrangement of Auspicious and Inauspicious Days In the following table a sample of MSS are collated to show at a glance some common variations in the way days are assigned as auspicious or not. Plus signs (+) indicate the day is regarded as auspicious; minus signs (-), inauspicious; plus and minus sign (±), mixed or neutral. Any sign followed by a plus or minus sign in superscript represents a qualified prognosis. For example, ±- represents a day that is mixed, but more negative than positive. The sign 0 represents a value missing from the manuscript. In the upper tier of the table are manuscripts with charts and lists that have simple, binary values (e.g., the simplified Circle of Petosiris, lit versus unlit days). In the lower tier are charts and lists with modified values (e.g., the Circle of Petosiris, which often distinguishes between "great," "medium," and "small" death or life; likewise, the chart by Melampous and its Christian versions specify exactly how dangerous or beneficial a given day is).

1

2

3

4

7

8

9 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Madr. BN4616:87

+

+

+

-

+

-

+

+

+

-

+

+

-

+

+

-

+

+

-

+

+

Madr. BN4616:87

+

-

+

+

+

-

+

+

+

-

+

+

-

+

+

-

+

+

-

+

+

Manuscript

5

6

-

-

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+

-

+

+

-

+

-

-

Manuscript

1

2

3 4

Madr. BN4616:61 (CCAG 1 1 .2:154) + + + Madr. BN 4631:159 Bonn Univ. 3632:270 Munich 287:136

5

+

-

+

-

6

8

9 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

-

+

+

+

-

+

+

-

+

+

-

+

+

-

+

+

-

-

+

+

-

+

+

-

-

+

-

+

+

+

-

+

"'

+

-

-

Naples IIC33:310

+

-

+

+

p.Lond. 121

+

+

+

+

+

+

+

-

-

Madr. BN4616:88

±

±

+

±

� ±

Madr. BN4616:91b

+

±

-

±

±

-

Madr. BN4616:92-95

+

+

-

+

-

+

Tannery, MemSc 9:50

7 +

-

-

+ +

+

-

-

+

-

-

+

-

+

-

-

-

+

-

-

+

-

+

+

+

-

+

+

-

+

+

-

+

+

-

+

+

+

-

+

+

-

+

+

-

+

+

+

-

+

+

+

-

+

+

-

+

-

-

-

+

+

� r -

-

+

±

±

±

+

±

±

+

+

+

±

± � -

-

+

±

+

-

+

±

+

±

+ r

+

+

±

-

+

+

�

±

+

+

+

-

+

+

+

+

+

r � +

+

+

-

-

+

-

+

+

-

+

+

+

-

+

-

-

+

-

+

- � � �

+

+

+

±

±

±

±

- � �

-

±

±

+

±

+

-

+

+

±

-

+

-

+

±

+

9. NUMEROLOGY AS A PART OF OTHER PROGNOSTIC TECHNIQUES Other prognostic techniques regularly employ number symbolism or numerology. To my knowledge, no one has systematically studied the numerological aspects of these techniques. My notes here are intended to suggest avenues of further study.

1.

Astrology is the most famous and most complicated form of Greek

prognostication. Practitioners use the positions of the stars and planets, in conjunction with circumstances about the subject (such as his or her birthday), to determine either the answer to a specific question, or to the subject's future in general.Z3 Number symbolism is incorporated in the arithmetical or geometrical proportions oftentimes used to assess the relationship of the stars and planets. Other numerological aspects can be incorporated into a horoscope, as noted in the technique discussed above, "Zodiacal Isopsephy." 2. Dream interpretation was as complex as astrology, and the number of manuscripts carrying oneirocritica shows that the technique was popular.24 Practitioners occasionally used numerology. Artemidorus (Dream Book 2.70; 3.28, 34; 4.24) advises that 23 On ancient astrology, the most accessible point of entry is Barton, Ancient Astrology.

24 On oneirokritika, see the translation and commentary by White, Interpretation of Dreams; Oberhelman, "Oneirocritic Literature"; and Mavroudi, Dream Interpretation.

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when called for, one can use isopsephy to interpret a dream. His technique, which relies on the reduction or assessment of numbers one hundred or less, is quite complex, and uses numerological procedures different from those discussed in this excursus. A second (non­ Artemidoran) numerological strand in dream interpretation incorporates more conventional numerological techniques, such as the calculation of the number of letters in the name of the day upon which the dream was seen, to help broker the interpretation (Paris, gr. 22, fols. 277v-278r [CCA G 8.3:3]; Paris, gr. 2381, fol. 62r [CCA G 8.3:46]). 3. Geomancy, prognostication using earth, was developed some time in later first millennium. The practitioner would take a handful of earth or stones and toss them. The resulting pattern would be read as a four-element series of odds and evens, and from this would be generated a matrix, from which the practitioner could determine the answer to the question by consulting a sixteen-item list.25 This list is similar to that found in the "Method of Chaleth," discussed above. The technique depends upon the odd-even number symbolism of ancient Pythagoreanism for the coherence of the list. It is also symbolic that this method both depends upon the lowest of the four elements for its medium and also frequently handles figures in sets of four. 4. Lot divination was one of the most widely practiced forms of prognostication in the ancient world. Practitioners would have the inquirer throw dice, or pick a number from one to ten. The resultant numbers would be checked against a list of values, either directly

zs

On geomancy, see above, n. 18.

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or after further operations.26 By virtue of the method, the number symbolism ten and six are invoked. Although numbers are not the focus of the procedure, they are integral to it. 5. There are a number of texts that help predict the future based on natural

phenomena such as thunder, eclipses, and earthquakes. These brontologia, ecliptologia, and

seismologia often invoke the date of the month, or the hour of the day, on which the phenomenon occurs to anticipate what is to happen. Occasionally these lists exhibit the authors' interest in numerical patterns and number symbolism.

26

For recent scholarship on lot divination, see van der Horst, "Sortes"; Stewart, "Oracles of Astrampsychus"; and idem, Sortes Astrampsychi.

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Excursus E The Ori ginal Sequence of Irenaeus, Against Heresies 1 Another Suggestion

In his 1991 article David Tripp argues plausibly and with concise logic that the original sequence of book one of Against Heresies was (a) chapters one through twelve (the Valentinian systems), (b) chapters twenty-three through thirty-one (the succession of heretics, beginning with Simon), (c) chapters thirteen through the first two sections of chapter sixteen (Marcus), and (d, £, g) the rest of the text through chapter twenty-two (the various heretics challenged, en masse, as a conclusion to book one).1 The stimulus for this proposed reorganization is the first section of book two's preface, which recapitulates the contents of book one in seven clauses, lettered by Tripp a-g. The order of this recapitulation, as he observes, seems not to reflect the order of the contents of book one as we have it. The relevant section of book two's preface, which is critical to Tripp's argument, and my own analysis here, reads:

In primo quidem libro, qui ante hunc est, 1 "Original Sequence." Unless otherwise specified, chapter numbers alone in this excursus refer to Against Heresies book one.

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(a) arguentes falsi nominis agnitionem ostendimus tibi, dilectissime, omne ab his qui sunt a Valentino per multos et contrarios modos adinuentum esse falsiloquium; (b) etiam sententias exposuimus eorum qui priores exstiterunt, discrepantes eos sibimetipsis ostendentes, multo autem prius ipsi veritati; (c) et Marci quoque magi sententiam, cum sit ex his, cum operibus eius omni diligentia exposuimus, et quanta ex Scripturis eligentes adaptare conantur fictioni suae diligenter retulimus, et quonam modo per numeros et per xxnn elementa alphabetae veritatem adfirmare conantur et audent, minutatim perexivimus; (d) et quemadmodum conditionem secundum imaginem invisibilis apud eos Pleromatis factam dicunt et quanta de Demiurgo sentiunt ac docent renuntiavimus; (e) et progenitoris ipsorum doctrinam Simonis magi Samaritani et omnium eorum qui successerunt ei manifestavimus, diximus quoque multitudinem eorum qui sunt ab eo Gnostici, et differentias ipsorum et doctrinas et successiones adnotavimus, quaeque ab eis haereses institutae sunt omnes exposuimus; (f) et quoniam omnes a Simone haeretici initia sumentes impia et irreligiosa dogmata induxerunt in hanc vitam ostendimus; (g) et redemptionem ipsorum et quomodo initiant eos qui perficiuntur et adfationes ipsorum et mysteria manifestavimus, et quia unus Deus Conditor et quia non postremitatis fructus et quia neque post eum est aliquid. Tripp argues that chapters twenty-three through thirty-one of book one cannot be identified with (e) for two reasons. First, since (a), (c), and (d) correspond to a continuum of text (l .pr.l-1 .20.3), (b) seems to correspond to no text, and therefore to no stage in the argument. The position of (b) in the preface, however, suggests that it should correspond to a key part of the argument of book one. Second, (b) seems to refer to a group of people who precede Valentinus' s teaching career, which means that the ex his of (c) refers to Simon and his line of succession. This phrase sets Marcus in succession to Simon, not to Valentinus. In a third line of argumentation Tripp points out that (g) implies that book one originally ended with a refutation of their rituals and an affirmation that there is only one God, the Creator, beyond whom there is no other. This, of course, is not the way book one ends. Tripp claims 381

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that his third argument addresses whether chapters twenty-three through thirty-one should be assigned to (b) or (e). I cannot see the connection. But the third argument is important for recovering the original order of book one, especially its conclusion, as we shall see. Tripp tentatively proposes that book one of Against Heresies was written originally in several scrolls. The scrolls were at some time inadvertently shuffled and a middle scroll what became our chapters twenty-three through thirty-one - were mistakenly placed at the end of book one. The mistake was an easy one to make, since no part of the book but the first states explicitly where it belongs in the sequence of Irenaeus' s argument. A later scribe, noticing the preface to book two did not correspond to the new and mistaken order of book one, inserted (e) so that the preface would conform to book one. The theory is stimulating, and the argumentation shows Tripp a keen reader of Irenaeus's text, but I believe most of it should not be accepted.2 First, the argument depends merely on the preface of book two. But a survey of the structure of the entirety of book two shows that it follows roughly the same order as book one, as we have it currently. The bulk of book two refutes the Ptolemaeans, Valentinians, and Marcus (2.1-2.30, corresponding to 1 .1-1.22), and the last chapters treats Simon and Carpocrates (2.31-2.34, corresponding to 1.23 and 1 .25), Basilides (2.35.1, corresponding to 1 .24.3-7), and the "Gnostics" (2.35.2-3, corresponding to 1 .29.1-1 .31 .2). To posit alteration in book one requires the supposition that the exact same alterations occurred to book two, an unlikely scenario, unless Irenaeus intentionally mixed up books one and two to follow the same new order. Second, Tripp's theory cannot account for 1 .31 .3-4, which clearly announces its place in the sequence of 2 I completed this excursus prior to publication of Thomassen's Spiritual Seed, which agrees (12-1 3) in

many respects with my critique.

