Plutarch's "De E Apud Delphos": Translation and Commentary

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2018-11-19 Plutarch's "De E apud Delphos": Translation and Commentary

Alexander, Judith Anne

Alexander, J. A. (2018). Plutarch's "De E apud Delphos": Translation and Commentary (Unpublished master's thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/34516 http://hdl.handle.net/1880/109187 master thesis

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UNIVERSITY OF CALGARY

Plutarch’s De E apud Delphos: Translation and Commentary

Judith Anne Alexander

A THESIS

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE

DEGREE OF MASTER OF ARTS

GRADUATE PROGRAM IN GREEK AND ROMAN STUDIES

CALGARY, ALBERTA

NOVEMBER 2018

ABSTRACT

Plutarch’s Parallel Lives are well known; less so the essays and dialogues grouped into his omnibus Moralia. One of these essays, De E apud Delphos (“De E”), contains a discussion of the meaning of a votive object, in the form of the letter E, first offered by the seven Sages to the Delphian god.

This translation, with its commentary, pays attention to technical matters discussed in the dialogue (number theory, the altar at Delos, the pentad, syllogistic logic, Being and

Becoming) that have sometimes been neglected in other translations. It also comments on themes encountered in the dialogue (divination, divine aid and prophecy, and nostalgia).

Plutarch’s description of the world at Delphi rewards the reader with insights into an intellectual, scientific, religious, and social world that has long departed. iii

PREFACE

The translation into English of De E was suggested to me as a possible subject for a master’s dissertation by Professor James Hume. In one of his seminars, which I had the pleasure of attending, he raised several tantalizing puzzles in the dialogue, and suggested that

I might pursue these while preparing a translation. At all times during the progress of this work, I have enjoyed the advantage of his indefatigable help and criticism, and his enormous store of classical and linguistic lore. Nevertheless, this translation is my own original, unpublished, and independent work.

Judith Anne Alexander

ACKNOWLEDGMENTS

I am grateful for guidance and support I have received from the Department of Classics and

Religion during my graduate and undergraduate studies, and during the writing of this thesis.

Reyes Bertolin, James Hume, and Peter Toohey instilled in me respect and awe for the Greek language, although they cannot be held responsible for my inability to master it. Others outside the department have also contributed to making my sojourn productive and personally rewarding. Ms. Christine Stark and the staff at the Business Library (a short walk from our department) cheerfully provided comprehensive advice and answers to my requests and questions and helped me navigate both the interlibrary loan service and our off-campus book depository. Professor Ozouf Amedegnato, in the School of Languages, Linguistics,

Literatures and Cultures, holds a freewheeling, bi-weekly seminar in linguistics, from which I have derived both pleasure and instruction. Jeremy Mortis advised me on the functioning of my computer and was steadfast in the face of even the most contrary events. Finally, I thank the department of Graduate Studies for the award of a Queen Elizabeth II Graduate

Scholarship for the 2016 calendar year. That grant not only helped with the necessities of life but also gave me the means to indulge in buying a book or two on occasion (well, on several occasions) and to attend two conferences.

DEDICATION

To John and to Lisa Friedland

ΧΑΡΙΣΤΗΡΙΑ

TABLE OF CONTENTS

ABSTRACT...... ii

PREFACE...... iii

ACKNOWLEDGMENTS...... iv

DEDICATION…...... v

TABLE OF CONTENTS...... vi

LIST OF FIGURES...... vii

LIST OF ABBREVIATIONS...... viii

EPIGRAPH...... 1

INTRODUCTION...... 2

NOTES ON THIS TRANSLATION...... 10

SCHEMA: STRUCTURE OF THE DIALOGUE...... 15

TRANSLATION…….………….…………………………………………………...... 16

COMMENTARY……………………………………………….……………………...41

APPENDIX A: PLUTARCH AND HERACLITUS...... 81

APPENDIX B: FREE INDIRECT DISCOURSE….……….……...... 99

APPENDIX C: THE TETRACTYS……………………………………………...……116

BIBLIOGRAPHY…………………………………...... 130

vii

LIST OF FIGURES All figures appear in Appendix C

Figure 1. The Pythagorean tetractys...... 118

Figure 2. The Platonic Lambda...... 121

Figure 3. The “filled in” Platonic Lambda...... 122

Figure 4. The tetractys of Franceso Giorgi...... 124

Figure 5. Nested Platonic Lambdas………………...... 124

viii

LIST OF ABBREVIATIONS

DICTIONARIES AND GENERAL REFERENCE WORKS (LISTED BY ABBREVIATIONS) Bergk Theodor Bergk. Poetae Lyrici Graeci. Leipzig, 1882. Bywater Ingram Bywater. Reliquiae, recensuit. Appendicis loco additae sunt Diogenis Laertii vita Heracliti, particulae Hippocratei De Diaeta libri primi, epistolae Heracliteae. Oxford, 1877. Diels H. Diels. Die Fragmente der Vorsokratiker. Berlin, 1906. Edmonds J. Maxwell Edmonds, Lyrae Graeca. London: W. Heinemann, 1922. GP J. D. Denniston, The Greek Particles. Oxford: Clarendon Press, 1954. Helmbold-O’Neil W. C. Helmbold, and Edward N. O’Neil. Plutarch’s Quotations. London: Blackwell, 1959. Kaibel George Kaibel. Comicorum graecorum fragmenta. Berlin, 1899. Kern Otto Kern. Orphicorum Fragmenta. Berlin, 1922. KRS G. S. Kirk, J. E. Raven and M. Schofield. The Presocratic Philosophers. 2nd ed. Cambridge: Cambridge University Press, 1983. LSJ H. G. Liddell and R. Scott, rev. by H. S. Jones. A Greek-English Lexicon, 9th ed. Oxford: Oxford University Press, 1940. (Reprinted with a Supplement 1968). Nauck August Nauck. Tragicorum Graecorum Fragmenta, 2 ed. Leipzig: Teubner, 1889. O’Neil E. N. O’Neil. Plutarch, Moralia: Index. Vol. 16 (Loeb Classical Library 499) Cambridge. MA: Harvard University Press, 2004. Stobaeus Ioannis Stobaeus Florilegium, (4 vols). Leipzig: Teubner, 1856. SEP The Stanford Encyclopedia of Philosophy. Ed. By Edward N. Zalta. World Wide Web URL: https://plato.stanford.edu/ SVF Hendrick von Arnim, Stoicorum Veterum Fragmenta, (3 vols). Leipzig, 1903-5. Wehrli Fritz Wehrli. Die Schule des Aristoteles. Basel-Stuttgart: Schwabe, 1945.

TITLES OF THE “MORALIA” CITED IN THE THESIS (LISTED BY ABBREVIATIONS)

Adv. Col. = Adversus Colotem An rect. dict. = An recte dictum sit latenter esse vivendum An seni res. = An seni respublica gerenda sit Aqua. an ignis = Aquane an ignis sit utilior De an. procr. = De animae procreatione in Timaeo De def. = De defectu oraculorum De E = De E apud Delphos De exil. = De exilio De fac. = De facie quae in orbe lunae apparet De gen. Socr. = De genio Socratis De Is. = De Iside et Osiride De mus. = De musica De Pyth. = De Pythiae oraculis De ser. num. = De sera numinis vindicta De soll. anim. = De sollertia animalium De Stoic. = De Stoicorum repugnantiis Non poss. = Non posse suaviter vivi secundum Epicurum PG = Praecepta gerendae reipublicae PQ = Platonicae quaestiones QC = Quaestionum convivalium QG = Quaestiones Graecae QN = Quaestiones naturales Quo. Adul. = Quomodo adulescens poetas audire debeat Sept. sap. con. = Septem sapientium convivium

The Lives cited are those of Solon, Marcellus, Pericles, and Theseus.

EPIGRAPH

ἁρμονίη ἀφανὴς φανερῆς κρείττων — Heraclitus of Ephesus (fifth century BC.)

Heard melodies are sweet, but those unheard Are sweeter; therefore, ye soft pipes, play on; Not to the sensual ear, but, more endear'd, Pipe to the spirit ditties of no tone:

“Ode on a Grecian Urn” — John Keats (1795-1821)

INTRODUCTION

At the beginning of De E apud Delphos, Plutarch writes to his friend Sarapion suggesting that they begin an exchange of letters and essays between colleagues at the Temple of Delphi and those at the Academy in Athens. While Plutarch mentions De E for the proposed literary exchange,1it and two sister dialogues, De Pythiae oraculis and De defectu oraculorum, have come to be called the Pythian Dialogues. These three dialogues describe different aspects of the running of the temple at Delphi, its spiritual and practical challenges, and its day-to-day life. Plutarch weaves his account of myth, history, and personal and professional digressions into a canvas embellished with both quotidian and arcane literary and philosophical lore.

These accounts are always interesting and instructive but are clearly an amalgam of facts, opinions, reminiscences, speculations, and pleasantries sometimes reported, it seems, just for the joy of rehearsing them.

Depopulation of the Boeotian countryside is the fulcrum on which De def. pivots. It begins by recounting a foundation myth: Zeus despatched his birds (either eagles or swans) to

“fly from the uttermost ends of the earth towards its centre”2 The birds then regrouped at the

1. Two other dialogues, De Is. and the incomplete De fac. are sometimes grouped with these. All touch on religious themes.

2. J. G. Frazer (Pausanias’s Decription of Greece, London: MacMillan, 1898, 315) comments that the birds are usually eagles, but swans (Plutarch) and crows (Strabo) are also mentioned. Golden figures of two eagles once stood on each side of the omphalos at Delphi. 3 omphalos at Delphi. The recounting of this myth is a marvellous contrast to the reputation of

Delphi in Plutarch’s time as desolate and deserted. The contrast is even clearer when we meet two travellers, Cleombrotus, coming from Egypt in the south-east and the other, the eminent grammarian Demetrios, from the wilds of Britain to the north-west.

The question posed in that dialogue, why so many of the oracles have ceased to function, is partly answered by the observation that the decrease in population had resulted in a lessened need for the services of the oracles. Plutarch deplored the decay and depopulation of this corner of his native land and provided his own personal interpretation by remarking that he was fond of Chaeronea, and did not wish, by leaving it, to make it less populous.3 He was part of the civic council of Chaeronea, serving terms as building commissioner and as archon. He commented in several places on his civic duties, and on his own part in maintaining the streets and public areas in the town. In two essays he describes both the

“hands on” responsibilities of a civic-minded young man and, later, the “leading by example” responsibilities of an older man whose physical powers have waned. He gives the example of

Epameinondas who, on being appointed telmarch by the Thebans, did not neglect his duties but elevated the position to one of importance and dignity. Plutarch explained that, when he was telmarch, he attended to his duties not for himself but for his native place.4

The third essay in the trio, De Pythiae oraculis, seeks to explain why the oracle at

Delphi no longer gave oracles in verse. The answer comes only after several digressions into

3. See Robert Lamberton, Plutarch. New Haven and London: Yale University Press, 2001, 52).

4. The first (PG, 15. 811 A-B) is addressed to Menemachus, a young man who has asked Plutarch for advice on taking up public life. The second (An seni res. 783 A) is addressed to Euphanes, Plutarch’s contemporary, who may have asked Plutarch for advice about retiring from public life. 4

“portents, coincidences, history, a little philosophy, and anecdotes of Croesus, Battus,

Lysander, and Battus” (Babbitt 1936, 256). The answer is that modern pilgrims require direct and simple answers not the grandiloquence, and flourishes of the hexameters of the past.

Modern pilgrims too (as also recounted in De E) tended to pose banal, and trivial questions to the oracle, which hardly deserved elegant verse in response.

The votive offerings left in the temenos at Delphi provide the setting for the question posed in De E. Amongst these, but apparently displayed inside the temple, were the aphorisms of the seven Sages and a representation of the letter E. The question broached in the dialogue is the meaning and symbolism of the E. Several possible answers are given: the E represents the number of Sages, the number five; the conjunction “if;” the hypethical syllogism; or the second person singular of the verb to be, “You are”,5

Plutarch (46? – 127?) was born and raised in Chaeronea, a small but historic town in

Boeotia, not far from Delphi. His life spanned the reigns of ten emperors, from Nero to

Hadrian. His family was well-to-do, he benefited from good schooling in Athens, married

Timoxena, apparently happily, and established a family of four sons and a daughter. The daughter, a second Timoxena, died in childhood and one son did not survive to adulthood. We know little of Plutarch’s life after his studies in Athens. He left Chaeronea to study, travelled

5. For those who would appreciate an overview of Plutarch’s life and work (and the Moralia), see Babbitt’s introduction in volume 1 of the Loeb editionLCL Moralia (1927, pp. 9-33).and the introduction in volume 1 of the Budé edition (1987, pp. vii-cccxxiv) by Jean Irigoin. The second also contains four appendices, the first listing the 227 Greek titles contained in the Lamprias Catalogue, the second the sixty-seven principal manuscripts of the Moralia available to us; and the third and fourth concordances, in both directions, between the seventy-eight titles in Maximus Paludes’ third manuscript and those in the printed edition of the Moralia (1572) by Henri Estienne.

5 in Italy and Egypt, seems to have led a successful life as a lecturer, and to have made friends in Rome. In middle life, around the year 92, he returned to Chaeronea, to live in a Greek enclave, away from political life and the distractions of the city. Whether this was calculated and “the smartest move of his career,”6 or just a personal decision to return to his birth place, we do not know. On his return, Plutarch served for many years as a priest of Apollo at Delphi, close to Chaeronea.

In De E, Plutarch is at pains to explain that the events he describes took place many years earlier. We meet Ammonius Plutarch’s teacher, Lamprias his brother, and Sarapion his friend, although without a doubt these portraits are to some extent fictional. Ammonius reappears in De def., where an older and wiser Lamprias is the master of ceremonies. Each appears in several of the Quaestiones convivales as befits their intimate relationships with

Plutarch. Sarapion speaks in De Pyth. and one of the banquets is given to honour his victory with a prize-winning chorus. Nevertheless, it is prudent to view these portraits as being, to some extent, fictional.