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book one, since it anticipates book two. By contrast, 1 .22.2, which Tripp would consider the original conclusion, does not announce the closure of one book and the beginning of another. Third, Tripp's interpretation of clauses (a-c) in the preface of book two is not the only one possible. Clause (a) may refer only to chapters one through nine (and not through twelve): multos et contrarios modos may refer to their methods (see f.1E8oboc; and f.1E8obda at

Against Heresies 1 .9.1 ), drawn from, but contradictory to, the sources upon which the methods depen d - nature, mathematics, and Scripture. Thus, room is made for (b) in chapters ten through twelve. This makes sense, since, just as the preface to book two promises that those in (b) precede those in (a), so, according to Irenaeus, Valentinus precedes the Valentinians who taught the system described in chapters one through nine. Irenaeus says as much in Against Heresies 1 .9.5, where he says that he is about to turn from this Valentinian circle to "the very fathers of this myth." Thus, what follows chapter nine is a new section altogether, treating the predecessors to the teachers of the system he has just exposed. Further, (b) makes it clear that (a) does refers not to Valentinus but to those who got their start from him, i.e., the second or even third generation. Then clause (c) states that Marcus comes ex his, that is, from Valentinus and other early teachers of the system, referred to in (b). Therefore, (a) refers to 1.1-1 .9, (b), to 1 . 1 0--1 .12, and (c), to 1 .13.1-1 . 1 6.2, all three sections dealing with the various Valentinian circles.3 Fourth, in 2.14.6 Irenaeus presents Marcus as a recent Valentinian, one who boasted to have achieved a new level of innovation.

3 See ibid., 14 and n. 14, for similar conclusions.

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What of Tripp's observation that (f) and (g) refer to chapters twenty-one and twentytwo? There is one problem with this. Clause (g) has two parts. The first, et redemptionem . . .

manifestavimus, refers to the exposure of the peculiar doctrine of "redemption" (cbroAu'rQWCHc;) discussed at length in chapter twenty-one. The second, et quia unus Deus . . .

aliquid, refers to the proclamation of the rule of faith in chapter twenty-two. That is, (g) refers to both twenty-one and twenty-two. To what exactly, then, does (f) belong? Tripp does not address this question, but I see no reason why (e) and (f) should not be taken together as a single unit describing the same range of text.4 After all, the first half of (e) presents three groups -Simon, his followers, and the "Gnostics" - ordered carefully according the three major sections of 1 .23.1-1 .32.2. The second half of (e) recounts the kinds of material to be found in this discussion: their differences, their doctrines, their chain of succession, and the traditions they have established. Clause (f), which indicates a discussion of the groups' daily implementation of Simon's doctrines, fits nicely in the class of subjects mentioned in the second half of (e). Thus, (a-f) follow perfectly well the order of book one. But only half of the problems motivating Tripp's suggestion have been resolved. He seems almost certainly right to identify (g) with chapters twenty-one and twenty-two of book one. This seems to be the only outstanding inconsistency between the sequences of book two's preface and the contents of book one. It is a significant difference, since whenever Irenaeus recapitulates an argument he has just made, he carefully orders its individual parts.5 Thus, according to Tripp, the content and position of (g) suggest that book one originally ended with chapter twenty-two. 4 This is how Thomassen groups the text as well; see Spiritual Seed, 13. s See 1 .14.9, which summarizes in order the previous 8 sections of chapter 14.

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It seems to me that if book one originally followed the sequence different from the we have today, then it followed that of the preface to book two.6 If this is the case- call it option one - then chapter twenty-two originally concluded book one, whose order was 1 .11.20, 1 .23-1 .31 .2, 1.21-1 .22, and 1.31 .3-1 .31 .4. But if book one as we have it today is its original order- option two - then chapter twenty-two was not the original ending, and clause (g) was mistakenly put at the end of the preface, instead of between (d) and (e). For the first option, I can think of no compelling argument. How did it happen? Was it accidental or intentional? If the latter, to what end? Tripp's original suggestion of misplaced scrolls seems not to apply here. The ostensibly rearranged portions are too small to occupy scrolls of their own. Further, to have 1 .31 .3 follow on the heels of 1 .22.2 creates a very disjointed narrative. The second option seems somewhat more plausible, on the grounds, for instance, that Irenaeus placed (g) last in his recapitulation so as to anticipate the major themes of book two. This is quite possible, but I do not find it compelling either, since the wording and placement of (g) does not serve much dramatic or rhetorical effect. Maybe Irenaeus finished book two's preface, then realized that he forgot to recapitulate the arguments of chapters twenty-one and twenty-two, a minor oversight. This argument for option two is more plausible. It posits that everything in the preface to book two perfectly reflects the contents of book one, except the final clause, which Irenaeus appended because he forgot a major stage in his argument in book one. I accept that this scenario is possible, but I do not find it convincing enough to end discussion on the matter. 6 There is another option, that book one originally followed neither order, but I can find no evidence to consider this anything more than a speculative possibility.

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I offer here a third, tentative option, one that I find more compelling than the other two options. Before explaining the suggestion, however, I must make some observations about book one. First, book one recounts two lines of succession. Irenaeus's primary interest seems to be the Valentinians, a school and movement that includes the Ptolemaeans, Secundus, Marcus, and a number of other writers who have a highly developed theology of aeons. Irenaeus does not place all these schools and teachers in a strict line of succession, but does so when he can, capping the line of development with Marcus, whose system is the most intricate and developed of the various Valentinian groups (see chapter 3). Further, when Irenaeus discusses the Valentinians, he focuses on their disagreements, in part to show how the succession of Valentinus produces rebels who reject their own roots, a tactic Tertullian also uses (Against the Valentinians). The other line of succession in book one centers on Simon, and follows sequentially a well-defined chain: Simon, Menander, Saturninus, Basilides, Carpocrates, Cerinthus, Ebionites, Nicolaitians, Cerdon, Marcion, and Tatian. Then follow others who fall under the rubric "Gnostic," the third group identified in (e), a group that can be seen as the most intricate and developed of the line derived from Simon. Thus, Irenaeus presents two lines of heretics: Valentinian and Simonian. This two-line system is reflected also in the plan of book two, which deals primarily with Valentinians, but then appends, without any attempt at smooth integration, the other groups discussed in the second half of book one, the ones descended from Simon (with the exceptions of Marcion and Basilides, on whom see below). A second observation pertains to transitions. At 1.22.2 Irenaeus nicely segues from his discussion on the Valentinian line of succession to that on the Simonian. But chapter 386

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twenty-three does not look back whatsoever to the preceding material, aside from the enim, the second word of the chapter. Rather than look back, the enim looks forward, as if it marks the beginning of a new treatise. Once Simon is introduced, Irenaeus does not mention Valentinus until 1 .28.1, when Irenaeus compares him in passing to Tatian. The next time Valentinus is discussed, at 1 .30.15, it presumes that the reader is aware that the aforementioned groups, especially the Ophite group discussed in chapter thirty, come from the school of Valentinus: Tales quidem secundum eos sententiae sunt: a quibus . . . multiplex

capitibus fera [de] Valentini scola generata esf.? The reason: the group under discussion identified the serpent with Wisdom, the wayward aeon whose childbearing led to the creation of the Demiurge and the subsequent material creation, according to the Irenaeus' s first Valentinian system, discussed in chapters one through nine. For Irenaeus to mark only this parallel is unusual. There is ample material in chapters twenty-nine and thirty, especially the former, suitable for comparison with Valentinus and Ptolemy. But Irenaeus does not use it, and he reserves any comparison for the end of the section. Indeed, in 1 .29.1, which introduces the Gnostics of chapters twenty-nine and thirty as among the groups derived from Simon, Irenaeus does not suggest that Valentinus was a part of Simon's line of succession. Thus, 1 .30. 1 5 - the last section of chapter thirty -is somewhat forced, as if Irenaeus thought that a simple fiat was enough to integrate this latest material with his exposition of the Valentinian schools, the subject of the first part of the book. The placement of 1 .31 .1-2 is also awkward, as if Irenaeus had arbitrarily decided to insert a discussion of this group (the so-called Cainites) without integrating it into the rest of book one.

7 [de] secluded by the editor. See Rousseau and Doutreleau, 1 .1 (SC 263): 311 .

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The next and last time Valentinus is mentioned in book one (1.31 .3), Irenaeus refers to the entire chain of heresies descended from Simon and explains - almost apologetically that he had to discuss them so as to show how the circles of Valentinus emerged. Irenaeus' s explanation is not very convincing. Despite the passing mention of Valentinus at 1 .28. 1, chapters twenty-two through twenty-eight do little if anything to show how the doctrines of Valentinus emerged. Chapters twenty-nine and thirty show the comparison somewhat better, by virtue of the typological similarities between the aeonology of the Barbelo-Gnostic system and that of the Valentinians, but the connection is not made explicit until 1 .30.15, which concerns itself, not with pleromas, syzygies, or aeons (the expected comparison), but with a more peripheral part of Ophite theology. Irenaeus's conclusion to book one claims an association between the Valentinians and the Simonians, but in his exposition of the Simonians he never argues for this claim, and he never makes the connection explicit. All this corroborates the widely shared view that Irenaeus adapted (if not copied) earlier heresiological material at 1 .22.1-1.30.2 (for convenience, let us call this section On

Simon, since it presents the successors of Simon).8 Aside from what I have already discussed, there are other reasons for isolating this particular section of text from the rest of book one.

On Simon makes no reference to, and has no bearing on, the rest of book one, and vice versa. The preface to book one promises discussions pertaining only to the Valentinian schools; it is completely silent about Simon and his successors. Compare this with the prefaces to books two through five, which state clearly the content of their books. The content of On s For various scholars' attempts to trace On Simon to earlier heresiological texts such as Justin Martyr's Syntagma, see the studies cited at Thomassen, Spiritual Seed, 10 n. 4 and Greer, "Dog and the Mushrooms," 147. For the Syntagma see Justin Martyr, Apology 1 .26.8 and Eusebius, Church History 4.11 .10.

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Simon differs from the rest of book one in important ways. There are no colorful, sarcastic asides, so characteristic of Irenaeus.9 The author of On Simon never directly addresses his reader, as in other parts of book one.10 Further, most of On Simon carefully names names, and puts them in a precise chain of succession, using transitional phrases such as successor and ex his. n In the rest of book one, Irenaeus follows a similar technique, but not with the same emphasis on chronology or succession: the discussion of first Valentinian system precedes the discussion of "Valentinus"; in going from one system to the next in chapters eleven and twelve, Irenaeus does not suggest who comes after whom the way On Simon does.12 Thus, I agree with previous scholars, who suggested that On Simon was taken nearly wholesale from a previous heresiology and inserted into book one. The awkward position of

On Simon may explain Eusebius's comment that Simon's doctrines and customs "are

9 E.g., Against Heresies 1 .8.1 : their interpretation of the Scriptures is like someone changing the mosaic

of a king to that of a dog; 1 . 1 1 .4: a Valentinian tetrad could be made out of a gourd, cucumber, and melon; 1 .14.8: crying babies glorify Marcus; 1 .15.4: the body of Truth must have come into existence after Kadmos. 10 Ibid . 1 .pr.2, 1 .9.1, 1 .12.2, 1 .14.9, and 1 .1 6.3. In these instances he is addressed ayanrp:i or, in the Latin translation, dilectissime. 11 Against Heresies 1 .23.5, 1 .24. 1 . A notable exception is chapters twenty-nine through thirty-one, which I discuss below. 12 Tertullian, Against the Valentinians 33-38, follows the order of Irenaeus's Against Heresies in its explication of the first Valentinian system. But the proponents ofAgainst Heresies 1 .1 1-1 .12, to whom Irenaeus refers as the myth's fathers (see above), Tertullian rearranges. He omits Valentinus (ibid . 1 . 1 1 .1 ) and the "more knowledgeable" Ptolemaeans (ibid. 1 .12.1 ) and discusses the groups from Against Heresies 1 . 1 1 .5, 1.12.3, 1 .1 1 .3, then 1 . 1 1 .2, in that order. Tertullian also treats them as successors to Ptolemy (Against the Valentinians 33.1 ) . Tertullian's order, like Irenaeus's, does not follow any chronological order.

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transmitted in Irenaeus's aforementioned book not superfluously."1 3 The implication of Eusebius's litotes is that it was easy to regard On Simon as a gratuitous addition. Not everything in On Simon is of even quality, and it should not be thought of as a single work. Note, for instance, that (e), from the preface to book two, claims to treat each of three different classes of heretics: Simon, his followers, and the "gnostics." The list in (e), like the rest of the preface, is very specific. It identifies in order the three subgroups discussed in 1 .23.1-4, 1.23.5-1 .28.2, and 1 .29-1 .31 . There is good reason to think that On

Simon originally consisted only of the first two sections (1 .23-28}, and that Irenaeus (or an intermediary) redacted it and added the third section (1 .29-31). The first two sections have characteristics distinctive from the third section. First, there is the language of (e), which makes the topic of the first two sections- Simon and his followers - a complete whole; it is unclear how the "gnostics" fit in, other than that they come "from him" (ab eo), which suggests that they came straight from Simon, with no intermediaries such as Menander or Satuminus. Second, groups and persons are identified by name in chapters twenty-three to twenty-eight. But the groups discussed in chapters twenty-nine through thirty-one are anonymous, or identified merely by alii, a term used frequently in the rest of book one, but not in On Simon. Third, at 1 .31 .2, Irenaeus claims that he himself assembled writings of a particular group (the so-called Cainites); this is the kind of self-referential comment found in the rest of book one, where he refers to himself, to his community, or to materials to which

1 3 Church History 2.13.5.

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he has special access. Nowhere else in On Simon does the author refer to himself. These three factors suggest that Irenaeus is the chief author of the third part of On Simon.14 Determining Irenaeus's source for the rest of On Simon is not the most pressing issue here. Rather, noting the awkward place of On Simon lends some plausibility to the third option I want to suggest, that Irenaeus produced two editions of the first two books of

Against Heresies. In his first draft of book one, Irenaeus dealt exclusively with the schools of Valentinus, the movement that posed the greatest concern to the recipient of the treatise. This original book one consisted of the preface, chapters one through the first section of chapter twenty-two, and concluded with the last section of chapter thirty-two. This original plan is best seen in the preface to book one, where Irenaeus mentions only the Valentinians and the Ptolemaeans, and nothing about Simon and his successors. According to my suggestion book one's preface would have described exactly -no more and no less -the original contents of book one. When lrenaeus started book two, his preface there contained only clauses (a-d) and (g). As he developed his argument, however, he realized that his refutation applied not just to the Valentinians, but to Marcion and his followers. Both groups share a notion of a split in the godhead, and Irenaeus' s argument depends essentially on this split. Irenaeus first

1 4 There is a fourth, weaker argument. Hippolytus, Refutation of All Heresies 6, draws heavily from

book one, except Against Heresies 1 .29-1 .31 . In pseudo-Tertullian' s Against All Heresies, the core of which dates to the early third century (DECL, s.v. Zephyrinus) the heretics of On Simon are discussed well before the Valentinians are. Filastrius, Book of Various Heresies, follows a similar order, despite his effort to revise the chronology to fit into the entire range of Biblical and ecclesiastical history. Hippolytus's omission and the Latin heresiologists' order do nothing to establish the authorship, order, and parts of On Simon, but they corroborate the notion that Irenaeus did not originally write On Simon, except possibly the last two chapters.

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introduces Marcion at 2.1.2, in the middle of his argument against the Valentinians' notion of the divinity and their invocation of the Father as Foresource. The phrase et Marcionis

bonus Deus comes almost as an afterthought, as if Irenaeus only then realized that Marcion' s theology illustrates his point even better. The remainder of book two deals with Marcion in many places, since Irenaeus' s arguments often apply to him just as well as they do to the Valentinians. While writing book two, however, Irenaeus noticed that in book one he had not discussed the origins of Marcion, whose system he was now refuting.15 This prompted him to revise book one, to change it from a expose merely of Valentinianism to a global heresiology, to put all the heretics of book two in some historical perspective, and to explain the appearance of Marcion. He consulted his library and found a brief history of Simon, Marcion, and other heretics - the raw material of our On Simon. He put this new material in the back of book one. He inserted a transitional paragraph (1 .22.2) to segue into On Simon, appended his new research on the "Gnostics," and then appended another paragraph (1 .31 .3) to bring the treatise back to the main subject, the Valentinian schools. The rest of book one went relatively untouched in this revision.16 Irenaeus then felt that he should 1s

This realization must have hit Irenaeus early on in writing book two. At 2.9.2 he mentions Simon and his succession and refers the reader to his discussion in book one. 1 6 An objection to this principle might be based upon 1 . 1 1 .1, where Irenaeus says the Valentinians' doctrine of the left-side Archon, accompanying the Demiurge, resembles "the falsely called gnostics whom I will be describing" ('toic; QT]8T]OOf.dVOLc; u¢' i] p&N tj!cvbwvvpwc; fvwanKoic;). This would suggest that when he wrote chap. 1 1, Irenaeus clearly planned to write chaps. 29-31, since these latter deal with the groups he calls "gnostics." but the objection does not hold, in my opinion, since just lines before this key (and puzzling) phrase in 1 . 1 1 Irenaeus claims that Valentinus got his start "from the so-called gnostic heresy" (imo 'If]c; i\c:yopiv11c; yvwanKf]c; aiQiac:wc;). To first call them so-called, and only a few lines later promise that he will term them so, is inconsistent. The contradictory terminology suggests multiple drafts. In producing the second edition, Irenaeus saw 1 .1 1 as an

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refute some of the heresies newly inserted into book one, so he tacked on an appendix to book two, the material covered in chapters thirty-one to thirty-fiveP This section corresponds loosely to some of the groups discussed in On Simon. Irenaeus then revised the preface to book two. He inserted (e-f) between (a-d) and (g), possibly for several reasons. First, to Irenaeus, (g) was still the natural culmination of the original argument, and so still seemed a natural way to conclude the recapitulation. Second, to insert (e-f) after (g) would require another clause, (h), to summarize and conclude the new book one in the same way (g) did for the old one. But every clause in the preface to book two corresponds to a substantial block of material. To insert a new clause, (h), would require commensurate material, and this does not exist at 1 .32.3-4. Third, inserting (e-f) in its current place reemphasizes the new argument of the revised book one: Valentinus' s chain of succession depends upon Simon's. To insert (e-f) after (g) would obscure that revised plan. This third option for explaining the difference between book one and the preface to book two, should it be correct, illumines an unusual aspect of Against the Heresies, Irenaeus' s uneven treatment of Marcion. In book one, Irenaeus treats Marcion only in passing, and has comparatively little to say about his theology. Marcion's "two-god" theology is summarized tersely at 1 .27.2, and Irenaeus's greatest concern is with Marcion's tampering of the Scriptures and his soteriology. But in book two the emphasis is quite different. He treats Marcion extensively. He also focuses on Marcion's distinction between the Father and the

appropriate place to alert the reader to the new material of the revised edition, but he altered only the second phrase, which might have read originally, mi.:; Myof-lEVOLI:; tjJ w bwV VflWs fvwanKoic;. 1 7 Greer, "Dog and the Mushrooms," 154 calls this section just that, an appendix.

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God who made the world, a doctrinal point only very briefly mentioned in book one. Nothing is made in book two of Marcion's treatment of Scripture. Should this suggestion be correct, two other points follow: 1. Irenaeus, pace Tripp, considered Marcus to be of the school of Valentinus, and he should be treated as such (see chapter 3); 2. The plan and structure of Against Heresies is to be assessed in light of the text's two instantiations: the earlier, pressing concern with Valentinian thought, and the subsequent, broader concern for placing Valentinus in the global genealogical tree of heresy, with Simon at the root.

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Excursus F Italian versus Eastern Valentinianism?

Three and only three ancient sources support the notion that the Valentinian school was geographically divided into an Italian branch and an Eastern one. The first source comes from the title to Clement of Alexandria's notes on the theology of Theodotus, written in the late second century: EK TON E>EOL10TOY KAI THE ANATOAIKHI: KAAOYMENHI: 11111AI:KAAIAI: KATA TOYI: OYAAENTINOY XPONOYI: ETIITOMAI ("Extracts from the Works of Theodotus and the So-Called Oriental Teaching at the Time of Valentinus").1 The second source, written in the early or mid-third century, comes from Hippolytus, who mentions an Italian and an Eastern division when he comes to the end of his discussion of the Valentinian system. The relevant text, in full:

Kai ytyovcv £vrcu8cv iJ l'HbaaKaAla atnwv bLTJQllf.lEVll, Kai KaAEL'rm iJ f.lEV £iva1:ot\LKTJ nc; bLbaaKaAla Ka'r ' a{novc;, iJ b£ 'hat\LWHKTJ. Ol f.lEV OVV am) n)c; 'hat\iac;, WV [anv 'HQaKAtwv Kai. TI'rot\Ef.lal:oc;, tiJuXLK6v ¢am 1:0 awf.la mu l11aou ycyov£vm, Kai bux 'r0l)'[0 E7Tl 'rOU �lX7T'rlGf.llX'rOc; 1:0 7TVEUf.llX

And hence the doctrine of these has become divided: and one doctrine, according to them, is termed Oriental, and the other Italian. They from Italy, of whom is Heracleon and Ptolemaeus, say that the body of Jesus was (an) animal (one). And because of this, (they maintain) that at his

1 Trans. Casey.

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w<; nEQLU'TEQa K£X'TEAftAv8E -'TOV'TECJ'TLV 6 A6yo<; 6 'TTJ<; f.!Y)'TQO<; avw8Ev, 'Tf]s L:ocpl.a<; ­ Kai. y£ywvE 'Tc}J lVvXLKc}J K£XL i:yftyEQKEV al'nov EK VEKQWV. wfn6 i:an, cpYJCYL, n) EiQYJf1€vov· "6 i:ydQas XQLan'>v i:K vEKQwv l:wonOLftan Kai. 'Ta 8vY)'TU CYWf1£X'T£X Uf.!WV," 'TOV'TECJ'TL [Kai.] 'TU \)JVXLKa, ou Kai. 'TU XO.LKa. 6 xou<; yaQ "uno K£X'TtXQav" i:Aft;\v8E· "yf] yaQ," cpYJCYLV, "d K(ai. Ei<; y)f]v anE;\ElJUt;J." oi b' av ano 'TTJs ava'ToAf]s A£yovmv, wv i:anv A,SLovL(Ko)<; Kai. BaQbYJULtXVYJ<;, on nvEvflanKov ijv 'TO awfla 'Tov aw'Tf]Qos· f1VEVf1£X yaQ ayLOV fj;\8Ev i:ni. 'TTJV MaQLaV -'TOV'TEanv i] L:ocpi.a -Kai. "i] bUV£Xf.! Ls 'TOU v\)J(a'TOV" -'TOV'TEG'TLV TJ bY)f.!LOVQY LKTJ 'TEXVYJ -LV£X bLan;\aa8ij 'TO uno 'TOU I1VEVf1£X'TO<; 'TlJ M£XQLq bo8£v.

baptism the Holy Spirit as a dove came down -that is, the Logos of the mother above, (I mean Wisdom) - and became (a voice) to the animal (man), and raised him from the dead. This, he says, is what has been declared: "He who raised Christ from the dead will also quicken your mortal and natural bodies." For loam has come under a curse; "for," says he, "dust thou art, and unto dust shalt thou return." The Orientals, on the other hand, of whom is Axionicus and Bardesianes, assert that the body of the Saviour was spiritual; for there came upon Mary the Holy Spirit- that is, Wisdom and the power of the highest. This is the creative art, (and was vouchsafed) in order that what was given to Mary by the Spirit might be fashioned.2