Without further ado, we can start to make our way through this dialogue, and gradually, with the help of commentary and digressions into Plutarch’s other writings, make the acquaintance of Plutarch’s family, friends, and associates.

ABOUT THIS TRANSLATION

After accepting the suggestion to translate De E from the Greek, I assessed my experience and aptitudes for the task. Much of my working life was spent as an adjudicator, with

6 See Jeremy McInerney,“‘Do you see what I see?’: Plutarch and Pausanias at Delphi.” In F. de Blois, The Statesman in Plutarch's Works vol. 1 2003: 43-55. 6 responsibility for writing decisions. Over the years, I learned to write clearly and concisely on demand on almost any subject, and to enjoy the experience to boot. Thus, I took heart from the notion that competence in translation requires, after knowledge of both languages involved, enthusiasm for the small details and the new discoveries that go into reproducing the thoughts and ideas of others and rendering them empathetically and coherently in a narrative, along with my own and my panel’s interpretation and understanding of the issues before us. In addition, some of my adjudicative work required writing back and forth between

English and French.

As an undergraduate I translated Daniel (from the Junius Manuscript), an anonymous

Old English poem of unknown date retelling the Biblical story. Also, in my undergraduate career I studied the innovative language used in an early Russian saint’s life, The

Autobiography of the Archpriest Avvakum, written by himself.7.

So, I began the project in the usual way, with dictionaries and reference books, just as

Seamus Heaney described his preparations for translating Beowulf:

It was labour-intensive work, scriptorium slow. I worked dutifully, like a sixth former at homework. I would set myself twenty lines a day, write out my glossary of hard words in longhand, try to pick a way through the syntax, get a run at the meaning established in my head, and then hope that the lines could be turned into metrical shape and raised to the power of verse…. What had been so attractive in the first place, the hand-built, rock-sure feel of the thing, began to defeat me. I turned to

7 . Avvakum (1620-82), an orthodox priest, cleric and quondam counsellor to the Tsar, battled the reforms of the Archpriest Nikon, and wrote this “life” to support and encourage schismatic Old Believers. He used a demotic Russian for his personal reminscences and descriptions as well as the formal Church Slavic used for biblical and religious topics and in church ritual. As part of the Tsar’s retinue, he also wrote in and was comfortable with the Chancellery Russian used in the court.. The most obvious sign of Avvakum’s iconoclasm is the title of his book. The first translation (into English) was made by the classicist Jane Harrison and her friend and student, Hope Mirrlees. (The Autobiography of the Archpriest Avvakum, written by himself. London: The Hogarth Press, 1924). 7

other work, the commissioning editors did not pursue me, and the project went into abeyance. (Beowulf: A New Verse Translation, New York: Farrer Strauss and Giroux, 2000, xxii)

Heaney did take up the work again. The differences between my circumstances and Heaney’s were that Plutarch wrote prose not poetry, a mannered and sophisticated prose but still prose and I did not have the luxury of shelving the project and getting on with other parts of my life, for at that long moment this was my life. So, I worked on lines in different coloured inks in notebooks until I moved on to innumerable electronic drafts.

My principles of translation are simple, to construct an English text that maintains the content, form, and function of the original Greek. Hewing to these principles is not so simple; the three criteria are not always independent, a pithy saying in Greek may require a less compact and elegant phrase in English to convey the same idea. The notions described by the terms “literal” or “close” translation, without explanation or qualification, are too fuzzy to be useful, although they do encapsulate the three criteria above. The notion of register is also important, but that is not a monolithic concept. It is more a will-o’-the-wisp, that changes from one passage to another within a work, as the speaker or subject changes. Often there is no clear “best” solution to a translation problem, and the best one can do is to satisfice. One creates a translation that meets minimum standards of intelligibility, accuracy, literacy, and readability and that conveys the tone and substance of the original. In addition, a translation should contain no factual errors, and display an understanding of, and at least some sympathy for, the social, political, and historical environment in which the original was written.

A translation can be buttressed by a commentary, which allows one to present extra information and interpretation. These comments may enlarge on the original text, describe difficult junctures in the translation, give background information on the events and characters 8 described in the text, or muse on possible interpretations of the text. Heaney has not provided a commentary, which scholars might have found useful, not even in the bilingual edition, where the original text is side-by-side with his translation. As he points out, for generations of scholars the main interest in the poem has been textual and philological but recently it has increasingly been recognised as an original creative work of art. I have provided a commentary, aware that it may not please everybody. For some it may be too intrusive and for others not informative enough.

To explain my approach, let us consider the first two lines of De E, for which I felt obliged to provide three separate comments, which you can find on page 41:

These lines, quite well written, which I came across a short time ago, my dear Sarapion, were, according to Diceratiids, said by Euripides to Archelaus.

The sentence contains four proper names. Sarapion has already been introduced, and any reader of this translation knows that Euripides was a Greek playwright. The other two personages must be identified if the reader is to make sense of the sentence. Since Euripides spoke to Archelaus they must have been in the same room, that is they were contemporaries. I discuss their relationship in the comments. The Greek ἃ Δικαίαρχος…οἴεται could have been translated as “which Dichaearchus thinks”, but since Plutarch could not have been privy to what Dicaearchus (a writer and student of Aristotle) thought, this is surely idiomatic. My translation for “according to Dicaearchus” marks the distance between knowing something directly and indirectly. Finally, since first sentences are so difficult to write and Plutarch had clearly toiled over this one, I wished to keep his significant first word στιχίδιον first.8

8. A diminutive of στίχος, a row of numbers or trees, a file of soldiers, or, as in this case, a line of verse. 9

Foregrounding the word gives the right suggestion for the literary and philosophical discussion to come.

My advisors have offered good advice that sometimes was not taken. They will certainly feel a frisson of recognition when Heaney explains that his publisher had appointed a professor of English to “keep a learned eye on him” and that, although the professor’s comments, “informed by scholarship and a lifetime of experience of teaching the poem,” were invaluable, nevertheless, he was often reluctant to follow his advice and “persisted many times in what we both knew were erroneous ways.”

Although less than a century has passed since Babbitt and Flacelière wrote, it is possible to add some new comments on De E. The first is that we have more news of Neobule

(section 5) in a papyrus fragment found at Oxyrhynchus, containing the longest surviving piece of Archilochus’ poetry. This was published in 1974 (the “Cologne Epode”). The second concerns the legendary aphorisms of the seven Sages, which were displayed at Delphi

(section 3). The third, again found in section 3, consists of questions posed to the oracles, found on newly discovered papyri, and painstakingly listed and translated by Hunt and Edgar.

Finally, Louis Robert (1968) describes a set of inscriptions discovered in the Greco-Bactrian city of Ai-Khanoum, Afghanistan. Clearchos (who may have been Clearchus of Soli), who signed the stele there, claimed that he copied them from those standing in the shrine at Delphi.

Further findings by Oikonomides (1987) of steles at Miletopolis on the Hellespont suggest that displays of the aphorisms were not uncommon in Hellenistic times. Such examples put meat on the bare bones of the dialogue and give us a richer appreciation of the milieu in which Plutarch wrote.

NOTES ON THIS TRANSLATION

The Greek text used for the translation is that of Frank Cole Babbitt (1936).9 I also consulted the texts of Robert Flacelière (1941 and 1974), Hendrik Obsieger (2013) and the electronic version of Bernardakis’ text (1891). The Obsieger text is especially useful because, on points of difficulty, he has almost invariably reviewed both the Flacelière and Babbitt texts. The

Greek text received good reviews for its simplification and clarification of the apparatus

(Thum 2014; Lamberton 2015; and Roskam, 2015). Nevertheless, all three reviewers decry the presentation of the Greek text (of nineteen pages), which has not been typeset to harmonise with the rest of this handsome book. The visual effect is jarring and the font itself is difficult to decipher (and, it seems, entirely in boldface). Since it is in Greek, and in the abbreviated Latin suitable for an apparatus, it presents a distraction to a reader attempting to read and understand it. Obsieger’s book has no translation of the Greek and the commentary is in German.

9. Babbitt (Moralia LCL 5, vii 1936) follows the text of Gregorius Bernardakis, with emendations. He has a minor Teubner edition based on the Manuscript Parisinus 1956, which was severely criticized by Wilamowitz and Pohlenz, in part for the use of that particular manuscript. Furthermore the electronic edition contains numerous typographical and punctuation errors. Successive Teubner editions moved in a very different direction. Bernardakis’ son and grandson, Demetrios Bernardakis and Panayiotis Bernardakis, continued his work and began publishing a complete edition of the Moralia, in eight volumes, beginning in 2010. To my knowledge, the dialogue, De E, has not yet appeared.

Babbitt restored several readings of the manuscripts and adopted some emendations proposed since the Bernardakis text was published, signalled by his initials in the apparatus.

There are few English translations of the complete Moralia,10 and the first by Dr.

Philemon Holland (1552-1637) is, in my opinion, the best. Holland was an approximate contemporary of William Shakespeare, Sir Thomas North, and the forty-seven scholars who prepared the translation of the King James Bible. Holland published his translation of the

Moralia and dedicated it to King James seven years before the new Bible appeared. Dubbed

“the translator generall of his age”,11 he produced the first English translations of several works by Livy, Pliny the Elder, and Xenophon, as well as the complete Moralia of Plutarch.

His only fault, in my opinion, was his penchant for colloquialisms that have rendered his translation, with the passing of time, woefully out of date. His virtues are attested by the re- edition of his translation of twenty dialogues from the Moralia, published in the Everyman’s

Library in 1911. Although this edition required a glossary of archaic words, its re-edition in this accessible format suggests that the Moralia were as popular in England as they were elsewhere in Europe. The foreword describes Holland’s strengths as his “accurate and thorough” translation and a “rare and consummate” knowledge of his mother tongue.

The Dryden translation (1684-94), made by “forty or fifty university men", was another exercise in collaborative translation. It was updated in 1874, by W. W. Goodwin, with an introduction by Ralph Waldo Emerson. Goodwin’s translation was an improvement over

10. By my count, there have been four complete editions of the Moralia (Holland, the Dryden edition [“by several hands”], the Emerson edition [translated by Goodwin], and the Loeb Classical Library), edition by several translators) and a few selections (Shilleto, Prickard and King). For comparison, from 1660 to 1975, four complete French translations of the Moralia (Amyot [in several editions], Ricard, Bételaud, and the Budé series), and seven collections had been published.

11. Oliver D. Harris, "William Camden, Philemon Holland and the 1610 translation of Britannia." Antiquaries Journal 95 (2015): 279–303. 12 the earlier effort, which Emerson found “careless and vicious in parts" (Goodwin, 4 17). The later Loeb Classical Library Moralia is not so much a collaboration as a joint production where different authors take full responsibility for certain parts of the work. There were more than a dozen authors involved in a publishing enterprise that extended from 1911 to 2004.

This gives to the volumes some of the attributes of Theseus’ ship, since various parts have been removed and new parts substituted. Both the Teubner and Budé publishing houses work with the same model.

The collection by C. W. King (1908) contains the Pythian dialogues and several other dialogues with religious themes.12 King defines theosophy as “knowledge of the things pertaining to God” and recommends that these essays be read by “every religious disputant”.

In his introduction he acknowledges his debt to his “ancient brother-fellow, the indefatigable

Philemon Holland.” The translation of A. O. Prickard (1918) is difficult to find but does appear on the Thomas Browne’s Miscellany (1864) website for the University of Chicago.

In addition to these English translations, I consulted the French translations of

Robert Flacelière (1941, 1976), Jacques Amyot (1572), Dominique Ricard (1784),

Frédérique Ildefonse (2006). and the Latin translations of Daniel Wyttenbach (1784) and

Wilhelm Xylander (1570).

The reader is warned that, although the Babbitt translation appears in both the Loeb edition of the Moralia (1936) and on the Perseus website. The companion Greek text in the

Loeb is Babbitt’s own adaptation while the Greek text on the Perseus site is from

Bernardakis’ Teubner edition. Furthermore, the Goodwin translation (1874), also available on

12. C. W. King. Plutarch’s Morals: Theosophical Essays. London: 1908. 13 the Perseus website, is a revision and modernisation of the much earlier translation by

“several hands” (1694), and obviously predates the Greek text of Bernardakis. In other words, there are two English translations and one Greek text on the Perseus website and neither translation was made from that Greek text.

Stephanus numbers, an innovation in Henri Estienne’s 1572 edition of the Moralia, are given throughout. Estienne had originally introduced these numbers in his edition of

Plato's complete works and they rapidly became standard notation. On the formatting of these numbers, I have followed the contemporary style of Babbitt, Flacelière, and Obsieger, who use exclusively the capital letter, that is either 123A or 123 A. I follow Obsieger’s model in using both the section number and the Stephanus number thus: 1. 123 A. In addition, all modern editions of De E break the dialogue into twenty-one sections. This was, I believe,

Wyttenbach’s innovation.

Notes and comments, numbered consecutively throughout the translation, appear at the end of the translation, that is after section 21. Each note begins with the appropriate

Stephanus number. There are essays on themes and other topics in the appendices.

On quotations from other works in the Moralia, where there is no note to the contrary the English translation is my own. In the cases where I have relied on the Loeb edition. I have added the name of the translator. All citations include the abbreviated title and the Stephanus number. For translations from modern languages, I have provided my own for the very few in

German and left the French untranslated, unless some ambiguity requires an explanation, where I give my own English translation.

On Greek proper names, Babbitt, Flacelière, and Obsieger use different translations for them. Babbitt’s proper names often seem old fashioned (for example, Heracleitus or 14

Archilaüs). Consequently, I have followed no model but used those spellings that appear to be, from my own reading, currently accepted English spellings (Heraclitus and Archelaus). In quotations, I have preserved the original spellings. Since two Plutarchs appear in the dialogue

– Plutarch the narrator and his much younger self – I have differentiated them by calling the latter “Young Plutarch.” There is also Plutarch the author, and when he appears in the commentary or the appendices I call him “Plutarch the author” or simply “the author.”