The third account is an allusion by Tertullian to two schools in Valentinianism: munus enim his datur unum: procurare concinnationem Aeonum et ab eius officii societate duae scholae protinus, duae cathedrae, inauguratio quaedam dividendae doctrinae Valentini ("These two [Christ and the Holy Spirit] have one duty -to stabilize the aeons. From the association of these two in this duty, two schools arise, two pulpits and the beginning (of sorts) of a division in the Valentinian teachings").3 Based on these three accounts scholars conclude that there was a significant division between the eastern and western (specifically Italian) branches of the Valentinian tradition. They accordingly use these three texts and the geographical distinction they legitimate to

2 Hippolytus, Refutation of All Heresies 6.35.5--6.35.7, trans. Macmahon. 3 Trans. Riley.

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classify various Valentinian texts and systems as eastern or western. I argue here that these texts cannot justify these claims. It has been recognized that the first text, the title to Clement's Extracts, is probably a later scribal addition.4 There are important differences that make this clear. The Exctracts purports to draw from Theodotus and from "the Valentinians" or "the followers of Valentinus," without suggesting any geographical parameters. The title is more specific, pointing to an eastern teaching. Whereas the Extracts refers to the Valentinians, that is, the successors to Valentinus, the title refers to contemporaries of Valentinus, not his successors. It is a very real possibility that the scribe simply made up the title, based on knowing that there was an eastern strain of Valentinianism. He need not have had special information to help him accurately identify the Extracts with eastern Valentinianism. As we shall see, Hippolytus knew there was a division, but he knew next to nothing about it. Why should we think any different of this scribe? Leaf through almost any catalogue of Greek manuscripts and you will come across several if not numerous treatises that are assigned blatantly incorrect titles or attributions. But let us suppose the scribe knew what he was talking about. In this case there are new problems to consider. The main one is that the scribe is far more precise than Clement is. The title claims that Clement consulted a body of texts, and that these came from two sources: Theodotus and the so-called Eastern school. This Eastern school was current in the time of Valentinus. It does not claim that this Eastern school was a sect of Valentinianism.

4 See Thomassen, Spiritual Seed, 28 n. 3 and refs. there. 397

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Indeed, it suggests that this eastern teaching was not Valentinian. There are two reasons why I say this. First, the Extracts refers frequently to oL Ouw\EvnvLavo( and oL arro Ovai\Evdvov. Had the title's scribe known the contents of the book, he would have used the same formulas that Clement did, something like 'rWV 8mb6'Wu K£XL n)c; A.vet'rOALKf]c; KaAOVf.lEVT}c; bLbaaKa;\(ac; n�.JV OuaAEvnvL£Xvwv E71L'rOf.1£XL By using Valentinus's personal name and not that of his followers the scribe has corrected Clement, specifying that Clement used source texts that are contemporary with Valentinus. Second, the phrase Ket'ril . . . XQOVovc; identifies only contemporaneity, nothing more. In Clement's corpus, the name of the person whose lifetime marks the era under discussion is embedded inside the prepositional phrase. In the Protrepticus he refers to Nikegoras of Zela, "in the days of Alexander"; in the Stromateis, to Ezra, "in the time of Artaxerxes king of the Persians."5 Both of these examples establish a chronological framework, but they do not imply any other relationship. Clement's use of the phrase is typical for Greek authors. Now, it may be argued that this is simply further evidence that the title was written by a later scribe, who used the phrase loosely. But if that is the case, then we must wonder what other terms in the title are used loosely, and we must still seriously question any special claims we make for this text.6 But for the sake of argument we have presumed here that the scribe knew what he was talking about. If he did, then we have new, more precise information about the content of the Extracts, namely, that it draws upon older texts that were current in

s Protrepticus 4.54.4; Stromateis 1 .22.149 .3. 6 For instance, Thomassen, Spiritual Seed, 28 n. 3, would have the Kai be epexegetical. Can this be so

straightforward if the KaTa . . . XQ6vout; phrase is used so loosely?

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the days of Valentinus and were known as "eastern." The implication is clear. The scribe would have us believe that the Valentinians whom Clement quotes were themselves quoting eastern texts that were current in Valentinus's day. But these texts need not have been Valentinian. In fact, in this scenario we cannot determine at all the relationship between the eastern teaching and Valentinus. For all we know, this eastern teaching had little or no formal connection with Valentinus and his school. Or maybe it was a system from which Valentinus drew to develop his own doctrines. Or maybe it drew inspiration from Valentinus. Whatever the case may be, the so-called eastern teaching does not come

from Valentinus. Not, at least, according to the vocabulary of the title of Clement's Extracts. Whether or not this scribe knew what he was talking about, the text proves to be very difficult for establishing anything more than the existence of an "eastern teaching" associated in some unknown fashion with Valentinus. The author of the title to the Extracts knew that there was something called the eastern teaching, and that it was associated with Valentinus in some way, temporally or otherwise. But we cannot say more than this without presuming too much of the text. As for the second proof text, there is reason to question whether Hippolytus knew anything whatsoever about the divisions in Valentinianism. The names he gives as representatives from each branch are suspect. Heracleon and Ptolemy, Hippolytus's examples of the Italian branch, so prominent in other heresiological literature, were well known in the third century (although we might question how "Italian" they really were). But the two examples Hippolytus gives of the eastern branch suggest he knew little if anything about this group. Axionicus is mentioned in extant literature only in Tertullian' s

Against Valentinus: solus ad hodiernum Antiochiae Axionicus memoriam Valentini integra 399

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custodia regularum eius consolatur ("At Antioch alone to this day Axionicus consoles the memory of Valentinus by a full obedience of his rules")? Tertullian' s point here is that in his era (the first decade of the 200s, or else in the days of his source) Axionicus was sui generis, a teacher unlike the other Valentinians, who have all widely departed from the doctrines of their founder. Tertullian's testimony to Axionicus does not square with Hippolytus's. Tertullian suggests that Axionicus was out on his own; Hippolytus makes him the center of a significant movement. Bardesanes, Hippolytus's other example, is also doubtful, since the only other ancient source that claims Bardesanes had any connection with Valentinianism states that he began there, but then rejected it.8 There is, in fact, little concrete resemblance between Valentinianism and Bardesanes' extant fragments and testimonies? Thus, Hippolytus has listed as the chief examples of the eastern Valentinians an isolated teacher from or at Antioch, and a Syriac writer who had only initial contact (if any at all) with Valentinianism. Throughout his earlier discussion of the Valentinian system Hippolytus mentions their many disagreements. The chief one pertains to monadic versus dyadic schemes (on which see chapter 2). He also mentions differences as to (1) whether Silence is a consort of the Father or not, (2) the source of the decad and duodecad, and (3) whether Silence is 7 Trans. Riley. 8 Eusebius, Church History 4.30. Thomassen, Spiritual Seed, 503, seems to wish retain the name

Ardesanes, in accordance with the single, error-riddled manuscript that contains Hippolytus's text. It seems clear to me, as to Marcovich and all other editors, that Bardesanes is meant: Ardesanes is nowhere in all of Greek literature attested as a personal name (as Thomassen admits), and the manuscript mangles numerous personal names, not to mention ordinary words. 9 Of the many ancient testimonies to Bardesanes, see, e.g., Epiphanius, Panarion 56, where no connection to Valentinianism is made, implicitly or explicitly. Had Epiphanius known of such a connection, he would have publicized it.

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among the thirty aeons.10 Of these, the first and the third are subsets of the monadic/dyadic dichotomy. Clearly, this dispute was important to Hippolytus. But when he distinguishes the Italian and eastern branches, he makes no suggestion that the monadic/dyadic issue was relevant. Rather, the only point of disagreement pertains to whether Jesus's body was spiritual or soulish. According to Hippolytus's terminology, the Italian Valentinians, by claiming that Jesus's body is soulish, were not thereby also claiming that he had no spiritual component. The claim is merely that the substance - the material cause, to use the Aristotelian terminology familiar in the third century - of Jesus's body is soul, and the spirit is the active agent- the efficient cause. The eastern Valentinians, according to Hippolytus, have switched that equation: the material cause is given by the Spirit, and it is molded by the efficient cause, which is the Demiurge, the lord of the soulish realm. Few Valentinian texts and testimonies corroborate Hippolytus' s solitary doctrinal distinction between oriental and Italic Valentinians. Irenaeus and Tertullian, for example, when recounting the Valentinian theory on the generation of Jesus, state that he consisted of four different substances, but they do not suggest that the Valentinians held to a hierarchy among the substances, or that they assigned to one or more substances material or efficient causes.1 1 The distinction, however, does appear in Hippolytus's description of the peculiar Valentinian system he knew, and there the Demiurge is the efficient cause to the spirit's material.J 2 Clement's Excerpts from Theodotus seems to refer to the opposite system, since it states that Jesus's body "was spun for him out of invisible psychic substance."1 3 Clement 10 Hippolytus, Refutation ofAll Heresies 6.30.3-5, 6.31 .3. 1 1 Irenaeus, Against Heresies 1 .7.2; Tertullian, Against the Valentinians 2 .7.2.

12

Hippolytus, Refutation ofAll Heresies 6.35.4. 1 3 Clement of Alexandria, Excerpts from Theodotus 59.4, trans. Casey.

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does not discuss a system that could be classed, based on Hippolytus' s single criterion, as eastern.14 This is further evidence that Hippolytus and Clement do not mean the same thing by ava'roALK� btbaaKaA[a; if they did, then Clement's account of the spiritual origin and constitution of Jesus's body would resemble the one Hippolytus offers for the eastern branch of Valentinianism.15 In light of the problems with the first two texts, the third text, by Tertullian, is hardly any clearer. His assertion that there are two schools is a polemic, a sarcastic use of the syzygies to lampoon the Valentinians. For all we know Tertullian knew of multiple Valentinian schools, yet chose to mention only two for rhetorical force.16 Certainly, in other parts of Adversus Valentinianos Tertullian emphasizes multiple schoolsP Even Thomassen, who would like to use this passage to corroborate the eastern-western Valentinian divide admits that we do not know exactly what this text means.18 The evidence, as I have presented it, shows that Clement and Hippolytus used

eastern to refer to two different groups. We know little or nothing about the group Clement refers to, either its doctrines or its relationship to Valentinus. As for the classification of second-generation Valentinianism into eastern and Italian forms, we depend completely

1 4 Casey, "Two Notes," 296, suggests that Excerpts from Theodotus 23.3 is eastern Valentinian, but this passage merely points out that the savior has two kinds of substances, the left and the right. It does not suggest any kind of causal hierarchy. The combination of soulish and spiritual matter in Jesus recurs at Against Heresies 1 .14.1-2, which Casey, loc. cit., presents as "Italian," once again erroneously, since he fails to take into account the causal roles at work in Hippolytus's distinction. 1 5 For other, similar internal problems with Hipplytus' s testimony, see Thomassen, Spiritual Seed, 43-

45. 16 See ibid., 39. 17 1 .4, 1 .33-38. 1s Spiritual Seed, 39-40.