For classical references other than to the Moralia, I have used the author’s name for the first appearance and later a shorthand. Thus, later references to Pausanias’ Travels in

Greece are simply to Paus. I have not listed these abbreviations separately, they are all in current use and usually decipherable. I have left some names in full to avoid confusion, for example, I have not abbreviated “Heraclitus” or “Herodotus,” for the obvious reason.

Finally, on the orthography of the epsilon. This appears in Greek texts sometimes as an E, EI, or εἰ. There has been controversy amongst editors over the form of the letter in the

Greek text – how Plutarch wrote it, and how it appeared in the pronaos of the temple. Both

Babbitt and Paton maintained εἰ although Babbitt wrote “E” in his English translation. The compiler of the Lamprias Catalogue used an “E”. I have used an “E” in the title and in the dialogue except where it is to be interpreted as something, such as “you are” or “if”, other than the letter.

Two coins (from the imperial epochs of Hadrian and Faustina the Elder) appear to show an E hanging in the pronaos of a temple, possibly Delphi (Imhoof-Blumer and

Gardner,1885). Some archeologists and numismatists have claimed a link, through Plutarch’s

De E, between these coins and the temple at Delphi, and to the seven Sages. For a brief account see Babbitt (1936, 195, 196). 15

SCHEMA: THE STRUCTURE OF THE DIALOGUE

The essay breaks into two main parts; an introduction (Part A) in the form of an epistle to

Sarapion, and the dialogue itself (Part B - B’). The second part is bookended by Ammonius’ opening and closing remarks. Within it, two sub-parts are devoted to the interpretation of the meaning of the E.

A Plutarch’s letter to Sarapion introducing the dialogue. (Section 1)

B Ammonius, presenting Apollo as the god of enquiry, philosophy, and prophecy, invites interpretations on the meaning of the sacred symbol “E”. (Section 2)

B. 1 Presentations of the participants. (Sections 3-7)

B. 2 Presentation of Young Plutarch. (Sections 8-16)

B’ Ammonius, in direct speech, reprises the arguments and opinions already heard, then asserts that the significance of the E lies not in its status as a letter or a number but in its semantic meaning as a salutation to the god. (Sections 17 – 21)

Plutarch writes to Sarapion that the dialogue is “about” a discussion of the meaning of the E, but the structure above does not suggest that the dialogue presents a definitive conclusion on what the E means, nor that that meaning is singular or unique.

TRANSLATION

SECTION 1 (384 D – 385 B)

Plutarch presents a letter to his friend Sarapion containing a proposal for an exchange of intellectual and literary gifts between friends in Delphi and in Athens. The first of these will come from Plutarch, a report on a discussion of the symbolic meaning of the E dedicated to Apollo. Plutarch begins his letter with a quotation from Euripides on the reciprocal demands that friendship makes on friends.

These lines, quite well written, which I came across some time ago, my dear Sarapion,1 were according to Dicaearchus2 said by Euripides to Archelaus:3

I, a poor man, should not wish to give a gift to you, a rich man, lest you think me a fool or that I am begging for a gift in return.

For a man of small means wins no favour when he gives paltry gifts to a rich man; it is just not credible that he expects nothing in return, and he acquires the reputation of being ill- mannered and servile.4 But see also that, so far as liberality and beauty are concerned, monetary gifts are inferior by far to those that come from learning and wisdom. It is good both to give such presents, and on giving them, to expect similar gifts from those who received them. In any case, I am sending to you and, through you, to our mutual friends in

Athens these Pythian dialogues, the first fruits as it were of our deliberations.5 But in return, I am expecting more and better ones from you and your friends, which are bound to be superior to ours in quantity and quality, inasmuch as you enjoy all the advantages of a big city, an abundance of books, and opportunities for discussion on a wide variety of topics. 17

It seems to me that our beloved Apollo, in the oracles that he gives to those who consult him, finds a remedy and solution for the problems that beset our daily lives. But, for those problems involving reason, he devises and poses problems that are consonant with our philosophical nature, creating within our souls a thirst for knowledge that leads us onward towards the truth. This is clear in many ways, but particularly with the dedication of the E at

Delphi, for it seems that it was not by fate nor by chance that this of all the letters came to take the seat of honour before the god, elevated to the rank of a holy offering and something that had to be seen. Those who first sought knowledge of the god saw an extraordinary power in it or used it as a token for another matter worthy of serious thought.

On many occasions in the school, when the subject of the E came up, I used to ignore it calmly and turn it aside. But just recently, my sons discovered me in animated conversation with some visitors who were at the point of departing from Delphi. It would have been churlish to avoid the subject, or to have excused myself from their discussion, for they were eager to hear about the E. So, I sat them down near the shrine and began to ask questions myself, and to seek answers with them. Then, under the spell of the place and the discussion itself,6 I recalled that, long ago, at the time when Nero visited the temple,7 I had heard another discussion on this very subject between Ammonius and others, when the same question had been asked in a similar way.

SECTION 2 (385 B – 385 D)

The priest Ammonius opens the discussion on the meaning of the E. Plutarch bookends the dialogue by giving Ammonius this introduction and then the last word (sections 17-21). In the intervening sections other speakers (Lamprias, an anonymous member of the group, Nicander the priest, Theon, Eustrophus and Young Plutarch) follow with different interpretations of the meaning of the E (sections 13-16).

It seemed to everyone present that Ammonius had set out and demonstrated, by reference to each of his names, that the god is no less a philosopher than a prophet. He is the “Pythian” to those who are just beginning to learn and to ask questions; the “Phaneaus” and the “Delian” to those to whom some part of the truth has been revealed and is becoming clearer; the

“Ismenian” to those who have gained wisdom and understanding; and the “Leschenorian” to those who are able to engage in and enjoy dialogue and philosophical conversation with others.8

“For,” he said, “the act of seeking for answers belongs to philosophy, and to wonder and doubt belongs to the seeking of answers, so it seems only right that many of the affairs of the god should be hidden in riddles that raise doubts and demand an answer to ‘why?’ 9

Consider, for example, that to feed the eternal flame, just one kind of firewood, fir, is burnt here; only the laurel is used for incense;10 statues of only two of the Fates stand here, while everywhere else three is customary;11 women may not approach the shrine to consult the oracle; then there is the matter of the tripod and many other analogous puzzles. 12 Many such questions have been posed to those who are not completely without reason or sensibility, and those questions have stimulated and encouraged them to investigate, behold, hear, and discuss them. Look, how these inscriptions, ‘Know yourself’ and ‘Nothing in excess’, have set in motion philosophical researches, and a veritable crowd of discussions has sprung from each one as from a seed!13 And, in my opinion, our topic of discussion is no less fruitful than any one of these.”

SECTION 3 (385 E – 385 F)

Lamprias responds that the explanation he has heard is quite straightforward – the Sages in fact numbered five. Since E is the fifth letter of the alphabet these five 19

dedicated an E to Apollo, repudiating the other two, to demonstrate that they were in fact five and not seven, three successive incarnations of the E are identified.

After Ammonius had said these things, my brother Lamprias spoke up. “In fact, the explanation that I have heard is straightforward and quite short. For it is said that the wise men, whom some call the Sages, namely Chilon, Thales, Solon, Bias, and Pittacus, were five in number.14 Later Cleoboulos the tyrant of the Lindians, and Periander the Corinthian, neither of them blessed with either honour or wisdom, were able to forge their reputations by force and through friends and favours, and arrogated to themselves the name ‘sage’. They then disseminated and broadcast throughout Greece maxims and aphorisms, which resembled some of the sayings of the original five.15 But those five, although appalled by this counterfeit, were not willing to challenge the insinuations of these two, nor were they willing, by a conspicuous quarrel over their good name, to arouse ill-feeling or enmity in such powerful men.

“So, the five, after meeting here and deliberating amongst themselves, dedicated as a votive offering the fifth letter of the alphabet, which also denotes the number five, thus affirming on their own behalf before the god that they were five, rejecting and disavowing the seventh and the sixth as not belonging to their group.

“To convince yourself that their account is on the mark, it is sufficient to listen to the explanation of those connected to the sanctuary.16 They describe the golden E as the E of

Livia, the wife of Caesar;17 the bronze E as the E of the Athenians; and the first and oldest, the wooden E, as the E of the Sages as it is called to this day, to denote a gift from not one man, but from all of them in common.”

SECTION 4 (386 – 386 C)

An anonymous member of the group reports the remarks of a Chaldean visitor who said that the significance of the E lay in its second place amongst the seven vowels and compared this to the second place of the sun amongst the seven wandering stars.

Ammonius smiled quietly, surmising that Lamprias was expressing his own opinion on the matter and was repeating a story from hearsay for which he could not be held responsible.

Someone else in the group commented that this was the same explanation that a

Chaldean stranger had been prattling about earlier;18 that there are seven vowel sounds amongst the letters;19 seven stars in the sky with autonomous and independent movements; the E is second in the list of vowels; amongst the seven planets the sun comes after the moon, which is first; and that nearly all Greeks identify Apollo with the sun.20 “But all these ideas”, he concluded, “come from star books and the rumours chattered about at the gates of the sanctuary”.21

Lamprias, it seems, had unwittingly antagonized the members of the sanctuary, because what he had said was not known to anyone amongst the Delphians, who brought forward the accepted opinion, circulated by the guides,22 that it is neither the form nor the sound of the letter, but only its name that carries symbolic significance.23

SECTION 5 (386 C – 386 D)

Nicander, a priest of Apollo, speaking on behalf of the Delphians, gives their understanding of the E. It represents the diphthong ει, meaning “if”. Those seeking advice from the god begin their questions with ει, and Nicander distinguishes this use of the conjunction from its conditional use in syllogisms. He describes another linguistic function of the ει – to express a wish.

“For, as the Delphians understand it”, said Nicander the priest, speaking on their behalf,24 “it

[εἰ] is the characteristic sign of every encounter with the god, and comes first in the governing 21 structure of the question that is used each time someone seeks counsel.25 They ask the god if they will win [a lawsuit], if they will marry, if it is advantageous to set out to sea, if they ought to take up farming, or if they ought to leave home.26 The god in his wisdom gives short shrift to those dialecticians who think that nothing comes from the inclusion of the conjunction ‘if’ in an expression and that it makes no real contribution to the meaning,27 for he considers all questions attached to that conjunction as realities, and he welcomes the questions.

“Furthermore, since we ask for personal counsel from the god as a prophet, but we come together to pray communally to him as a god, so they [the Delphians] think that the word ‘if’ is used to express a prayer or a wish, no less than to pose a question. ‘If only I could’ is the usual expression of a wish. 28 For example, Archilochus wrote ‘If only it might be granted to me to touch the hand of Neobule’.29 As for the phrase ‘if only’, one can say that the second word is not necessary,30 just as ‘surely’ is hardly necessary in Sophron’s, ‘She, too, is surely desirous of children’.31 Or in Homer’s, 32 ‘And surely I will bring your strength to naught’. So, as they say, the optative force is quite clear in the ‘if’.” 33

SECTION 6 (386 D – 387 D)

Theon gives another interpretation of the E, linking it through the conjunction εἰ (“if”) to the syllogism used in dialectics and logic. Almost the entire section is in direct speech. Theon, defending dialectics, claims that the conjunction “if” is a fundamental part of the structure of a syllogism, which allows us to form conditional statements and logical propositions. Theon explains that Apollo often exploits this construction when he announces his opaque oracles; he then gives a spirited summary of Stoic dialectics and propositional logic.

After Nicander had gone through his explanation, my friend Theon,34 whom you know, asked

Ammonius if Dialectic, who had just been so roundly insulted, was to be permitted to speak freely in her turn.35 When Ammonius encouraged him to speak for her and come to her aid, 22

Theon said, “Certainly the god is a dialectician’s dialectician, as most of his oracular pronouncements demonstrate, since he both creates and resolves ambiguities. Moreover, as

Plato said, when the god gave the oracle to the Delians to double the size of their altar, work requiring the highest skill in geometry, he was not demanding a new altar, but asking the

Greeks to study geometry.36 So, in this way, when the god gives obscure oracles, he exalts and recommends the understanding of logical reasoning as necessary for those who would understand him. For clearly in logical reasoning this hypothetical conjunction, ‘if’, has the greatest power [of all conjunctions] since this construction, the syllogism, is the most logical of all propositions.

“For how else could a syllogism be, given that even animals have knowledge of the existence of things, but Nature has given to humans alone the capacity to see and judge consequences? Certainly, wolves and dogs and birds perceive by their senses that it is day and there is light, but only human beings conceive by ratiocination that, ‘if it is day, then there must be light’.37 For only human beings understand the notions of antecedent and consequent, their apparent connection to each other and their consonance and difference, and that distinction is the principal source of logical demonstration.38 Philosophy is the search for the truth, the light of the truth is demonstrative reasoning, and the foundation of demonstrative reasoning is the syllogism. Thus, it was fitting that the power that initiates and produces this syllogism, ‘if’, was consecrated by wise men to the god, who is, above all else, a lover of the truth.

“Furthermore, the god is a prophet and the art of prophecy is about the future, which comes from the present and from the past. There is nothing whose beginning is without cause, nor whose future is without reason; for everything coming into being comes from something 23 that came into being in the past, and they are all knitted together following a succession that takes them from their inception to their term.39 Thus, he who has the natural capacity to connect causes and link them together; also knows how to foretell ‘all things that are, the things to come, and the things that are in the past’. 40 Homer had good reason to examine the present first, and to follow it with the future and the past. For the syllogism is based on the power of inference from the present as, for example, ‘if an event occurs now, then some other has preceded it’; and again, ‘if an event occurs now, then another will follow it’. In effect, skill and logic, as has been said, lie in the knowledge of consequences, but the minor premise is substantiated by perception.

“Also, and I cannot keep myself from saying this, although the expression is somewhat forced, this is the tripod of truth, that is, argument, which first establishes the relation of cause to effect (the major premise), then adds the assertion of this or that fact (the minor premise), which leads to the completion of the demonstration (the conclusion).

Therefore, if the Pythian Apollo, through his love of music, clearly enjoys both the song of swans and the thrum of the lyre,41 should it astonish us then, that through his love of dialectic, he finds the ‘if’, which he sees philosophers use so freely and so often, both agreeable and charming?

“Hercules himself, before he had delivered Prometheus from his chains, and before he had been amongst the sophists who associated with Chiron and Atlas, as a young man was a regular yokel,42 disdaining dialectic and mocking reason with its, ‘if the antecedent is true, then so is the consequent also.’43 He decided to take the oracular tripod by force, and to compete with the god in his divinatory art. Then in the fullness of his years, he too became quite good, or so it seems, at both divination and dialectic.”44 24

SECTION 7 (387 E – 387 F)

Eustrophus claims that the E is the token and sign of the pentad, the number five. Plutarch the narrator then provides the transition to the next part of the dialogue, where Young Plutarch explores the importance of the pentad.

When Theon had finished speaking, it was, I think, Eustrophus the Athenian who said to us,

“Look how eagerly Theon defends logical argument, all but donning the lion skin.45 In this way, we who see in Number the natures and principles of all things and all beings, without exception, whether human or divine, we who see Number as the leading cause and author of all that is beautiful and valuable are not likely to bear this peacefully and silently. On the contrary, we must offer to the god the first fruits of our beloved mathematics, which we hold so dear.46 For neither in form, nor significance, nor in mode of pronunciation do we think that the E, in itself, differs from any of the other letters, but it has been revered as the token and sign of a great and lordly number, the pentad, whence wise men called numbering ‘counting by fives’.”47

Eustrophus was not saying these things to us in jest, but because at that time I was applying myself enthusiastically to my mathematics. Nevertheless, I was to observe the maxim “Nothing in excess” just as soon as I became part of the Academy.48

SECTION 8 (388 – 388 E)

Young Plutarch sets out to show the importance of the pentad, represented by E. His method of argument is to describe and concatenate the disparate circumstances where the number five is important. This demonstration by exhaustion of the cases continues for eight sections. It ends without having surveyed every possible use of the pentad; only the reader is exhausted. Then I said that Eustrophus’ explanation had most gracefully resolved the difficulty with

Number.49 “For”, I continued, “all numbers but one are distributed into the odd and the even, and that one, the monad, can be both even and odd (since it becomes odd when added to an 25 even number, and even when added to an odd number). Then two begins the even numbers and three the odd. Furthermore, five results when these two numbers are added together, and so five has been honoured as the first compound of the first simple numbers, and has been called ‘marriage’, from the similarity of the even number to the female and the odd number to the male. For in the division of numbers into two equal parts, the even number breaks cleanly and leaves a sort of void that waits to be completed. But when an odd number is so partitioned there is always a productive middle part left after the division. Also, this number is more productive than the even numbers, because when it is combined with an even number the result is always odd. So, the odd number is superior to the even and is itself never overpowered.

“Moreover, adding a number to one of its own kind displays this difference: an even number added to one of its kind never produces an odd number; it never steps outside its natural attributes; being weak and imperfect; an even number is incapable of producing a number different from itself. On the other hand, odd numbers combine with other odd numbers to produce a crowd of different even numbers because their generative powers are always effective. But now is not the time to describe the properties and differences of the numbers. Let us simply recall that the Pythagoreans call five ‘marriage’ because it is produced from the union of the first masculine and the first feminine number.

“Five has sometimes been called ‘Nature’ because when it is multiplied by itself it results. For, just as Nature takes wheat in the form of seed and scatters it on the ground and in the meantime produces many forms and shapes, so she leads this work to its logical end, and at that end she displays its beginning – wheat.50 In the same way, whenever other numbers are multiplied by themselves they produce different numbers, but only the five and six, when 26 multiplied by themselves, reproduce and repeat themselves.51 Thus, six times six is thirty-six and five times five is twenty-five. And again, six does this only once,52 when it is squared. On the other hand, five generates this result with every multiplication; it produces either ten or itself in turn when it is added to itself, and this continues for them all, the number copying the first principle for ordering the whole.53 For the first principle preserves the cosmos, and then out of the cosmos perfects itself. ‘All things are exchanged for fire’, as Heraclitus said, ‘and fire is exchanged for all things, just as gold is for goods and goods for gold’.54 The pentad, on successive additions of itself to itself, begets nothing alien to itself nor incomplete; its changes are constrained. That is, it is either itself or a perfect whole.”

SECTION 9 (388 E – 389 D)

This section segues from the pentad, which begets nothing alien to itself, to the two faces of the one god who is worshipped at Delphi. This god suffers changes, but measured and predictable changes, just as the pentad cycles through the tens and itself and the cosmos preserves itself through its cycles. “Now, if someone were to ask what this has to do with Apollo,55 we should reply that it concerns not only him but also Dionysus,56 who has a claim to Delphi no less important than that of Apollo himself. For we hear the theologians,57 sometimes in verse, sometimes in prose, asserting and hymning that the god, by his nature, is deathless and immortal. Yet, because of his personal destiny or rule, he himself undergoes transformations, sometimes having his nature kindled into fire, making all things alike, and at other times taking on all kinds of changes in his shape, emotional affects, and powers, as the world does today. He is still

[despite these changes] called by the best known of his names [Apollo].58

“But more learned men, concealing his transformation into fire, call him Apollo for his oneness and Phoebus for his purity without stain. And, as for his transformation and realignment into wind, water, earth, or stars, or into different kinds of plants or animals, they 27 speak in riddles of his passivity and his transformation, as a tearing-apart or a dismemberment. Then they call him Dionysus, Zagreus, Nyctelius, and Isodaetes;59 they recount destructions and disappearances, returns-to-life, and regenerations, using riddles and myths appropriate to those transformations mentioned earlier. And to the other [Dionysus], they sing dithyrambic verse full of passion and change and erratic roaming and dispersion.

For, as Aeschylus says:60

It is fitting that the dithyramb should be present in Dionysus’ revels.

But for Apollo they sing the paean, orderly and temperate music. Artists portray him in paintings and sculptures as ageless, unchanging, and forever young, and the other, Dionysus, in many shapes and forms. In short, to the first they attribute consistency, regularity, and unfailing gravity, and to the other, an uneven mix of caprice, childishness, insolence, gravity, and mania, and they invoke him: 61

… of the orgiastic cry, leader of wine-maddened women, flourishing in their frantic honours.

They thus, not inappropriately, seize upon the attributes associated with these transformations.

“But the periods of these cycles are not the same, the one that they call ‘satiety’ is longer than the one they call ‘craving’.62 Having observed this proportion, they chant the paean at their sacrifices for the greater part of the year but, when winter comes they use the dithyramb for three months in their observances before the god. Thus, as three is to one, so is the relation of the period of orderly disposition to that of fiery destruction.”63

SECTION 10 (389 C – 389 F)

Young Plutarch describes the importance of the pentad (symbolised by the E) in music. He compares the highly mathematical approach to musical harmony developed by the Pythagoreans with that of empiricists who analysed musical ratios “by ear”, that is, through the senses. 28

“But this subject has been drawn out beyond all reasonable proportion.64 It is clear that people associate the pentad with Apollo because sometimes it generates itself out of itself, just as fire does, and at other times it generates the decad, just as the cosmos does.

“And as for music, which is particularly pleasing to the god, can we think that this number five plays no part in it? For the most part, the working of harmony is, in a word, concord.65 There are five of these concords and no more, as thinking demonstrates even to someone who claims to understand this through the senses and through playing unthinkingly on the strings [of the lyre] or the stops [of the flute]. The origin of all concord comes from the ratios between numbers; the ratio of the fourth is 4:3, of the fifth 3:2, of the octave 2:1, of the octave plus a fifth 3:1, and of the double octave 4:1.66

“But the concord composed of an octave and a fourth that the harmonikoi introduce in addition to these ratios,67 saying that it steps outside the measure, cannot be accepted because it privileges auditory perception over logic and is tantamount to being beyond logic.68 Let us not speak of the five stops of the tetrachord,69 nor of the first five ‘modes’ or ‘keys’ or

‘scales’, whatever their right name is,70 nor of the changes by which, through a tighter or looser string, the remaining lower and higher notes are achieved. We must ask whether, although the number of possible notes is large, even infinitely large, there are only five elements in melody – the quarter-tone, the semitone, the tone, the tone and a half, and the double-tone. For there is nothing else within the upper and lower bounds of these notes [that is, within two octaves], or between them, that can produce melody.”71

SECTION 11 (389 F – 390 A) 29

Young Plutarch continues his examples of the importance (and ubiquity) of the pentad (and the E) with Plato’s claim, that, by analogy to the Platonic solids, there can be no more than five worlds.

“There are many other examples [of the pentad] that I shall put to one side”, I continued,72

“and simply call on Plato, who, arguing for one world, said that if there are other worlds besides ours then there could be up to five, but no more.73 On the other hand, even if our world is unique and the only one of its kind, as Aristotle believes,74 then it is in some way composed and conjoined of five worlds;75 one of earth, another of water, the third of fire, the fourth of air and the fifth of high heaven – which some call light, some ether, and some the fifth substance – and this last world is the only one blessed with autonomous motion and spins by its own nature, not as a result of some accidental external force.

“And for this reason, Plato, understanding that the most complete and beautiful forms in nature number five, the pyramid, the cube, the octahedron, the icosahedron, and the dodecahedron, fittingly associated those forms with these five bodies, each to each.”76

SECTION 12 (390 B)

Young Plutarch continues that living creatures enjoy exactly five senses, and that there are exactly five elements: earth, air, water, fire and ether.

“Furthermore, there are some who associate the powers of the different senses with the primal elements,77 given that there is the same number of each. They perceive that touch marks resistance and is earthy, taste adopts through water the quality of that which is tasted, and sound comes from the air, which when it is struck takes on the sound of a voice or a noise. Of the remaining two, smell, which comes from heat, corresponds to fire, and finally sight corresponds to the ether and light because the eye, given its nature, emits light and produces a homogeneous mixture and a coalescence of these two kinds of ‘light’. No living creature 30 possesses any other sense besides these five and no other element exists in the world besides these five, but a wonderful assorting and pairing has come into being between the five and the five.”78

SECTION 13 (390 C – 390 F)

Young Plutarch turns from science to a literature with an example of the use of the pentad in Homer, with a short digression on the attributes of the pentad. He then moves on to another example – the five classes of animate beings.

At that point I stopped and after a moment said, “Eustrophus, what has become of us that we almost passed over Homer?79 For was he not the first to divide the world into five parts? He gave the three in the middle to the three gods [Zeus, Poseidon, and Hades], and the two extremes left out of the partition, the earth, and Mount Olympus, one delimiting the things below and the other high heaven above, were to be held in common.

“The discussion must be taken further back, as Euripides says.80 Those who vaunt the tetrad do not teach us something paltry, for all solid figures owe their coming into being to this number. For every solid body has depth drawn out from length and breadth. A point is the monad having position, which stands as the support of length; and length without breadth is duality, and then length that broadens along the line brings about the genesis of the plane and is threefold. Then, when depth is added to these, a solid is created which is fourfold.81 It is clear to everyone that the tetrad, having led nature forward to the completion and construction of a solid mass, tangible and firm, has nevertheless left it with the greatest want. For this inanimate thing, as has been said, is simply deprived,82 unfinished and not good for anything whatsoever, unless it has a soul using it appropriately. 31

“Thus, the balance and power of the five, with greater force [than other numbers], has not allowed animate beings to develop indiscriminately into unlimited kinds,83 but has produced the five forms of living things. For there are gods, then demi-gods and heroes, after them comes the fourth kind, men, and then comes the fifth kind, animals lacking reason.

“Furthermore, should you wish to partition the soul in accord with Nature, the first part, and the least transparent, is the nourishing instinct, and the second the perceptive abilities, then the appetitive and spirituous impulses after that. Finally, the last faculty is reason, and with this the soul achieves the perfection of its nature, have reached its culmination in the fifth degree.”84

SECTION 14 (390 F – 391 A)

This section continues another property of the pentad - it is the sum of the squares of the first two numbers. Young Plutarch does not explain why squareness is such a noble quality, but I conjecture that the next three numbers (3, 4, 5), the Pythagorean triple, could explain it. The squares of these numbers have intriguing properties. This is no more than speculation, but it may help us to understand where Young Plutarch’s argument is going. “And now this number, which has so many and such esteemed powers, also has a noble origin, not the derivation that I have already given, made up from the existing dyad and triad, but the one generated by adding together the beginning of all number and the first square number.85 For the beginning of number is the monad and the first square number is the tetrad; and from an ideal form and from finite matter, these generate, as it were, the pentad.86 If, moreover, as some rightly hold, the monad is square – its power being itself and being contained in itself – then the five, engendered by the first two squares, does not lack a noble pedigree.”

SECTION 15 (391 A – 391 E) 32

In this disjointed section, Young Plutarch first diverts us with the parallel between Plato’s and Anaxagoras’ rediscoveries of old truths, then uses two obscure examples to show that Plato acknowledged the importance of the pentad, and, by extension, the symbol E. Undeterred by these examples, which appear to be of the tetrad, Young Plutarch finishes off with a quotation by Socrates (in the Philebus) from an apparently well known Orphic verse.

“But,” I said, “I fear lest the most important matter of all, when it is mentioned, may embarrass our Plato, just as he said that Anaxagoras was embarrassed by the name of the moon, when he tried to claim an old theory about moonlight as his own. Has not Plato spoken of this in his Cratylus?”