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upon Hippolytus. The two teachers he or his source assigns to eastern Valentinianism suggest that Hippolytus knew little more about this group than their position concerning the essence of Jesus's body, if that. Hippolytus' s isolated, doubtful witness presents more questions than it answers. In sum, it is clear that two writers in antiquity knew about an eastern school that was associated with Valentinus or Valentinians. The particulars of that association are completely unknown to us because the two writers are either inconsistent or vague. We know nothing about this school's doctrines, and we cannot even say if it was Valentinian.

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Excursus G The Structure of Clement of Alexandria's Excursus on the Decalo gue

Clement's excursus on the Decalogue, Stromateis 6.133-48, demonstrates the principle, discussed earlier in book six, that Christians can use the four mathematical disciplines in a beneficial way.1 In his excursus Clement applies arithmetic to Scripture, and, vice versa, Scripture to arithmetic. The excursus models how an a dvanced Christian might attempt to use his education -especially in arithmetic or geometry - to understand the Bible. The excursus begins by considering the question, What is a decalogue? Clement explains how the Ten Commandments typify other decalogues found in creation, and then turns in the second part of his excursus to expound the individual Commandments (see outline below). One by one, he goes through the various Commandments, spending the most time on the Commandment to keep the Sabbath holy. There Clement pursues a lengthy tangent, to discuss the relationship between the numbers six, seven, and eight (§138.5).2 He interrupts this tangent- which draws from Jewish, Christian, and Hellenistic arithmology - with yet another, an arithmological interpretation of the Transfiguration 1 On the four mathematical disciplines, the quadrivium, see excursus B4.

2 In this excursus, the symbol § refers to Clement of Alexandria, Stromateis book 6.

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(§140.3), arguably the centerpiece of the entire excursus on the Decalogue. To buttress his reading of the Transfiguration, Clement explains it in light of the episemon and the mismatch between the alphabet and the alphabetic numerals, the so-called Milesian system of numeration (see excursus C). From there, Clement returns to the lore surrounding the numbers six, seven, and eight, then finishes the excursus by explaining several of the remaining commandments of the Decalogue. Although Clement appears to meander considerably within the excursus, there is a discemable ring structure at work, evident below. Clement's discussion on the Commandments frame that on the six, seven, and eight, which itself frames the account of the Transfiguration.

133.1 133.1-2 1 33.3 133.4 133.5 1 33.5-134.1 1 34.2 1 34.3 1 35.1-2 135.3--4 136.1-2 136.3 136.4-137.1 137.2 137.3 137.4-138.4 138.5 1 38.6 139.1 1 39.2 139.3 139.4

Introduction to the Decalogue The Decalogue an image of the creation of nature The heavenly decalogue The earthly decalogue The ark a symbol of wisdom The Decalogue as the two covenants and the two warring parts of man The human decalogue How the Decalogue relates to the human decalogue On the ruling principle (iJYEf10VLK6v) Difference between the fleshly spirit and the ruling principle On the care of the fleshly spirit Man an image of God according to the Logos. The Decalogue applies twofold to the human decalogue's two parts Explication of the Decalogue First Commandment (TIQWTfJ . . . ivmt\i]): God is one Second Commandment (bn'nEQOc; . . . t\6yoc;): Don't use God's name for creation Third Commandment (TQLToc; . . . t\6yoc;) : Rest on the Sabbath Excursus on the connection between eight and seven, seven and six On six Cosmogony and meteorology Embryology Pythagorean epithet: "midpoint" Pythagorean epithet: "marriage" Organic motions On seven

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1 40.1 140.2 1 40.3 140.4-141.2 1 4 1 .3 141.4 141 .5 141.6-7 141.7-142.1 142.2-4 143.1 143.2 144.1 144.2 144.3-6 145.1 145.2 145.3 145.4-6 145.7 146.1-2 146.3 147.1 147.2 147.3 147.4-148.3 148.4

Pythagorean epithets: "motherless," "childless" On eight Pythagorean epithets: "cube," "fixed sphere" On the Transfiguration Exegesis of Transfiguration: Christ is the episemon Ogdoad On the episemon and the disjunction between numbers and letters Examples of the episemon in Scripture Sixth day of creation Sixth hour of salvation Geometrical relationship of seven to eight and six to seven Heavens and vowels represent the seven glorifying the ogdoad What is rest? (after Aristobulus) Rank and honor in creation, and its unfolding in time On seven Archangels, planets, Pleiades, the Bear Phases of the moon Strings on the lyre Orifices Ages of life (after Solon) Diagnosis of sickness See also Hermippus David's testimony to seven and eight (Ps 89.7-10) On the process of creation (Gn 2.2) The Decalogue = iota = Jesus [Fifth] Next Commandment (n:iflmoc; iE,fi c; . . . A6yoc;): Honor father & mother Next Commandment (i:'n:nm . . . ;\oyoc;): Against adultery NT prooftext: Gal 5.20, Col 3.5 OT prooftext: Jer 2.27 Next Commandment (;\6yoc; in:aKo;\ov8 Ei): Against murder Next Commandment (Mer a bE: wi:rrov . . . A6yoc;): Against theft Pagans err by misappropriating credit for the function of the universe Tenth Commandment (biKa'roc; . . . A6yoc;): Against covetousness

Inspection of the outline might suggest that the excursus, as we have it, is incomplete, or that Clement was careless. He omits the Second Commandment, and he identifies the Third as the second (§137.3) and the Fourth, as the third (§137.4). Once he finishes his longer exposition of the Fourth/third Commandment, he discusses the next Commandment, the Fifth, as the fifth (§146.1). Thus the numbering seems to get back on track after the Fifth

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Commandment, except that Clement discusses only four more, and he does not refer to the Ninth Commandment. To resolve these inconsistencies is important, because they call into question Clement's commitment to number symbolism. These mismatches cannot be attributed to mere forgetfulness. Philo is just as prone to forgetfully meander as Clement is, if not more, but Philo carefully touches on every Commandment in both of his extant discourses on the Decalogue.3 Clement, a careful reader of Philo, is not likely to have missed or misnumbered four Commandments if he was, like his predecessor, attempting to expound the entire Decalogue. Further, Clement elsewhere quotes the Second and Ninth Commandments, so he was neither unaware of their existence, nor working from a deficient Biblical text.4 A further argument against Clement's forgetfulness that in other parts of his excursus he carefully composes numerically governed lists, as we will see, below. There are two obvious ways to resolve the problems in enumeration. The first would be to identify passages where Clement conflates Commandments. For instance, one could see in §137.3 a reference to both the Second and Third Commandments, and therefore a conflation of the two. But Clement's wording suggests that he was not considering the Second. He mentions nothing of idols or likenesses (LXX Ex 20.4, Dt 5.8: dbwAov . . . 61-lo[wl-la) and nothing of the promise God makes to visit punishment on the third and fourth generations. This is telling. Clement is already focusing on the numerical features of the Bible and the Second Commandment is a prime candidate for an arithmological reading

3 Philo, Quis rerum divinarum heres 35 (167-73), De decalogo.

4 Instructor 3(12).89; Protrepticus 1 08(10).5; Instructor 3(12).89; Stromateis 2.32(7).4; Who is the Rich Man to be Saved? 4.5

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of the numbers three and four. But Clement does not go this way. Instead, Clement's second commandment is a prohibition against taking (or putting) the name of the Lord God "upon a vain thing,"

a

phrase that clearly depends upon only the Third Commandment.5 Thus,

Clement does not refer to the Second Commandment at §137.3. In a similar fashion, to account for Clement's apparent omission of the Ninth Commandment, some have tried to identify it with his treatment of the Eighth, or even that of the Tenth, but there is, in my opinion, nothing explicit in the Greek to suggest this association.6 The expected buzzwords - tjJwbOj.lClQWQi)m:u:;;, ro\lla(ov, j.lClQ'WQ(a, and tjlwb6c; (LXX Ex 20.1 6, Dt 5.20) - their cognates, and their synonyms are nowhere in §§147.3-148.6, where they would be expected to appear, if Clement were indeed conflating texts. A second way to resolve the discrepancy might be to compare the jump from Three to two and Four to three with Clement's proposal (upcoming at §138.5), that the eight is to be identified with seven, and seven, with six. That is, if Clement felt the numbers six, seven, and eight could be transformed one into another, why couldn't the numbers of the Commandments? This does not work for four reasons. First, the introductory formulas of §§137.3 and 4 invoke none of the language involved in the excursus detailing the relationship between six, seven, and eight (§§138.5-145.7). Second, this proposal has Clement omit a Commandment that has the potential to make such a point more explicit. After all, if Clement had intended to explain the shift of the Fourth Commandment to the third, he would not have likely passed by without comment the numerical phrase, "the

5 LXX Ex 20.7, Dt 5.11 : ov AiJ fltJn:l . . . inl. fl1X'HXL4-J; Clement, turning the "vain thing" into the accusative: flTJ bciv Aaflf)avnv flT)b£ bwpEQE LV bd -ra ycvT)-ra K£XL fllXTa.L£X. 6 See the attempts in ANF 2.515nl, 2.522 and SC 446:356n4.

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third and fourth generation," part of the Second Commandment? Such a phrase is ripe for this kind of explanation. Third, unlike the upcoming subexcursus on the Transfiguration and the episemon, where Clement emphasizes the abrupt intrusion of a figure (the episemon) and does not mention a subsequent loss, here the emphasis is the reverse: we have the loss of a Commandment, and nothing "entering in" to effect the shift. As we shall see, the shifting of six to seven and seven to eight depends for its force on the disruption created when Christ became human. No such reflection on the Incarnation is at work in Clement's numbering of the Commandments. Fourth, even if the misnumbering of the Fourth Commandment could be justified by this analogy, the absence of the Ninth Commandment remains unexplained . My suggested solution is simpler, and somewhat more pedestrian. At the opening of the discussion of the Decalogue, Clement proposes to treat his subject "in a cursory manner." (§133.1 : KCX'[(X 7WQCXOQOflrlV). He uses this same phrase twice in the rest of his extant corpus, once to introduce an overview of a few of the earliest Greek philosophers and elsewhere to describe the manner in which David prophesied Christ's divinity in Psalm 23 (24).8 But in the first of these two passages Clement does not present a complete catalog of

pre-Socratic philosophers, and in the second he suggests that David, in some haste, only briefly touched upon this Christological theme. Thus, Ka'H'x TWQCXOQOflrlV, as Clement uses it elsewhere, suggests that not all the Commandments will be discussed, and that the composition will show something of the author's haste. This is why, at the beginning of his discussion of the Decalogue, Clement states that he will bypass, for the time being, a 7 Ex 20.5, Dt 5.9. 8 Clement, Exhortation 5.64; idem, Stromateis 7.10.58.3.