“Certainly”, said Eustrophus, “but I do not see anything in that case analogous to our own.”87

“Nevertheless, I presume you know that in the Sophist, Plato shows that there are five overarching classes:88 being, identity, difference, and besides these the fourth and fifth, movement and stasis. And then in the Philebus, using a different method for his distinction, he says that infinity is one class, and finity another, and that from the mixing of these all genesis takes place. As to the cause of their mixing, he posits a fourth class, and he has left the fifth class, how things so combined are controlled in their dissociation and disengagement, for us to think about.89 I conjecture that these classes are no more than a reflection of the others, since generation corresponds to being, the infinite to movement, the finite to stasis, the mixing principle to identity, and the dissociating principle to difference. Even if these classes are different, there would nevertheless be five different types and differences, in the one case as in the other.

“You might say that someone inquiring into this understood it before Plato did, because that man dedicated an E to the god as a sign and symbol of the number that explains 33 the universe.90 Furthermore, he [to get back to Socrates], understanding that the Good appears in five qualities, of which the first is measure, the second symmetry, the third mind, the fourth sciences, arts and true opinions concerning the soul, and the fifth pure pleasure unmixed with pain (if there is such a thing) ends with the Orphic verse: ‘In the sixth generation, bring to a stop the ritual of song’.”91

SECTION 16 (391 D – E)

A short section remarking on an obscure link between the number five (and hence the E) and a divinatory practice whose exact nature cannot be disclosed to the uninitiated. It also marks the transition of the dialogue to Ammonius, the last speaker.

Then I said, “Following up on what has been said to you, I shall sing one short verse to the wise men in Nicander’s circle. ‘On the sixth day after the new moon’,92 namely when you go with the Pythia to the Prytaneum, the first of your three lots is a five – she casts a three and you a two, each with reference to the other.’93 Is that not so?”

“Yes, indeed,” said Nicander, “but the reason for it must not be divulged to others”.

“Very well,” I said, smiling, “if ever the time comes when we have been consecrated to the god, and he has granted to us to know the truth, then this should be placed beside all that may be said about the five.”94

And that is, as I remember, how the discussion of the arithmetical and mathematical encomia to the letter E came to its end.

SECTION 17 (391 E – 392 A)

Ammonius responds to Young Plutarch’s paean to the pentad by observing that every number displays remarkable qualities. He then recalls Lamprias’ discussion of the seven Sages and reviews the different interpretations offered by the others of the E as a grammatical or ordering device. He says that he will focus on the E as the 34

second person singular of the verb to be, “you are” [εἰ], which, he says, is the only correct address to the god.

Ammonius, in as much as he too believed that a not negligible part of philosophy is found in the study of mathematics, was pleased with the direction of the discussion. He said, “It is not worthwhile to argue too exactly with the young over these matters, except to say that every number exhibits not a few attributes for those who wish to praise and laud it. What need is there to speak of the other numbers? For the description of all the powers of the sacred heptad of Apollo would take all day to enumerate, and yet still not all of them would have been discussed.95 Then too, we should be claiming that the Sages were ‘at war’ with usual practice and ‘the weight of longstanding tradition’, if we say that they ousted the heptad from its front- row seat at the theatre,96 and then dedicated, as somehow more fitting, the pentad to the god.97

I believe that this expression is not a number, a ranking, a logical connective, or any other incomplete part of speech; it is a greeting and address to the god, complete in itself, which, as soon as it is uttered prompts the speaker to reflect upon the power of the god. For the god, addressing each of us, as we approach him in this place, greets us with ‘Know yourself’, which means no less than ‘Hello’. We in our turn reply to the god, ‘You are’, which is the truthful and truthfully spoken response, and the only address proper to him only as Being.”

SECTION 18 (392 B – 392 E)

Continuing his analysis of the E as a symbol for “you are” Ammonius demonstrates that we mortals we who never are but are always becoming. Ammonius draws the corollary that no person is ever one person but is, through time, many persons, the Platonic distinction between Being and Becoming (consider, for example, Timaeus’ asking about the difference between that which is existent always and has no becoming, and that which becomes and never is (Timaeus 27. D).

“For we do not share in any real part of Being since every mortal nature is between coming into being and being destroyed,98 and presents a dim, unstable apparition and phantom of itself. If you will your mind to understand the nature of Being, it is as if you have made a frantic effort to clasp water in your hand; the more you squeeze and press it into itself, the more it defeats your attempts to seize it. Just as reason, striving for too much clarity about things that experience change or modification, is baffled by a thing’s coming into being and passing into destruction, and then is unable to understand even one other thing that endures or really exists.

“‘It is not possible to step twice into the same river’, Heraclitus said.99 Nor is it possible to encounter a mortal being in one and the same state on two separate occasions.100

For a being changes its state so suddenly and swiftly that it both disperses and comes together and disperses again, or rather not again or later, but all at once; it is instantaneously both coming together and departing, is both ‘present’ and ‘absent’.101 Whence the thing coming together does not reach being because it never stops or ceases from its formation.

“This unceasing coming into being develops the embryo from the seed, makes the nursling, the child, then in order, the boy, the stripling, the grown man, the older man and the aged man; each of these stages is in its turn the means that destroys the one before it. But we have a laughable fear of one death, we who have died so many times and even now are dying.

For as Heraclitus said, ‘the death of fire is birth for air and the death of air is birth for water’, and it is clearer still in ourselves.102 The man in his prime is destroyed and gives birth to the geriatric, the young man is destroyed to turn into the man in his prime, the child into the young man and the infant into the child; he who yesterday was destroyed makes way for today’s person, and today’s is dying into tomorrow’s. For no-one stays the same, nor is he one 36 person; we are all many beings, made from matter drawn and poured into one shape and common mould.103

“Otherwise how, if we stay the same, do we take pleasure today in things different from those in which we took pleasure yesterday? How do we love, hate, admire, and condemn things different from those that we loved, hated, admired, and condemned before? Why do we speak other words and feel other passions? Why do we no longer have the same form, face, or thoughts? For it is unlikely, if there is no change, that we should have different experiences, nor that he who changes would be the same person that he was. But, if he is not the same person now that he was then, then he does not properly exist, but he changes his very being and becomes one person after another. Our senses, through ignorance of what is, lie to us that that which seems to be is that which is.”

SECTION 19 (392 E – 393 A)

Ammonius, continues with the implications that follow from interpreting the E to mean “you are”. Mortal substances were denied true Being in section 18, and here Ammonius describes true Being – it is not possible to say of something that is (in other words, that has true Being) either that it was or that it will be.

“Then what is it that Being really is? It is everlasting, without beginning, indestructible, impervious to decay, and no instant of time brings change to it.104 For time is in motion, moving we imagine with material stuff, always flowing onward and uncontained, but, as if in a leaking vessel, shedding birth and destruction.105 To say of time ‘then’ or ‘before’ or ‘it will be’ or ‘it has been’, is an immediate admission of its non-being. For to speak of what has not yet happened as ‘being’ or of what has ceased to be as ‘is’, is both simple-minded and inappropriate. Reason, set free to comment, would wholly demolish the main basis of our understanding of time, as when we say, ‘it has been’, ‘it is here’, or ‘now’. For the notion of 37 the present is squeezed out into the future or back into the past and it must be split apart, as happens for those wanting to see it at a precise instant in the present. So, if the same thing happens to nature, measured by time, as happens to time, the measurer, then there is nothing in nature that remains in Being, but all things are coming into being or are being destroyed, according to their connections with time.106 Hence, to say of something that is, either that it was or that it will be, is not sanctioned by divine law. For these are some of the displacements, mutations, and deviations of something that, by its nature, does not abide in

Being.”

SECTION 20 (393 A – 393 D)

This section completes the interpretation of the E (as “you are”) begun in sections 18 and 19. Section 18 asserted that we (mortal beings) have no part of Being, section 19 described Being, and this section asserts that god meets the description of Being. Hence, he is.

“But the god,107 it must be said, is; and he is for no particular time, but forever,108 a forever that is motionless, outside time, and undeviating,109 where there is neither before nor after, neither future nor past, neither older nor younger.110 But he, being one, has with one now filled forever and only when ‘Being’ is as he is, is it truly being. It has neither become nor is it about to become, for ‘Being’ never did begin and it will never end. So, when we worship him, we must greet and address him in the same fashion ‘You are’, or even, by Zeus, as some of the ancients did,111 with the address, ‘You are one’.

“For the divine is not manifold, as each one of us is manifold and becoming who we are from a patchwork of different experiences, and a collection of all kinds of happenings indiscriminately jumbled together.112 But Being must necessarily be one, just as the One must 38 be. Difference on the other hand, in its divergence from being, arises out of non-being into genesis.

“So, the first of the names of the god suits him well and the second and the third. For he is A-pollo, denying the many and the manifold. As he is alone and one, so he is Ieius. He is

Phoebus, perhaps because the ancients called all things that are chaste and pure ‘phoebus’,113 just as, I believe, the Thessalians say to this day of their priests, who spend the days of ill omen living in seclusion in the open air that they are ‘following the rule of Phoebus’.114 The

One is absolute and pure, for pollution arises from mixing different things and, as Homer said, somewhere, when ivory is being reddened [dyed], the dyers say that it is being polluted; they say that the mixing of colours destroys them, and they speak of such mixing as

‘destructive’.115 Surely then, to be both one and unmixed befits the unsullied and uncorrupted.”

SECTION 21 (393 D – 394 C)

Although Ammonius accepts the identification of Apollo with the sun, he categorically rejects Young Plutarch’s interpretation of the alternating cults of Apollo and Dionysus at Delphi as reflecting the two faces of one god and the rhythm of the cosmos. He ends his exposition by contrasting, and then reconciling, the maxim “Know yourself” with the E, the symbol for “You are” and then reprising and expanding the list of names for Apollo.

“As for those who believe that Apollo and the sun are one and the same, it is fitting that they should be welcomed and loved for their piety, in that they posit their conception of the god as the most honorable thing amongst all the things they crave to know. Let us awaken them from that most beautiful of sleep-visions where they dream of the god, and urge them to advance higher and to behold him in his true nature, but also to honour this image of him as the sun, and let them feel awe towards the sun’s generative powers, so far as something apprehended 39 by the mind can stand for something seized by the senses, or a mutable thing can stand for one that does not change, lighting up, as it manages to do, certain reflections and likenesses of the god’s kindness and blessedness.

“But as for his raptures and transformations when he sends out fire,116 raptures that they say tear him apart as he pushes the fire down, extending it towards the earth, the sea, the winds, and living things, and as for the violence undergone by both living creatures and plant life,117 to listen to such accounts is impious. In these accounts he seems more lowly than the poet’s child who builds castles in the sand and then scatters them, playing a game with the universe, building a world that did not exist, and, after it has been created, destroying it over and over again.118 To the contrary, insofar as he has come into the world in one way or another, he holds it substance together and governs its bodily weakness and its tendency towards destruction.

“It seems to me that to address the god with the words, ‘You are,’ is especially destructive of this theory and argues against it, asserting that no raptures or transformations take place in him, and that these acts and experiences belong to some other god, or rather demigod, whose appointed domain is nature, coming into being, and destruction. This is immediately clear from their names, which are directly opposed and antithetical. For one is called Apollo, the other Pluto; one the Delian, the other Aïdoneus; one Phoebus, and the other

Scotios.119 The Muses and Memory accompany the one, Oblivion and Silence the other.120

One is Theoros and Phanaeos; the other ‘the Lord of the dark night and sluggish sleep’,121 and he is also ‘of the gods the most hated by mortal men’.122 But Pindar sang not unpleasantly of

Apollo: ‘Towards mortals he has been judged the gentlest’, 123 and, similarly, Euripides quite rightly spoke of 40

libations for the departed dead, and songs, but not such as golden-haired Apollo welcomes;124 and even before him, Stesichorus:125

The harp, games, song, and dance Apollo loves the best, But the lot of Hades is sorrow and wailing.

And it is clear that Sophocles assigns to each god his own instruments: ‘Neither the harp nor the lyre is welcome for laments’.126 It was not for a long time, indeed only recently, that the flute dared make itself heard in sentimental airs; during earlier times, it drew forth lamentations and provided on these occasions a service neither highly esteemed nor much appreciated. But then, those conflating divine matters with the business of the demi-gods fell into confusion themselves.

“It seems that, in one way the E, ‘You are’, stands in opposition to the phrase, ‘Know yourself’, but in another way it is consistent with it. For the first is addressed to the god with awe and respect, proclaiming his eternal being, while the second is a reminder to mortal men of their nature and their frailty.”127

SECTION 1 COMMENTARY and NOTES 1. (1. 384 D) Sarapion was a poet and Stoic philosopher living in Athens. Plutarch himself had spent part of his youth in Athens, a university city, and he visited it from time to time as an adult. Sarapion (an Egyptian name; others occur in the dialogue) may have come from Hierapolis in Syria. He also appears in QC I, 10, 1. 628 A-B as a successful producer of choruses (Jones 1980, 229). Nothing of his work has survived, although he may be the author of two iambic trimeters (Bowie 2002, 45) collected in Stobaeus. Sarapion also appears as an active discussant and critic in De Pyth. 5. 396 F and 18. 402 F.

2. (1. 384 D) Dicaearchus was a student of Aristotle, a philosopher and writer. Only fragments of his work have survived. There is a tradition that Euripides wrote a tragedy, Archelaus, and that he died while in refuge at the Macedonian court of that king. If Euripides wrote such a play, it has been lost (William Ridgeway, “Euripides in Macedon.” Classical Quarterly 20, 1926, 1-19, and Scott Scullion, “Euripides and Macedon.” Classical Quarterly 53, 2003, 389-400).