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discussion of why and how the decad is holy (§133.1). Instead, he moves straight into a discussion of the antitypes of the Decalogue. Against my proposal, that the excursus is a cursory treatment of the Decalogue, is this. Clement seems to enumerate carefully each of the Commandments as he goes from one to the next. The specific ordinals he uses are "first," "second," "third," "fifth," and "tenth." Clement seems to proceed systematically through the Commandments. But observe two features in Clement's vocabulary. First, the phrase used to introduce the Fifth Commandment is strange: 0 b£ 71Ef171Toc; £.Si]c; £an Aoyoc; (§146.1). "Next" and "fifth" are redundant. Indeed, "next" is a superfluous clarification of "fifth," and "fifth" has the hallmarks of someone who wanted to clarify what "next" meant. Could a copyist prior to the eleventh century have inserted 71Ef171Toc; to bring the reader back on track? This suggestion, offered by Descourtieux, makes sense, since from this point on, no other Commandment is assigned a number until the last, called the "tenth."9 Second, only the first Commandment is properly called a "commandment" ( £vToAr'J). The others are called "accounts" or "discourses" (A6yoc;). This change in terminology may be important, since Clement uses EVToAi} to refer specifically to the Ten Commandments, whereas A6yoc; is more versatile (cf. §§134.1, 1 36.4). Clement presents the First, calling it a "Commandment." The second he calls a A6yoc;, not an EVToAt1, referring now to the points of his narrative, not to the Commandments (since he intended to cover the Decalogue cursorily, each Commandment's number was not as important). The so-called fifth A6yoc; is really just the "next" point for discussion (adopting the worthwhile

9 See SC 446:352 n. 1.

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suggestion that 71Efl7l'TO� is a later scribal addition). By the time Clement reaches the last Commandment a mild anacolouthon enters into his narrative, and he calls it the tenth t\6yo�, instead of the tenth EV'Tot\fj, since he stopped numbering the points of his discourse long ago, probably forgot about the original plan while writing his two lengthy tangents (§§138.5-145.7), and this was the last Commandment to be discussed. Clement intended to discuss cursorily only several of the Ten Commandments. His interest in the Decalogue got the better of him and he wound up discussing most of the Commandments. My solution draws from two of Clement's tendencies -his meandering and his precise wording - to make sense of his apparent carelessness. As shown in chapter 8, Clement was anything but a careless writer.

41 1

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Abbreviations

ANF

Roberts, Alexander, James Donaldson, and A. Cleveland Coxe, eds. Ante­

Nicene Fathers. 1885-87. Reprint, Peabody, Mass.: Hendrickson, 1 995. BCNH. E

Bibliotheque copte de Nag Hammadi. Section " E tudes"

BCNH.T

Bibliotheque copte de Nag Hammadi. Section "Textes"

BT

Babylonian Talmud

CAG

Commentaria in Aristotelem Graeca

CCAG

Catologus codicum astrologorum graecorum. Brussels, 1 898-1940.

CCL

Corpus Christianorum, series Latina

CCCM

Corpus Christianorum, Continuatio Mediaevalis

CIL

Corpus Inscriptorum Latinorum

CPG

Geerard, Maurice. Clavis Patrum Graecorum. 5 vols. Turnhout: Brepols, 1974-87.

CQ

Classical Quarterly

CSEL

Corpus Scriptorum Ecclesiasticorum Latinorum

DECL

Dopp, Siegmar, and Wilhelm Geerlings; eds. Dictionan; of Early Christian

Literature. Trans. Matthew O'Connell. New York: Crossroad, 2000.

412

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FGrH

Jacoby, Felix. Die Fragmente der griechischen Historiker. Berlin: Weidmann, 1923-58.

FOTC

Fathers of the Church. Washington, D.C.: Catholic University of America Press, 1947-.

IG

Inscriptiones Graecae. Berlin: Georgium Reimerum, 1 903-.

IG P

IG. Vol. 1, Inscriptiones A tticae Euclidis anna (403/2) anteriores. 3rd ed. 1981-98.

IGLS

Inscriptions grecques et latines de la Syrie. Beirut-Paris: P. Geuthner, 1 929-.

IGUR

Moretti, L. Inscriptiones Graecae Urbis Romae. Rome, 1 968-90.

JJP

Journal of Juristic Papyrology

LSJ

Liddell, Henry George, and Robert Scott. A Greek-English Lexicon. Rev. Henry Stuart Jones et al. 9th ed. Oxford: Clarendon Press, 1 996.

LCL

Loeb Classical Library

LThK

Lexikon for Theologie und Kirche. 3rd ed. Freiburg im Breisgau: Herder, 19932001.

LXX

Septuagint

NH

Nag Hammadi

NHS

Nag Hammadi Studies (later called Nag Hammadi and Manichaean Studies)

NP

Cancik, Hubert, and Helmuth Schneider, eds. Der Neue Pauly: Enzyklopiidie der

Antike. 1 9 vols. Stuttgart: J. B . Metzler, 1996-2003. NT

Novum Testamentum: An International Quarterly for New Testament and Related Studies

OCD

Hornblower, Simon, and Antony Spawforth, eds. Oxford Classical Dictionary. 3rd ed. Oxford: Oxford University Press, 1996. 413

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PG

Patrologiae cursus completus, Series graeca. 161 vols. in 166 pts. Paris, 1 85766.

PGM

Priesendanz, K., et al., eds. Papyri Graecae Magicae: Die Griechischen

Zauberpapyri. 2 vols. Stuttgart: Teubner, 1973-74. PL

Patrologiae cursus completus, Series latina. 221 vols. in 222 pts. Paris, 1 84480.

PRE

Pauly's Real-Encyclopi:idie der dessischen Altertumswissenschaft. Stuttgart: J. B. Metzler, 1837-52.

SBL

Society of Biblical Literature

sc

Sources chretiennes

SEG

Supplementum Epigraphicorum Graecorum

SP

Studia Patristica

SVF

von Amim, Hans Friedrich, ed. Stoicorum veterum fragmenta. 4 vols. Stuttgart: Teubner, 1 968.

TLG

Thesaurus Linguae Graecae

TRE

Krause, Gerhard, and Gerhard Muller, eds. Theologische Realenzyklopi:idie. Berlin: De Gruyter, 1977-.

VChr

Vigiliae Christianae

WUNT

Wissenschaftliche Untersuchungen zum Neuen Testament

YT

Jerusalem Talmud

ZDMG

Zeitschrift der Deutschen Morgenli:indischen Gesellschaft

ZPE

Zeitschrift for Papyrologie und Epigraphik

414

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De divinatione F alconer, William Armistead, trans. De senectute. De amicitia. De divinatione. LCL 154. 1 923. Reprint, Cambridge, Mass.: Harvard University Press, 1 938. Clement of Alexandria

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SUihlin, Otto, L. Friichtel, and Ursula Treu, eds. Clemens Alexandrinus. Vols. 2 (3rd ed.) and 3 (2nd ed.). GCS 52(15), 17. Berlin: Akademie-Verlag, 1960-70. Van Den Hoek, Annewies, ed. Stromate IV. Trans. Claude Mondesert. SC 463. Paris: Cerf, 2001. Wilson, W., trans. ANF 2:299-567.

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Filastrius of Brescia

Book of Different Heresies Heylen, F., ed. Filastrii Brixiensis Diversarum hereseon liber. CCSL 9. Turnholt: Brepols, 1957. Pp. 208-324.

First Apocalypse of James (NH 5.3) Schaedel, William R., and Douglas M. Parrott, eds. "The (First) Apocalypse of James." In Nag Hammadi Codices V,2-5 and VI with Papyrus Berolinensis

8502,1 and 4. Ed. Douglas M. Parrott. NHS 1 1 . Leiden: Brill, 1979. Pp. 65-103. Galen

Protreptic to Medicine Wenkebach, E., ed. "Galens Protreptikosfragment." Quellen und Studien zur

Geschichte der Naturwissenschaften und Medizin 4.3 (1935) 90-120. Gellius, Aulus

Attic Nights Serra, F., ed. Noctes Atticae. Pisa: Giardini, 1993-.

Gospel of Philip (NH 2.3) Schenke, Hans-Martin, ed. Das Philippus-Evangelium: (Nag-Hammadi-Codex II,3).

Berlin: Akademie Verlag, 1 997.

The Gospel of Truth (NH 1.3) Attridge, Harold W., and George W. MacRae, eds. "The Gospel of Truth." In

Nag Hammadi Codex I (the Jung Codex). NHS 22-23. Leiden: Brill, 1985. 22:55-122; 23:38-135. 425

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Grammatici Graeci. See Dionysius Thrax Gregory of Nazianzus

Orations [43] Boulenger, Femand, ed. Discours funebres en l 'honneur de son frere Cesaire et de

Basile de Cesaree. Paris: Picard, 1908. Hellanicus

FGrH 4. Heracleon. See also Origen, Commentary on John Fragments Wucherpfennig, Ansgar. Heracleon Philologus: Gnostische Johannesexegese im

zweiten Jahrhundert. WUNT 142. Tiibingen: Mohr Siebeck, 2002. Hermas

The Shepherd of Hermas Whittaker, Molly, ed. Die apostolischen Vater. Vol. 1, Der Hirt des Hermas. GCS 48. 2nd ed. Berlin: Akademie Verlag, 1967. Hermetic fragments Nock, A. D., ed. Corpus Hermeticum. Trans. A. J. Festugiere. 4 vols. 6th ed. Paris: Belles Lettres, 1983. pseudo-Herodian IIEpi apLe11wv

Estienne, Henri, ed. Thesaurus graecae linguae. Paris: A. Firmin Didot, 1 831-65. 8:345 (appendix). Hierodes 426

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On the Golden Poem Kohler, Fridericus Guilelmus, ed. Hieroclis in aureum Pythagoreorum carmen

commentarius. Stuttgart: Teubner, 1974 Hippocrates

On Hebdomads Roscher, W. H., ed. Die hippokratische Schrift von der Siebenzahl. Studien zur Geschichte und Kultur des Altertums 6. 1913. Reprint, Paderbom: Schoningh, 1967. Hippolytus

Refu tation of All Heresies Marcovich, Miroslav, ed. Refutatio omnium haeresium. Patristische Texte und Studien 25. Berlin: De Gruyter, 1 986. Macmahon, J. H., trans. ANF 5:9-153. Wendland, Paul, ed. Refutatio omnium haeresium. GCS 26. 1 91 6. Reprint, New York: Olms, 1977. Homer

Iliad Allen, Thomas W., ed. Homeri Ilias. 3 vols. Oxford: Clarendon Press, 1931.

Odyssey von der Miihll, P., ed. Homeri Odyssea. Basel: Helbing & Lichtenhahn, 1962. Iamblichus. See also Theology of Arithmetic Commentaries on Plato; On the Soul

427

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Dillon, John M., ed., trans., and comm. Iamblichi Chalcidensis in Platonis

Dialogos Commentariorum Fragmenta. Leiden: Brill, 1 973. Common Mathematical Knowledge Festa, Nicolaus, ed. Iamblichi de communi mathematica scientia liber. Corrected by Udalricus Klein. 1891. Reprint, Leipzig: Teubner, 1975.

The Pythagorean Way of Life Deubner, Ludwig, ed. Iamblichi De vita Pythagorica liber. Corrected by Udalricus Klein. 1937. Reprint, Stuttgart: Teubner, 1 975. Dillon, John, and Jackson Hershbell, trans. On the Pythagorean Way of Life:

Text, Translation, and Notes. Texts and Translations 29. Atlanta: Scholars Press, 1991.

De mysteriis des Places, E duard, ed. Les mysteres d'Egypte. Paris: Les Belles Lettres, 1 966. Irenaeus of Lyon

Against Heresies. For parts of book 1, see also Epiphanius, Panarion Rousseau, A., L. Doutreleau, et al., eds. Contre les Heresies. 1 0 vols. SC 263-64 (Book 1), 293-94 (Book 2), 210-1 1 (Book 3), 1 00 (Book 4), 152-53 (Book 5). Paris: Cerf, 1979-2002. [Referred to by book and volume. E.g., Rousseau and Doutreleau ed., 2.2

=

SC 294]

Unger, Dominic J., and John J. Dillon, trans. St. Irenaeus of Lyons Against the

Heresies. Ancient Christian Writers 55. New York: Paulist, 1992. Roberts, Alexander, James Donaldson, and W. H. Rambaut, trans. ANF 1 :315567. 428

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Harvey, W. Wigan, ed. Sancti Irenaei episcapi Lugdunensis libri quinque adversus

haereses. 2 vols. Cambridge: Cambridge University Press, 1 857. Fragments Harvey, W. Wigan, ed. Sancti Irenaei episcopi Lugdunensis libri quinque adversus

haereses. 2 vols. Cambridge: Cambridge University Press, 1 857. 2:47051 1 . Jordan, D. Hermann. "Armenische Irenaeusfragmente." Texte und

Untersuchungen 36.3 (1913). Proof of the Apostolic Preaching Ter Mekerttschian, Karapet, and S. G. Wilson, eds. "The Proof of the Apostolic Preaching with Seven Fragments." Patrologia Orientalis 12 (1919): 655-731 . Isidore of Seville

Etymologies Lindsay, W. M., ed. Isidori Hispalensis episcopi Etymologiarvm sive Originvm

libri xx. 2 vols. Oxford: Clarendon Press, 191 1 . Jerome

Letters Hilberg, Isidore, ed. Sancti Eusebii Hieronymi Epistulae. 2nd ed. CSEL 54-56. Vienna: Verlag der Osterreichischen Akademie der Wissenschaften, 1996.

De viris illustribus

429

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Bernoulli, Carl Albrecht, ed. De viris inlustribus. 1 895. Reprint, Frankfurt, Minerva, 1 968. John Chrysostom

Homilies on John PG 59:23-482. John of Damascus

Philosophical Chapters Kotter, Bonafatius, ed. Die Schriften des Johannes von Damaskos. 5 vols. Patristische Texte und Studien 7. Berlin: De Gruyter, 1969. 1 :47-142. John Lydus

On the Months Wunsch, Ricardus. Liber de mensibus. 1 898. Reprint, Stuttgart: Teubner, 1 967. John of Mirfeld Works Horton-Smith Hartley, Percival, and Harold Richard Aldridge, trans. Johannes

de Mirfeld of St. Bartholemew's, Smithfield: His Life and Works. Cambridge: Cambridge University Press, 1 936. John Philoponos

Commentary on Aristotle's De anima Hayduck, Michael, ed. Joannis Philoponi in Aristotelis de anima libros

commentaria. CAG 15. Berlin: Reimer, 1 897. Julian

To the Untaught Dogs 430

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Rochefort, G., ed. Oeuvres completes. 2 vols. Paris: Les Belles Lettres, 1963. 2.1:144-73. Julius Pollux

Onomasticon Bethe, Erich. Pollucis onomasticon. 2 vols. Lexicographi Graeci 9. 1931 . Reprint, Leipzig: Teubner, 1967. Justin Martyr

Apologies; Dialogue with Trypho Goodspeed, E. J., ed. Die iiltesten Apologeten. Gottingen: Vandenhoeck & Ruprecht, 1915. pseudo-Justin Martyr

Exhortation to the Nations Otto, J. C. T., ed. Corpus apologetarum Christianorum saeculi secundi. 9 vols. 3rd ed. 1879. Reprint, Jena: Mauke, 1879. Vol. 3. Lactantius

Divine Institutes Brandt, Samuel, and George Laubmann, eds. L. Caeli Firmiani Lactanti Opera

omnia. CSEL 19. Vienna: F. Tempsky, 1 890-97. Lamprias. See also Plutarch

Catalogue Sandbach, F. H., trans. Moralia. Vol. 15. LCL 429. C ambridge, Mass.: Harvard University Press, 1969. Pp. 3-29. Leonides of Alexandria 431

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Page, D. L. Further Greek Epigrams. Cambridge: Cambridge University Press, 1981. Pp. 503-41 .

Logica et Quadrivium Heiberg, J. L., ed. Anonymi Logica et quadrivium: cum scholiis antiquis. Copenhagen: Andr. Fred. H0st & S"m, 1929. Lucian

Vitarum auctio Harmon, A. M., trans. Lucian in Eight Volumes. Vol. 2. LCL 54. Cambridge, Mass.: Harvard University Press, 1915. Pp. 450-510.

De lapsu inter salutandum Kilburn, K., trans. Lucian in Eight Volumes. Vol. 6. LCL 430. Cambridge, Mass.: Harvard University Press, 1959: 172-88. "Lysis." See Pythagorean texts Macrobius

Dream of Scipio Regali, Mario, ed. Commento al Somnium Scipionis. 2 vols. Biblioteca di studi antichi 38, 58. Pisa: Giardini, 1983-90. Magical texts Priesendanz, K., et al., eds. Papyri Graecae Magicae: Die Griechischen

Zauberpapyri. 2 vols. Stuttgart: Teubner, 1 973-74. Marcus [Magus]. See Irenaeus, Against Heresies

Marsanes (NH 10.1)

432

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Funk, Wolf-Peter, Paul-Hubert Poirier, and John D. Turner, eds. Marsanes:

NH X, Bibliotheque Copte de Nag Hammadi, Section "Textes" 27. Louvain: Peeters; Quebec: Presses de l'Universite Laval, 2000. Pearson, Birger A., ed. Nag Hammadi Codices IX and X. NHS 15. Leiden: Brill, 1981. Pp. 211-347. Martial

Epigrams Shackleton Bailey, D. R., ed. Epigrams. 3 vols. LCL 94, 95, 480. Cambridge, Mass.: Harvard University Press, 1993. Martianus Capella

On the Marriage of Philologia and Mercury Willis, James, ed. Martianus Capella. Leipzig: Teubner, 1983. Maximos of Tyre

Dialexeis Hobein, H., ed. Maximi Tyrii philosophumena. Leipzig: Teubner, 1910. Melampous. See Dionysius Thrax Moderatus of Gades Fragments Mullach, F. W. A., ed. Fragmenta philosophorum Graecorum. 1 860-81 . Reprint, Aalen: Scientia, 1 968. 2:48-49. Monoi:mus. See Hippolytus, Refutation ofAll Heresies Nag Hammadi. See also individual treatises

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Layton, Bentley, trans. The Gnostic Scriptures. Garden City, N.Y.: Doubleday, 1987. Robinson, James M., ed. The Nag Hammadi Library. Rev. ed. San Francisco: Harper & Row, 1988. Nemesius

On the Nature of Man Morani, Moreno, ed. Nemesii Emeseni De natura hominis. Leipzig: Teubner, 1 987. New Testament Nestle, E., et al., eds. Novum Testamentum graece. 27th rev. ed. Stuttgart: Deutsche Bibelgesellschaft, 2004. Nicomachus of Gerasa. See also Theology ofArithmetic

Introduction to Arithmetic Hoche, Richard, ed. Nicomachi Geraseni Pythagorei introductionis arithmeticae

libri ii. Leipzig: Teubner, 1866. D'Ooge, Martin Luther, trans. Introduction to arithmetic. With studies in Greek arithmetic by Frank Egleston Robbins and Louis Charles Karpinski. New York: Macmillan, 1926. Odo of Morimond

Analytica numerorum et rerum in theographyam Lange, Hanne, ed. Analytica numerorum et rerum in theographyam. Traitt�s du XIIe siecle sur Ia symbolique des nombres. Copenhagen: E. Paludan, 1989. 434

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On Simon. See under Irenaeus, Against Heresies On the Mysteries of the Greek Letters Hebbelynck, A., ed. Les mysteres des lettres grecques. Louvain, 1902.

[On the Numbers] Delatte, E tudes, 171-75. Origen

Commentary on John Blanc, Cecile, ed. Commentaire sur saint Jean. 5 vols. SC 120, 157, 222, 290. 385. Paris: Cerf, 1 966-92. Heine, Ronald E., trans. Commentary on the Gospel according to John. 2 vols. FOTC 80, 89. Washington, D.C.: The Catholic University of America Press, 1989-93.

Against Celsus Borret, Marcel, ed. Contre Celse. 5 vols. SC 132, 136, 147, 150, 227. Paris: Cerf, 1967-76.

Letter to Gregory Thaumaturgus Koetschau, Paul, ed. Des Gregorios Thaumaturgos Dankrede an Origenes. Freiburg: Mohr, 1 894. Pp. 40-44.

Origin of the World (NH 2.5/13.2) Painchaud, Louis, ed. L 'E crit sans titre: traite sur l 'origine du monde (NH II, 5 et

XIII, 2 et Brit. Lib. Or. 4926[1]). With two contributions by Wolf-Peter Funk. BCNH.T 2 1 . Quebec: Presses de l'Universite Laval, 1995. Pachymeres, George 435

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Quadrivium Tannery, P., ed. Quadrivium de Georges Pachymere. Revised by E. Stt�phanou. Vatican City: Biblioteca apostolica vaticana, 1 940. Pappus of Alexandria

Synagoge Hultsch, Fridericus, ed. Pappi Alexandrini collectionis quae supersunt. 3 vols. 1876-78. Reprint, Berlin: Weidmann, 1965. Philo

Allegorical Interpretation (Leg. all.); On Abraham (De Abr.); On Rewards and Punishments (De praem. et poen.); On the Contemplative Life (De vita cont.); On the Creation of the World (De opif. mundi); On the Decalogue (De dec.); On the Preliminary Studies (De congr. erud. gratia); On the Special Laws (De spec. leg.); On the Unchangeableness of God (Quod Deus sit immut.); Who Is the Heir of Divine Things ? (Quis rerum div. heres) Cohn, Leopold, Paul Wendland, et al., eds. Philonis Alexandrini opera quae

supersunt. 7 vols. 1896-1930. Reprint, Berlin: de Gruyter, 1 962-63. [On Arithmetic] Staehle, Karl, ed. Die Zahlenmystik bei Philon von Alexandreia. 1 931 . Reprint, New York: Garland, 1987.

Questions and Answers on Genesis (Quaest. in Gen.) Petit, Fran�oise, ed. Quaestiones in Genesim et in Exodum: Fragmenta Graeca. Les oeuvres de Philon d' Alexandrie 33. Paris: Cerf, 1978.

436

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Mercier, Charles, ed. Quaestiones et solutiones in Genesim: e versione armeniaca. Les oeuvres de Philon d' Alexandrie 34ab. Paris: Cerf, 1979. Philolaus Fragments and testimonies Huffman, Carl A., ed. Philolaus of Croton: Pythagorean and presocratic: A

Commentary on the Fragments and Testimonia with Interpretive Essays. Cambridge: Cambridge University Press, 1993. Photius

Biblioteca Bekker, Immanuel, ed. Photii bibliotheca. Berlin: G. Reimeri, 1824-25. Henry, Rene, ed. Bibliotheque. 9 vols. Paris: Les Belles Lettres, 1 959-91.

Pinax of [Kebes] Prachter, K., ed. "Cebetis tabula quanam aetate conscripta esse videatur." Diss. Marburg, 1885.

Pistis Sophia Schmidt, Carl, ed. Pistis Sophia. Trans. Violet MacDermot. NHS 9. Leiden: Brill, 1978. Plato

Parmenides; Republic; Timaeus Burnet, John. Opera. 5 vols. 1900-1907. Reprint, Oxford: Clarendon Press, 1967-73. Pliny the Elder

Natural History 437

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Rackham, H., et al., trans. Natural History. 1 0 vols. LCL 330, 352, 353, 370, 371, 392, 393, 418, 394, 419. Cambridge, Mass.: Harvard University Press, 1967-75. Plotinus

Enneads Henry, Paul, and Hans-Rudolf Schwyzer. Plotini opera. 3 vols. 1951-73. Reprint, Oxford: Clarendon Press, 1977. Plutarch. See also Lamprias

Genesis of the Soul in the Timaeus; The Obsolescence of Oracles; On the E at Delphi; Roman Questions; Table Talk Babbitt, Frank Cole, et al., ed. and trans. Moralia. Vol. 1 LCL 197. Cambridge, Mass.: Harvard University Press, 1927. Hubert, C., et al., eds. Plutarchi moralia. Leipzig: Teubner, 1925-.