3. (1. 384 D) It is not clear whether Plutarch attributes this quotation to Dicaearchus or to Euripides. Babbitt (1926, 199) assigns it to Euripides (Nauck, Euripides, frag. 969), although Helmbold-O’Neil attributes it to both Euripides and Dicaearchus (frag. 77). The fragment is written as a trimeter. The sentiment, but not necessarily the source, is important to Plutarch, since he is basing the direction of his proem on the notion of gift giving and fair exchange. Later Young Plutarch, citing Heraclitus, gives another instance of fair exchange (gold for goods…).

4. (1. 384 E) The pair of phrases “ill-mannered and servile … generosity and beauty” illustrates Plutarch’s arguably best known stylistic device, the doublet, balanced repetition, or “semi-synonym” (Sandbach, 1939). This particular figure has a chiastic structure, a common trope that also appears in Heraclitus. Some of these doublets are also hendiadyses (a figure where two words connected by a copulative conjunction express a single complex idea).

5. (I. 384 E) The notion of the first fruits orginated in sacrificial cults in classical times and in Old Testament scripture. While not central to Christian ritual, it came to be used metaphorically in the New Testament and later Christian writings, (H. D. Betz 1971, 218). Two millenia later, on admitting “Kwanzaa” into the English dictionary in 2009, the OED described it as the festival of the celebration of the literal “first fruits of the harvest”. So, the concept is still current and it still transcends parochial

interpretations. The phrase is used again (ἀπάρξασθαι τῷ θεῷ τῆς φίλης μαθηματικῆς, 7. 387 E) and appears in Plutarch’s De aud. 6.40 B; and Sept. sap. con. 6. 151 E.

6. (I. 385 B) Flacelière (1941, 33) notes that from this vantage point near the shrine one has a splendid view of the lower parts of the sanctuary, the ravine of Pleistos and Mount Kirphis. Tourists today still marvel at the imposing site of the temple. One can understand how Plutarch could have been influenced by the beauty and majesty of the place to recall an earlier meeting, or even to conceive the idea of writing of such a meeting. In addition, Plutarch was near the place where the three Es are said to have been displayed. Their presence would have contributed to the holiness of the place. This is, I believe, the only instance in the dialogue where Plutarch comments on the natural environment.

7. (I. 385 B) Nero visited the temple in 67 AD by our reckoning (Cassius Dio, Historia Romana, 62 20.5). The priests at Delphi kept meticulous chronological records, but Plutarch has not given us a precise date.

SECTION 2: COMMENTARY and NOTES

8. (2. 385 B) These five epithets reflect the progressive ascent through four levels of the getting of wisdom and understanding. Apollo was the slayer of the Python, and Pythian (compare πυνθάνομαι, “I inquire”) is an analogy to the first steps of an initiate. At the second level two names reflect dawning understanding. Apollo the “Delian” was born on the island of Delos, and the epithet allegorises the clarity (δῆλος, ‘‘clear”) of new understanding and of dawning revelation, which is also captured in “Phaneaus” (φαίνω, “I show, I bring to light”). At the third level, Apollo “Isemnios” fathered the Boeotian river-god Ismenos (an inversion of the usual epithet “son of”), which is analogous to those at the third level who “know” (ἴσµεν, first person plural of the perfective of εἴδω “I have seen”, and the present of οἶδα, “I know”). Pindar’s first Hymn to Zeus opens with Melia “of the golden spindle”, who bore Ismenos on the site of the oracular Ismenion near Thebes (Fontenrose 1978, 142; Hardie 2000, 20). At the fourth and final level, Apollo is “Leschenorios” from the Lesche, a large clubroom at Delphi built by the Knidians in 450 BC. The stem appears in λεσχηνεύω (“I converse”) and as the second term in the compound ἕλλεσχος (“that which provides material for conversation”), both suited to Ammonius’ analogic purpose. This progression, where the final stage of knowledge lies in conversation and communication, suggests that for Ammonius the acquisition of knowledge is a communal and social venture (as the dialogue itself exemplifies).

We may be sceptical about these linguistic derivations. Three of the names – Ismenos, Pythia and Delos–may be no more than toponyms. Babbitt comments on this section: “Plutarch’s attempt to

connect Ismenian with ἴδ (οἶδα) can hardly be right” (1936, 203). On the same passage, Flacelière calls the proposed etymologies “purement fanatasistes” (1941, 75 fn. 12). There are other etymological excursions within the dialogue: Young Plutarch contrasts the names and habits of Apollo and Dionysus (9. 388 F) and he recalls Socrates’ remarks on the name of the moon (15. 391 B). Ammonius returns to etymology in his final speech (21. 394 A).

Babbitt’s remark raises an interesting problem. He conflates the views that Plutarch attributes to Ammonius with those of Plutarch himself. It is a useful shorthand, but not always a defensible interpretation. I shall be at pains to attribute the views expressed by the speakers to the speakers themselves. Further, to attribute views to the speakers in the narrative is not necessarily to attribute them to the historical persons on whom these characters may have been modelled.

9. (2. 385 C) To my knowledge, the addition of the second “the seeking of answers” was introduced by Paton in 1893; it has been accepted by all editors since. When affairs of the god are hidden in riddles, we are led from the riddle into philosophy. Thus the rationale for including the second ˂τοῦ δὲ ζητεῖν ˃ is that it completes the path from uncertainty to inquiry to the beginning of philosophy through a syllogism. Certainly, enquiring, wondering, and doubting, or aporia, is the starting point of every philosophical investigation. This recalls “wonder is the feeling of a philosopher and philosophy begins in wonder” (Socrates in Theaetetus 155c-d).

10. (2. 385 C) The laurel tree was sacred to Apollo. The original temple to Apollo at Delphi was built with branches of laurel brought from Tempe (Paus. 10.5.9). The pass of Tempe, running from Macedonia into Thessaly along the river Peneus, was frequented by Apollo and the Muses (Herodotus Histories, 1.173). Finally, the Pythia chewed bay leaves while she was sitting on the tripod.

11. (2. 385 C) Pausanius, describing Delphi and its environs, describes the statues of the two Fates near the altar of Poseidon within the shrine; “but in place of the third Fate there stand by their side Zeus, Guide of Fate, and Apollo, Guide of Fate” (Paus 10.24.4) For the significance of the substitution of Zeus and Apollo, see Auguste Bouché-Leclercq (1879, 1.21):

Pindar [522-443 BC], né dans un pays fertile en oracles, était l’interprète de l’oracle apollinien de Delphes, alors à l’apogée de son prestige et son influence…. Dans le temple de Delphes, non loin du siège de fer où Pindar s’essayait, dit-on, pour chanter des hymnes en l’honneur d’Apollon, on voyait un groupe de statues représentant Zeus Mœragète et Apollon Mœragète associés à deux Mœres et tenant la place de la troisième. La théologie et l’art symbolisait ainsi cette union intime de la fatalité at la Providence, dont la raison ne devait jamais parvenir à élucider le mystère.

12. (2. 385 C) The matter of the tripod may be the question of how the Pythia performs divination. These mysteries come up in a mutilated passage in section 16. For the operation of the Pythia, see Parke and Wormell (1956 1, 24) and Bouché-Leclercq (1888, 3.89, fn. 2).

13. (2. 385 C) The imperative used in “look how these inscriptions…” (ὅρα δὲ καὶ ταυτὶ τὰ προγράμματα…) means more than simply “look”; a spiritual understanding is implied (Obsieger (2013, 116). The same construction appears earlier at “but see also that” (ὅρα δὴ ὅσον) (1. 384 D).

SECTION 3: COMMENTARY and NOTES

14. (3. 385 D) Ammonius, as we see later, is not persuaded by Lamprias’ argument that there were only five Sages, although numerous references link them to maxims displayed at Delphi, and in other places. Only Plutarch links them to the E. There are several accounts of the seven Sages, and their names vary. In Sept. sap. con. (1. 146 B), Plutarch (or Pseudo-Plutarch) tells of a symposium held in the distant past at Delphi for the sages, which not only the seven Sages but in addition “at least twice that number” attended. Their discussion of different forms of government conveys a pervasive “anti-tyrannical bias” (Aalders 1977, 32). The sages at that banquet were Thales, Bias, Pittacus, Solon, Chilon, Cleoboulos, and Anacharsis. Other participants included Aesop (probably a rough contemporary), and two women, Melissa and Eumetis. Periander arranged for the dinner,which was held near the shrine of Aphrodite. Plutarch discusses the sages (Life of Solon, 12. 4), noting that the group at Delphi “summoned to their aid from Crete Epimenides of Phaestus, who is reckoned as the seventh Wise Man by some of those who refuse Periander a place in the list”. The wise men, besides Solon, named there are Bias of Priene, Periander of Corinth, Pittacus of Mitylene, and Thales of Miletus. Thales is described as the “only wise man of the time who carried his speculations beyond the realm of the practical, while the rest earned the epithet from their excellence as statesmen”. The lists of wise men in other works are not consistent. Diogenes Laertius gives twelve who appear in one or other of the lists: Thales, Solon, Periander, Cleoboulos, Chilon, Bias, Pittacus, Anarchas the Scythian, Myson of Chenae, Pherecydes of Syros, Epimenides the Cretan, and Pisistratus the tyrant. (DL, 1.13). Plato gives us seven: Thales of Miletus, Pittacus of Mytilene, Bias of Priene, Solon of Athens, Cleoboulos of Lindus, Myson of Chenae, and Chilon of Sparta, describing them as enthusiasts, lovers and disciples of the Spartan culture, whose wisdom was exemplified by the short, memorable sayings that fell from them when they assembled together. (Plato Protagoras, 342e-343a).

Pausanias visited Delphi and commented on the wise men and their maxims, but not on the E. He gives us the seven names on Plato’s list, adding that of Periander, whose entitlement to a place amongst them was controversial. He adds that two of the sages dedicated to Apollo at Delphi the celebrated maxims, “Know yourself,” (γνῶθι σαυτόν, Thales of Miletus) and “Nothing in excess” (μηδὲν ἄγαν, Solon of Athens) (Paus 10.24.1).

15. (3. 385 D) Obsieger (2013, 123) interprets Lamprias’ description of “maxims and aphorisms” to mean that the transgression of the two rogue sages was some sort of plagiarism, or at least an appropriation of voice. Lamprias does not explain how they transgressed but Pseudo-Plutarch may be suggesting that, since Greek philosophers and thinkers were expected to walk the talk, their roles as tyrants made them unacceptable as sages. Cleoboulos and Periander were tyrants, of Lindos and Corinth respectively.

16. (3. 385 F) Flacelière comments that those connected to the sanctuary were more likely to be temple attendants (néocores) or accredited guides (périégètes) than priests (1941, 77, n. 20).

17. (3. 385 F) We can infer that “Livia, the wife of Caesar” is the wife of Augustus, since there was apparently no other Livia, wife of Caesar. I can find no contemporaneous account of Augustus at Delphi, although there is circumstantial support for such a visit. Augustus credited Apollo with his success at the Battle of Actium (31 BC) and increasingly identified with Apollo as his patron. That decisive battle took place near an old Apollonian sanctuary, which Augustus restored. He also offered ten ships from the spoils to the god and sponsored both the sanctuary in Delphi and the Delphic Amphictyony (Dietmar Kienast, Augustus: Prinzeps und Monarch, Berlin, Primus Verlag, 2009, 461- 462). Kienast gives the Chronicle of George Synkellos (ninth century) as his authority for the story that Augustus dedicated his sword to the Delphic Apollo. If Augustus visited Delphi with Livia, that visit would have been around 20 BC.

SECTION 4: COMMENTARY AND NOTES

18. (4. 386 A) The adjective (or noun) “Chaldean” was not, by Plutarch’s time, a mark of ethnicity but a term for astronomers and astrologers. The province of Chaldea in the Achaemenid Empire (539–330 BC) disappeared from the historical record during the time of the Roman Empire.

19. (4. 386 B) The “seven sounds amongst the letters that make a complete sound by themselves” are the vowels. A consonant is an alphabetic or phonetic element that forms a syllable when combined with a vowel. The seven vowels are α, ε, η, ι, ο, υ, and ω. The Greek alphabet, with its

vowels, was a distinct innovation from the Semitic consonantal system, and part of the relatively recent evolution of an oral culture to one with a written language. Dionysius Thrax (170-90 BC), a student of Aristarchus, produced our earliest extant Greek grammar (Τέχνη γραμματική) setting out the classification of vowels and consonants (Obsieger 2013, 127; Robins, 1957; and Di Benedetto, 1990).

Notice that Plutarch is shifting the ground beneath our discussants’ feet. Lamprias has just described the Wise Men as dedicating “that one of the letters which is fifth in alphabetical order and which stands for the number five”, saying that the (rump of) the Wise Men used the E (which also happens to be a vowel) because it represented their number – five. The Chaldean is talking exclusively about the vowels in the Greek alphabet, and making a point about the equivalence of the number of vowels in Greek and the number of wandering stars in the sky. By using these two ways of comparing letters and numbers, he has introduced an astrological dimension into the discussion. He then compares the elements lying in second place in those two series – the E and the sun.

20. (4. 386 B) The E is a symbol of Apollo because it occupies the same place within the hebdomad of vowels as does the sun, another symbol of Apollo, within the hebdomad of the wandering stars. The seven celestial bodies, the Moon, the Sun, Mercury, Venus, Mars, Jupiter, and Saturn (ἀστέρας πλανεται), are visible to the naked eye. Their independent movements differentiate them from the fixed stars outside the solar system. The designation as wandering stars appears in Aratus’ Phaenomena, a tract hugely popular in Imperial Rome, in part because of Cicero’s translation (Aratea). Lucretius also used it when he denounced the notion that the universe is the result of intelligent design (De Rerum Natura, chapter 5). See also Ellen Gee, Aratus and the Astronomical Tradition, 2013, chapter 3.

21. (4. 386 B) Babbitt (1936, 207) has described the sentence “[they] come from star books and the rumours chattered about at the gates of the sanctuary” as being as obscure in the Greek as in the English. No one has disputed his opinion. The source of the problem lies in the apparent idiom ἐκ πίνακος καὶ πυλαίας. The first word, πίναξ, is straightforward, but polysemic. It can mean a piece of lumber, a board, a plank, a slab of slate, a writing surface, a tablet, or a votive tablet. It can also refer to an astrological tablet, or the booklets of fortunes used by fortune tellers. The second, πύλη (here as an adjective πυλαίας), can be a toponym or a geographical feature (a mountain pass, a sea strait). It can also mean a gate, an entrance, one wing of a double door, or the gates to Hell. These two words have been yoked here in Plutarch’s favourite construction, a doublet.

Plutarch constructed this section by first describing in the indirect speech of unidentified speaker, the way the Chaldean spoke (he “spoke nonsense”, “played the fool” or “prated”). The Chaldean used the imperfect tense, suggesting that he might have gone on at length. Next comes a crescendo of the Chaldean’s claims – the seven stars, the seven vowels, the sun, and the E in the same place in their respective hebdomads, and the sun almost universally recognized as a symbol of Apollo.. Finally, in direct speech, signalling the climax of his description, the speaker exclaims, “But all of these ideas come from star books and the rumours chattered about at the gates of the sanctuary.” We know what he means, even if we cannot parse every word.

There is a similar phrase, denoting much the same thing –μετεωρολόγοι καὶ ἀδολέσχαι τινές (“sky-watchers and chatterers” or “high thinkers and great talkers”) but with ambiguous connotations. The first term has a history of serious usage, but in Aristophanes’ Clouds, meteorological investigation, using this word, is consistently and satirically associated with the Sophists (228-230, 333, 360; see also Trivigno 2012, 58). Plato uses the words several times in Book 6 of The Republic,where a helmsman is accused by his crew of being a “star-gazer and chatterer”. Plato compares the captaining of a ship to the management of the ship of state (Rep. 448e, 489a, and 489c). His point is that some star-gazing, or “high-talking” is required to attain a theoretical as well as a practical understanding of one’s craft.

22. (4. 386 B) Lamprias suggested earlier that his interpretation of the E could be supported by listening to “the explanations of those connected to the sanctuary” (γνοίη τις ἂν ἀκούσας τῶν κατὰ τὸ ἱερὸν, 3. 385 F). Here Plutarch speaks specifically of “guides” who must be amongst those in the group. Elsewhere, Plutarch mentions a guide called Praxiteles (QC, 3. 675 and 8. 4. 723). C. P. Jones discusses the descriptions given by Pausanias and Plutarch of guides at some religious sites. In De Pyth. Diogenianus, a young man from Pergamum, is being led around the sanctuary by Plutarch’s friend Philinus and other learned men. Philinus describes the guides going through their prepared speeches, paying no attention to their little flock until they are asked to shorten their monologues and drop the discussion of the inscriptions. Later, when the visitors begin to contribute their own abstruse opinions, Theon comments, “We seem, my friend, to be rather rudely depriving the guides of their proper job” (ἀλλὰ καὶ νῦν ὦ παῖ, δοκοῦμεν ἐπηρείᾳ τινὶ τοὺς περιηγητὰς ἀφαιρεῖσθαι τὸ οἰκεῖον ἔργον, 7.397 E).

The guides that Pausanias might have had and those that Plutarch might have known were “local informants who are able to hold their own in the company of ‘the educated’ and those

belonging to the kind of society that Plutarch portrays in his Moralia, with its mixture of sophists, professors of literature, philosophers, lawyers, doctors, and wealthy amateurs”. (Jones 2001, 36).

23. (4. 386 C) The guides believe that the name “εἰ”, carries the symbolism, not, as Lamprias asserted, the pentad or the letter E. As we see later, Ammonius puts forward the view that the significance of “ει”, lies in its semantic meaning, “you are”.

SECTION 5: COMMENTARY AND NOTES

24. (5. 386 C) Nicander also appears in De def. (51. 438 B), where he is an officiating priest during the incident of a Pythia who became ill during an interpretation of an oracle. In that passage, Nicander is called a prophet (προφήτης). This may simply describe his function as an assistant to the Pythia but it is probably not an exact synonym for priest (ἱερεὺς). His speaking on behalf of the temple personnel suggests that his role in the dialogue is to present a specifically religious explanation of the meaning of E, opposed to the views of the Stoics, which appear later in the dialogue.

25. (5. 386 C) Wyttenbach has read σχῆμα (“form, shape, construction, or figure”) as ὄχημα (a vehicle, animal or mechanical, for carrying freight, including human beings). Obsieger prefers the latter reading, although Goodwin has produced the reasonable, “a conveyance and form of prayer to the God”, where “conveyance” means a grammatical structure. Nevertheless, the phrase, “the shape and form of every prayer to the god” has rhythm, reflects the semi-synonyms “σχῆμα καὶ μορφὴ”, and avoids the possible hendiadys in “a conveyance and form of prayer”.

26. (5. 386 C) Nicander claims that “if” [εἰ] is the first word in the phrase containing the question used by a suppliant as he addresses the god. For the sake of comparison, I have included some examples of such questions contained in a collection of selected papyri (Hunt-Edgar 1932, 436-439). They provide two complete addresses to oracles (#193, and #194) and twenty-one single sentence questions to the oracle portmanteaued into entry #195, all demonstrating Nicander’s contention. These are papyri from the Christian era, up to the fourth century AD. I reproduce the first five of the short questions for the oracle and the two longer addresses in Greek and English (my translation)::

195. From a List of Questions to an Oracle (about the year 300)

εἰ λήμψομαι τὸ ὀψώνιον (if I am to receive an allowance) εἰ μενῶ ὅπου ὑπάγω (if I am to remain where I am going) εἰ πωλοῦμαι (if I am to be sold) εἰ ἔχω ὠφελίαν ἀπὸ τοῦ φίλου (if I am to receive what is owed me by a friend)

εἰ δέδοταί μοι ἑτέρῳ συναλλάξαι (if I am allowed to enter into a contract) The rest of the twenty-one questions have the same structure, although the substance varies. These are clearly not complete sentences so I have refrained from punctuating them. They lack context and have the artificial air of our own FAQs. One can imagine that such a list might have been available at the temple to help suppliants formulate their questions. In contrast, consider the two complete addresses to the oracle, where the context, the “by whom and to whom”, is established at the outset:

193. Question to an Oracle (P. Oxy. 1148. 1st cent. AD)

Κύριέ μου Σάραπι Ἥλιε εὐεργέτα. εἰ βέλτειόν ἐστιν Φανίαν τὸν υἱό(ν) μου καὶ τὴν γυναῖκα αὐτοῦ μὴ συμφωνῆσαι νῦν τῷ πατρὶ α(ὐτοῦ), ἀλλὰ ἀντιλέγειν καὶ μὴ διδόναι γράμματα· τοῦ-τό μοι σύμφωνον ἔνεν-κε. ἔρρω(σο).

O Lord Sarapis Helios, beneficent one. (Tell me) if it is fitting that Phanias my son and his wife now quarrel with me, his father, but oppose me and do not contract with me. Tell me this truly. Goodbye.

194. Question to an oracle (P. Oxy. 1149. 2nd cent. AD)

Διὶ Ἡλίῳ μεγάλωι Σεράπ[ι]δι καὶ τοῖς συννάοις. ἐρωτᾷ Νίκη εἰ σ[υ]μφέρει μοι ἀ[γο]ράσαι παρὰ Τασαρ[α]πίωνος ὃν ἔχει δοῦλον Σαραπί-ωνα τ[ὸ]ν κα[ὶ Γ]αΐωνα. [τοῦτό μ]οι δός.

To Zeus Helios great Serapis and his fellow gods. Nike asks if it is to my advantage to buy from Tasarapion her slave Sarapion also called Gaion. Grant me this.

Indirect questions are used in these two addresses, since the petitioner prefaces his question with a syntagma “tell me”, “I ask” or “Nike asks”. The interrogative use of εἰ is derived from the conditional, where the protasis is elided thus, “do tell me whether you will save me” (σὺ δὲ φράσαι εἴ με σαώσεις). This helps us to understand the next point about the identity of the dialecticians.

27. (5. 386 C) “Those dialecticians”were not only grammarians but also logicians who investigate the meaning of syllogisms. The construction of the syllogism contributes to its meaning, (just as word order contributes to the meaning of an English sentence) and it may be expressed with or without the “if”. Simple indirect questions to the god are compressed syllogisms, introduced by an interrogative εἰ; and they have real premises. According to Nicander, the god understands that all these questions proceed from real premises.

28. (5. 386 C) “If only I could’ is the usual expression of a wish”. Despite its appearance here in a verse from Archilochus, the expression ‘εἰ γὰρ’ was used most often in the “exalted style of tragedy” (GP 1959, 93), and the εἰ in wishes was, from Homer on, seen as a conditional. Nevertheless, it can be

difficult to make a distinction between wish and condition, as the variations in editors’ punctuations show. “The difference between ‘If only James were here! He would help me.’ and ‘If only James were here, he would help me.’ is merely the difference between an apodosis at first vaguely conceived, and then clearly defined, and an apodosis clearly envisaged at the outset.” (GP 1950, 90). Nicander asserts that γὰρ reinforces εἰ and turns “if” into “if only” just as θε does to εἴ in εἴθε

29. (5. 386 D) We owe the fragment “to touch the hand of Neobule” to Plutarch (Bergk, frag. 402; Helmbold-O’Neil, frag. 6). Almost nothing substantial written by Archilocus, a lyric poet from the seventh century,was known to have survived, until recently. In 1974, an almost complete poem was discovered in Cologne on a second-century papyrus. This poem, about Neobule and attributed to Archilochus, complements the fragment cited by Plutarch, and gives us quite a different perspective on the story of Neobule. In the old story of the Parian Lycambes and his daughter Neobule, Lycambes had betrothed Neobule to Archilochus, but later reneged on the agreement. Archilochus responded so violently that Lycambes, Neobule, and one or both of his other daughters committed suicide (Gerber 1997, 50; 1999, 75; QC, 3. 10. 657-659). Nevertheless, when R. Merkelbach and M. L. West (1974) translated the new poem, they interpreted it differently. On their interpretation, Archilochus had wreaked revenge on Lycambes by debauching his younger daughter. Next, in 1975, Miroslav Marcovich provided a commentary and a competing interpretation, writing:

I am in strong disagreement with [Merkelberg and West’s] interpretation. I think we have to do with a fresh and naïve love story. The main purpose of this paper is, however, to improve our text of the poem by offering a somewhat different edition of the papyrus and to provide it a literary-philological commentary. The time for a definitive literary assessment of the poem has not yet come. The two modern interpretations of the poem are difficult to reconcile. Certainly, since Nicander is making a grammatical argument, the structure of the phrase (that is, the use of “if”) is more important than the semantic content and the narrative of the poem. We are not required to come to a definitive interpretation of the poem. But we can ask ourselves why, to a illustrate a fine point in grammar and within the context of a discussion of the meaning of the E held at one of the foremost oracles in Greece, Nicander introduced this colourful and controversial story. Our ignorance of the conventions of Plutarch’s time and place make it difficult to interpret this story in its recently expanded context. We may never completely understand this passage, nor Nicander’s choice of examples. 30. (5. 386 D) I have chosen to translate “καὶ τοῦ ‘εἴθε’ τὴν δευτέραν συλλαβὴν παρέλκεσθαί φασιν” with the paraphrase ‘if only’, one can say that the second word is not necessary”, using

“second word” instead of “second syllable” (τὴν δευτέραν συλλαβὴν) in full awareness of the stricture to translate the words on the page.

31. (5. 386 D) Sophron, a contemporary of Euripides, wrote in the Doric dialect, hence we find the forms δευομένα and δευμένα in different editions of the fragment (Kaibel 1899, 160 1). Obsieger prefers the Doric, but gives a complete list of the variants. As to the word θην, it is an enclitic with a vaguely affirmative connotation used almost exclusively in poetry.

32. (5. 386 D) This is a citation from Iliad, 17. 29, where Menelaus is threatening Euphorbus during their encounter over the disposition of the body of Patroclus.

33. (5. 386 C) Nicander has used three quotations to illustrate his conclusion, “so, as they [the Delians] say, the optative force is quite clear in the ‘if’.” Considering the first use of “if” – εἰ γὰρ – he argues that γὰρ is an intensifier that strengthens εἰ to the equivalent of the Latin “utinam”, or the English “if only” or “would that”, thus the simple conditional has the added connotation of yearning or need. He then remarks that the exclamation εἴθε (would that) is of the same structure as εἰ γὰρ, so that the second syllable of εἴ-θε performs the same function as γὰρ in εἰ γὰρ. The next step is to associate the second syllable of εἴ-θε with θήν, meaning “surely now”, which gives θήν the same semantic coloring as γὰρ in εἰ γὰρ.

Nicander asserts that εἰ γὰρ and εἴ-θε have the same structure and perform the same function, and thus demonstrates the equivalence of the particles γὰρ and θε, but gives us no example of the εἴ-θε in actual use. His last two examples are on the use of θήν, which, he asserts performs the same function as θε. In any case, he has demonstrated that εἰ is used in addresses to the god, but this is not the only use of the conjunction. As Ammonius says later, it is also in common use in everyday speech.

SECTION 6: COMMENTARY and NOTES

34. (6. 386 E) Plutarch’s friend Theon (as opposed to another friend Theon, a grammarian) appears in QC. 630 A, and is probably the Theon of De Pyth.who leads the discussion in Non poss. suav. Given his modest demeanour, his deference to Ammonius, and his concern for Dialectic, he is probably a young man and a student. He expounds Stoic ideas and is probably known to Sarapion.

35. (6. 386 E) Plutarch, the narrator, describes Theon’s and Ammonius’ personification of “Dialectic”. Other translations also preserve the personification (Babbitt, Holland, King, and Amyot). Dialectics (or logic) was one of the seven liberal arts considered the basis of a good education in the Middle Ages. In early Greek literature, especially Homer, personification played an evocative and

picturesque part. The liberal arts, the seasons, human emotions, and so on continued to be portrayed in art and literature as beautiful young women up to the Middle Ages and beyond.