Isis and Osiris Gwyn Griffiths, John, ed. Plutarch 's De Iside et Osiride. Cambridge: University of Wales Press, 1 970. pseudo-Plutarch

On Music Ziegler, K., ed. Plutarchi moralia. Vol. 6.3. 3rd ed. Leipzig: Teubner, 1966. Pp. 1-37. Porphyry

On the Soul

438

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Bidez, J .. ed. Vie de Porphyre, le philosophe neo-platonicien, avec les fragments des

traites Peri agalmtiton et De regressu animae. Leipzig: Teubner, 1913. Life of Pythagoras Nauck, A. Porphyrii philosophi Platonici opuscula selecta. 2nd edn. Leipzig: Teubner, 1886. Reprint, Hildesheim: Olms, 1963. Pp. 17-52. Presocratics (Archytas, Democritus, Philolaus, Solon) Diels, Hermann, and Walther Kranz, eds. Die Fragmente der Vorsokratiker:

Griechisch und deutsch. 6th ed. 1951. Reprint, Zurich: Weidmann, 198587. Produs

Commentary on the First Book of Euclid 's Elements Friedlein, Gottfried, ed. Procli Diadochi in primum Euclidis elementorum librum

commentarii. 1873. Reprint, Hildesheim: G. Olms, 1992. Commentary on Plato's Republic Kroll, Wilhelm, ed. Procli Diadochi in Platonis rem publicam commentarii. 2 vols. 1899-1901. Reprint, Amsterdam: Hakkert, 1 965.

Commentary on the Timaeus Festugiere, A.-J., ed. and trans. Commentaire sur le Timee. Paris: J. Vrin, 196668. Taylor, Thomas, trans. The Commentaries of Proclus on the Timaeus of Plato, in

Five Books: Containing a Treasury of Pythagoric and Platonic Physiology. London, 1820.

Commentary on the Parmenides 439

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Morrow, Glenn R., and John M. Dillon, trans. Proclus ' Commentary on Plato's Parmenides Cambridge: Cambridge University Press, 1987. Psellos, Michael

Interpretation of the Twenty-Four Letters Duffy, J. M., and D. J. O'Meara, eds. Michaelis Pselli philosophica minora. Vol. 1,

Opuscula logica, physica, allegorica, alia. Leipzig: Teubner, 1989-92. Opusculum 36. Tannery, Paul, ed. Diophanti Alexandrini Opera omnia: cum Graecis

commentariis. Leipzig: Teubneri, 1 893-95. 2:41 . Ptolemy [Valentinian]

Letter to Flora Quispel, Gilles, ed . Lettre a Flora. 2nd ed. SC 24 bis. Paris: Cerf, 1966. [Claudius] Ptolemy

Harmonics During, Ingemar, ed. Die Harmonielehre des Klaudios Ptolemaios. Goteborgs Hogskolas Arsskrift 36. Goteborg: Elanders, 1930. pseudo-Pythagoras

Golden Poem Diehl, Ernest, ed. Theognis. Corrected by Douglas Young. 1 971 . Reprint, Stuttgart: Teubner, 1 998. Pp. 86--94. Pythagorean texts (pseudo-Archytas, "Lysis")

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Diels, Hermann, and Walther Kranz, eds. Die Fragmente der Vorsokratiker:

Griechisch und deutsch. 6th ed. 1951. Reprint, Zurich: Weidmann, 198587. Thesleff, Holger, ed. The Pythagorean Texts of the Hellenistic Period. Abo: Abo Akademi, 1965.

Revelation to Marcus. See Irenaeus, Against Heresies Scholia in Dionysius Thrax. See Dionysius Thrax Seneca

Letters Reynolds, L. D., ed. L. Annaei Senecae Ad Lucilium epistulae morales. Oxford: Clarendon Press, 1965. Septuagint Rahlfs, Alfred, ed. Septuaginta: Id est Vetus Testamentum graece iuxta LXX

interpretes. 1935. Reprint, 2 vols. in 1, Stuttgart: Wiirttembergische Bibelanstalt, 1979. Sextus Empiricus

Against the Logicians (= Against the Mathematicians 6-7); Against the Physicians Mau, Jiirgen, and Hermann Mutschmann, eds. Sexti Empirici opera. 4 vols. 1914. 2nd ed. Leipzig: Teubner, 1984. Simon Magus. See Hippolytus, Refu tation of All Heresies Simplicius

Commentary on Aristotle's Physics

441

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Diels, Hermann, ed. Simplicii in Aristotelis physicorum Iibras octo commentaria. 2 vols. CAG 9-10. Berlin: Reimer, 1882-95. Socrates Scholasticus

Ecclesiastical History Hansen, G. C., ed. Histoire ecclesiastique. Translation by Pierre Perichon and Pierre Maraval. Introduction and notes by Pierre Maraval. SC 477, 493. Paris: Cerf, 2004-. Solon. See Presocratics

The Sophia of Jesus Christ (NH 3.4) Barry, Catherine, ed. La Sagesse de Jesus-Christ (BG, 3; NH III,4). BCNH.T 20. Quebec: Presses de l'Universite Laval, 1993. Speusippus of Athens. See also Presocratics Fragments and testimonies Taran, Leonardo, ed. Speusippus ofAthens: A Critical Study with a Collection of

the Related Texts and Commentary. Philosophia Antigua 39. Leiden: Brill, 1981. Stobaeus

Eclogae Hense, Otto, and Curtis Wachsmuth, eds. An thologium. 5 vols. 1 884-1912. Reprint, Berlin: Weidmann, 1958. Syrianus

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Kroll, Wilhelm, ed. Syriani in metaphysica commentaria. CAG 6.1 . Berlin: Reimer, 1902. Tacitus

Annales Heubner, Henricus, ed. Ab excessu divi Augusti. Stuttgart: Teubneri, 1983. Tertullian

Against the Valentinians Fredouille, Jean-Claude, ed. Contre les Valentiniens. SC 280-81. Paris: Cerf, 1980-81 . Riley, Mark Timothy, trans. "Q. S. Fl. Tertulliani Adversus Valentinianos: Text, Translation, and Commentary." PhD dissertation, Standford University, 1971 . Published online http://www.tertullian.org/articles/riley_adv_val/riley_OO_index.htm. Accessed October 2005.

On the Soul Waszink, J. H., ed. De anima: Edited with Introduction and Commen tary. Amsterdam: Meulenhoff, 1947. pseudo-Tertullian

Against All Heresies Kroymann, E., ed. Opera. 2 vols. CCSL 1-2. Tumholt: Brepols, 1 953-54. 2:1399-1410.

The Tetraktys Suspending and Apportioning All Things Four-fold Delatte, E tudes, 187. 443

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Themistius

Analyticorum posteriorum paraphrasis Wallies, Maximilian, ed. Themistii analyticorum posteriorum paraphrasis. CAG 5. 1 . Berlin: Reimer, 1900.

In Aristotelis libros de anima paraphrases Heinze, Richard, ed. Themistii in libros Aristotelis de anima paraphrasis. CAG 5.3. Berlin: Reimer, 1899. Theodore of Asine Testimonies Deuse, Werner, ed. Theodoros von Asine: Sammlung der Testimonien und

Kommentar. Palingenesia 6. Wiesbaden: Franz Steiner Verlag, 1973. pseudo-Theodosios of Alexandria

On Grammar Gottling, Karl Wilhelm, ed . Theodosii Alexandrini grammatica. Leipzig: Libraria Dykiana, 1 822. Theodoret

Compendium of Heretical Fables PG 83:336-556.

Letters Azema, Yvan, ed. Correspondance. 3 vols. SC 40, 98, 1 1 1 . Paris: Cerf, 1955-65.

On Providence PG 83:556-773.

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d e Falco, Victorius, ed. (Iamblichi) theologoumena arithmeticae. Corrected by Udalricus Klein. 1 922. Reprint, Stuttgart: Teubner, 1975. Waterfield, Robin, trans. The Theology of Arithmetic: On the Mystical,

Mathematical and Cosmological Symbolism of the First Ten Numbers. Grand Rapids, Mich.: Phanes, 1989 Theon of Alexandria

Commentary on Ptolemy's Almagest Rome, A., ed. Commentaires de Pappus et de Theon d'Alexandrie sur l 'Almageste. 3 vols. Studi e testi 54, 72, 1 06. Rome: Biblioteca apostolica vaticana, 1931-43. Vols. 2 and 3. Theon of Smyrna

Mathematics Useful for Reading Plato Hiller, Eduard, ed . Theonis Smyrnaei philosophi Platonici expositio rerum

mathematicarum ad legendum Platonem utilium. Leipzig: Teubner, 1878. Theophilus of Antioch

To Autolycus Grant, Robert M., ed. Ad Autolycum. Oxford: Clarendon Press, 1 970.

The Tripartite Tractate (NH 1 .5) Attridge, Harold W., and Elaine Pagels, eds. "The Tripartite Tractate." In Nag

Hammadi Codex I (the ]ung Codex). NHS 22-23. Leiden: Brill, 1985. 22:159-337, 23:217-497. Thomassen, Einar, ed. Le traite tripartite (NH I, 5). BCNH.T 19. Quebec: Presses de l'Universite Laval, 1989. 445

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Tzetzes, John

Chiliades Kiesslingius, Theophilus, ed. Historiarum variarum Chiliades. Leipzig, 1 826.

A Valentinian Exposition (NH 1 1 .2) The Facsimile Edition of the Nag Hammadi Codices. Vol. 10, Codices XI, XII, and XIII. Leiden: Brill, 1973. Turner, John D., ed. "NHC Xl,2: A Valentinian Exposition 22, 1-39,39." In Nag

Hammadi Codices XI, XII, XIII. Ed. Charles W. Hedrick. NHS 28. Leiden: Brill, 1990. Pp. 89-1 72. pseudo-Valentinus (Irenaeus, Against Heresies 1 . 1 1 . 1 ). See Irenaeus Varro

Nine Books of Disciplines Ritschl, Friedrich. Opuscula philologica. 5 vols. 1866-79. Reprint, Hildesheim ; New York : Olms, 1978. V ettius Valens

Anthologies Bara, Joelle-Frederique, ed. Anthologies, Livre I. E tudes preliminaries aux religions orientales dans !'Empire romain III. Leiden: Brill, 1989. Vitruvius

De architectura Granger, Frank, trans. On Architecture. 2 vols. LCL 251, 280. Cambridge, Mass.: Harvard University Press, 1931-34. Xenocrates 446

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Fragments and testimonies Isnardi Parente, Margherita, ed. Frammenti. Naples: Bibliopolis, 1 982. Xenophon

Memorabilia Marchant, E. C., ed. Memorabilia and Oeconomicus. LCL 168. Cambridge, Mass.: Harvard University Press, 1968. Zeno Fragments

SVF 1 .

STUDIES ORDERED BY MODERN AUTHOR Apatow, Robert. "The Tetraktys: The Cosmic Paradigm of the Ancient Pythagoreans."

Parabola 24.3 (1999): 38-43. Armstrong, Arthur Hilary. "Dualism." In Wallis, Neoplatonism and Gnosticism. Pp. 33-54. Attridge, Harold W., and George W. MacRae, eds. "The Gospel of Truth." In Nag Hammadi

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