36. (6. 386 E) Theon claims that Socrates used dialectics to successfully interpret an Apollonian oracle. The story goes that the oracle at Delphi told the Delians that by building a new altar at Delos according to certain requirements they could be delivered from the plague that was then afflicting them. After a couple of unsatisfactory attempts, the Delians consulted Socrates (according to Plutarch in De gen. Socr. 7. 579 A), who interpreted the oracle as a covert method to spur the Delians to learn mathematics and geometry. Socrates’s knew, as apparently the Delians did not, that Apollo set great store by geometry, and practised it himself. Alice Riginos, in her work on the life of Plato, states that she has not been able to trace information about Apollo’s interest in geometry beyond Plato (Riginos 1976, 145; Kouremenous 2011, 349). Plutarch reports another anecdote about Plato’s (and Apollo’s) interest in geometry. He asks the question, “What did Plato mean when he said that god always plays the geometer?” at a symposium held to celebrate Plato’s birthday (QC 8. 718 C-F). Plutarch claims that Plato deplored the mechanical apporach to the solution of the cube problem, as introduced by Eudoxus and Archytas.

37. (6. 387 A) The proposition “if it is day then it must be light” was used in Stoic teaching of elementary dialectics. Flacelière, citing Sextus Empiricus (SVF. 2 216, and 279), shows that this example was part of the elementary curriculum. Other examples of the “if it is day…” construction occur in Chrysippus (SVF 2, 726 ff.); Sextus Empiricus, Outlines of Pyrrhonism, (1 62-72); and Aelian, De Natura Animal. (4, 59). The proposition is reminiscent of the Heraclitean fragment (Diels 99, Kahn 46, Bywater 31), which Plutarch (or Pseudo Plutarch) gives in Aqua. an ignis (957 A):

Ἡράκλειτος μὲν οὖν, “εἰ μὴ ἥλιος,” φησίν, “ἦν, εὐφρόνη ἂν ἦν”. For as Heraclitus says, “If there were no sun, it would be perpetual night”.

Despite his differences with the Stoics, Plutarch displays a strong affection for Chrysippus, or certainly a strong predilection for writing about him. Chrysippus is not mentioned by name in De E, only by his work. He appears often in the Moralia; O’Neil (2005, 142-146) has dozens of references over five close-printed pages. Diogenes Laertius (Book 7) says that Chrysippus wrote 705 books (some of more than one volume) and names them all.

38. (6. 387 A) Obsieger makes the connection from αἰσθάνομαι, αἰω, to perceiveto Plutarch’s De soll. anim. (13. 969 A), where Plutarch discusses Chrysippus’ theory of perception.

39. (6. 387 B) Here we recognise the Stoic theory of divination, that all acts and events are intimately linked and that “he who has the natural capacity to connect causes and link them together, also knows how to foretell”. These links may be beyond human understanding, although sometimes Providence reveals them. Although we may not see the link between the flight of a bird or the colour of the liver of a sacrificial victim, and the outcome of a battle, it is not impossible that there is one. (Bouché-Leclercq 1879-1882, 2: 59-60)

40. (6. 387 B) It was said of Kalchas, the bird interpreter and priest of Apollo, that he knew “all things that are, the things to come, and the things that are in the past.” (Iliad, 1. 70). The phrase “bird interpreter” resonates with the “wolves and dogs and birds” introduced in the syllogism. The use that Theon can make of a literary allusion suggests that he is indeed a good student.

41. (6. 387 D) Swans and lyres appear in the Homeric Hymn 21, to Apollo, where the swan sings with clear voice to the beating of his wings, while Apollo thrums his high-pitched lyre. Nevertheless not all swans are musical, as Lucian reports on his encounter with boatmen in northern Italy when he quizzed them on the swans living on their river (probably the Po): We are always on the water and have worked on the Eridanos since we were children, almost; now and then we see a few swans in the marshes by the river, and they have a very unmusical and feeble croak; crows and daws are Sirens to them. As for the sweet song you speak of, we never heard it or even dreamt of it, so we wonder how these stories about us got to your people. (Lucian, On Amber, quoted by Krappe 1942, 354) There are two kinds of swans – the mute (Cygnus olor) and the whooper (Cygnus musicus or ferus). For those born in the high latitudes of the northern hemisphere, the idea that a swan’s call could be musical is laughable. The swans are physically alike, but their calls and habits differ. The whooper swans of the North descend into western and central Europe during their yearly migrations. With their musical calls and rhythmic wing beats they could be well be Apollo’s swans. The god himself, in his blond, Hyperborean incarnation, migrated yearly to the Amber Isles (Krappe 1942; De def.).

42. (6. 387 D) The phrase “a regular yokel” is literally, “a real Boeotian”. For the Athenians “Boeotian” was a byword for an uneducated and unsophisticated person from the countryside. Pindar, Hesiod, and Plutarch himself, hardly ignorant or uncultured men, were from Boeotia, as was Hercules and that great riddler, Oedipus.

Pierre Guillon points to Athens as the nexus of this prejudice against the Boeotians, a prejudice that appears to have existed even in prehistory (La Béotie antique 1948, 79-92). As to its

cause, some blame the climate. Cicero (De fato, 4 71) observes, “Athens has a light atmosphere, whence the Athenians are thought to be more keenly intelligent; Thebes a dense one, and the Thebans are fat-witted accordingly”. By putting into Theon’s mouth, ‘le préjugé habituel contre ses compatriotes’ (Flacelière 1941, 81) Plutarch does not hesitate to laugh at his own origins. Nevertheless, by not keeping the word “Boeotian”, I may be missing the irony that Guillon sees (1948, 85) in “Hercules, a real Boeotian, began by disdaining logic”. (See below.)

43. (6. 387 D) Hercules, a demi-god in the Olympian pantheon, was an important figure at Delphi. A month was named after him, and the theft of the tripod was illustrated on a pediment. Since Theon is expounding Stoic philosophy, it follows that he would give an account of Hercules, the incarnation of wisdom for the later Stoics. Plutarch also has the Cynic, Didymus Planetiades, mention the legend when he responds testily to Demetrius’ invitation to discuss the reason for the obsolescence of the oracles. He points out that at Delphi the tripod (sc. the oracle) is constantly occupied with shameful and impious questions…about treasures or inheritances or unlawful marriages (αἰσχρῶν καὶ ἀθέων ἐρωτημάτων… περὶ θησαυρῶν ἢ κληρονομιῶν ἢ γάμων παρανόμων διερωτῶντες De def. 7. 413 A). The myth of the struggle for the tripod between Hercules and Apollo, in which Zeus intervened, is very old and illustrations appear in early vase painting (Burkert 1982, 121).

44. (6. 387 D) Theon accepts that the E is in fact “if”, and that the syllogism “if the first then the second” represents the young ruffian who ridiculed the E and then the older man who inevitably fought with the god. Nevertheless, in his later years this ruffian became a prophet and dialectician.

There is a different interpretation of this passage; one that relies on the argument that there are no problems with the text in “if the first then the second”. Alain Lernould (2000) argues that to carry off the tripod and to fight with the god signifies the negation of philosophy by the brutality of the young Hercules, and that Theon manages to integrate this episode into his argument for the supremacy of Apollo and of dialectic in a “quite Pascalian manner”. In other words, Theon gives a typically Stoic allegorical interpretation of the taking of the tripod, where this unfortunate exploit is presented as the inverse image of moral perfection.

SECTION 7: COMMENTARY and NOTES 45. (7. 387 E) By qualifying his introduction of Eustrophus with “I think”, Plutarch the author is establishing to Sarapion that he is recalling, perhaps inexactly, a past conversation. He uses the present tense (οἶμαι) and Eustrophus the aorist. By the end of the section this identification of Eustrophus is secured by the intimacy described between Eustrophus and Young Plutarch.

46. (7. 387 E) Notice Eustrophus’ repetition of Plutarch’s imagery of first fruits (1. 384 E). Indeed, this could be Plutarch speaking.

47. (7. 387 E) Counting by fives generates the five times table. The verb πεμπαζομαι evolved to mean counting or computation in general. Obviously, there is a physical analogue – the fingers on one hand. Plutarch includes this example in another discussion of the number five (De def. 429 F). There is another mnemonic that allows us to count to twelve (and from there to sixty, or 5 x 12) – the number of joints on the four fingers of one hand, forgetting the thumb. This is also the derivation of the term “dactylic hexameter” (one long and two short syllables, in the same order as the three joints of a finger).

48. (7. 387 F) The ironic tone of this sentence suggests, to me at least, that Plutarch in his maturity, while not denying the importance of the study of mathematics in any young person’s education, might have found Eustrophus’ views on mathematics (and even Young Plutarch’s) over enthusiastic. See appendix B for a discussion of free indirect discourse, and its role in expressing irony. In contrast to Wyttenbach’s τάχα δὲ μέλλων, Obsieger follows Sieveking, Flacelière, Cilento, and Babbitt in preferring τάχα δὴ μέλλων. He finds parallels for τάχα δη as "soon" in Sept. sap. con. 2. 148 A and De soll. an. 2. 96 A. The irony in this sentence is strengthened by the use of δὴ, (“verily”, “actually”, or “indeed”), according to Denniston (GP 229). Denniston is writing about Greek literature up to the end of the fourth century (320 BC) and so does not include quotations from Plutarch; he does, however, comment on many of the authors Plutarch quotes.

SECTION 8: COMMENTARY and NOTES In this section, I have relied heavily on the ideas in Theologoumena Arithmeticae, which is a compilation of a text with the same name by Nicomachus of Gerasa and a lost work, Peri Dekados, by Anatolius. Waterfield comments that it “often reads like little more than the written-up notes of a student” (Waterfield 1988, 23). He considers the work valuable for three reasons: it preserves material that might otherwise have been lost, it demonstrates that arithmology survived amongst the Greeks alongside “hard” mathematics, such as that of Euclid, and it is a witness to the survival of Pythagorean ideas long after the time of the Pythagorean school.

50. (8. 388 C) Plutarch does not signal this as a reference to Heraclitus but it is reminiscent of, “every point on a cycle (or a circle) is simultaneously the beginning and the end” (Ξυνόν γαρ αρχή και

πέρας επί κύκλου περιφερείας κατα τον Ηερικλειτον).The source for this fragment is Porphyry, Quaestiones Homericae, Iliad XIV, 200 (Bywater 70, Diels 103, Kahn 94). Nevertheless, resonances exist both between the rhythms of nature, the cyclic return of the numbers five and six, and the notion of mercantile exchange.

51. (8. 388 E) That only the five and the six, when multiplied by themselves, reproduce and repeat themselves is clear both in the Greek and the decimal numbering system. In the decimal system 5 x 5 = 25, and 6 x 6 = 36. The five and the six reappear as the last digits in the multiplication. The same result appears in the Greek system, where ε x εʹ = κ εʹ, and ϝ x ϝʹ = λϝʹ.

52. (8. 388 E) It is not quite correct that, “six does this only once, when it is squared”. All the higher powers of six end in six (216, 1296, 7776, and so on). Similarly, all the higher powers of five end in five (125, 625, 3125,…). For the powers of five and six, there is complete parallelism between the Greek and decimal systems.

53. (8. 388 E) The five generates this result with every multiplication, it produces either ten or itself in turn. In our number system the sequence is {5, 10, 15, 20, 25, 30,…}; in the Greek, it is {εʹ, ιʹ, ιεʹ κʹ, κεʹ, λʹ, λεʹ, μʹ, μεʹ, νʹ, νεʹ,…}. The alternate terms have εʹ as the last digit, and every literate and numerate Greek would know (I imagine) that the numbers ιʹ, κʹ, λʹ, μʹ, νʹ, … represent the tens.

54. (8. 388 E) The comparison, “like gold for goods and goods for gold” is one of the three instances in the dialogue where Plutarch explicitly cites a fragment from Heraclitus (see also 18. 392 C, and 18. 392 D). Plutarch himself is the authority for this fragment. Obsieger’s text has: πυρός τε ἀνταμείβεσθαι πάντα φησίν ὁ ̔Ηράκλειτος καὶ πῦρ ἁπάντων, ‘ὅκωσπερ χρυσοῦ χρήματα καὶ χρημάτων χρυσός’, which is slightly different from Diels’: πυρός τε ἀνταμοίβη τὰ πάντα καὶ πῦρ ἁπάντων, ὅκωσπερ χρυσοῦ χρήματα καὶ χρημάτων χρυσός (Diels 90 , Bywater 22, Kahn 40). Bywater’s version is different again. Discussing these differences is beyond the scope of this translation, nevertheless the question of how to introduce new scholarship and new discoveries into existing compilations of fragments is an interesting one.

The verb ἀνταμείβομαι (middle, meaning “to give or take in exchange, to requite or punish, i.e. to give punishment in exchange for bad behaviour”) appears only once in the fragment but is part of each half of the simile. Its meaning shifts slightly, from the cosmic context where all things are

consumed in fire to its mercantile meaning of goods for exchange and gold as a medium of exchange and a store of value.

The economic concepts of gold as a store of value and a medium of exchange may have been common coin in the ancient world. Pindar begins the Fifth Ismenian Ode with an apostrophe to Theia, mother of the sun:

Illustrious mother of the solar beam, Mankind, bright Theia, for thy sake esteem The first of metals, all-subduing gold; And ships, oh queen! that struggle in the deep, With car-yoked coursers o’er the plain that sweep, To honour thee, the wondrous contests hold. (Trans. by C .A. Wheelwright, 1846)

Pindar has taken the simile of exchange that appears in Heraclitus and transformed it into a metaphor for the power and primacy of gold, a substance that subdues all others by the ease with which it facilitates the exchange of commodities. Webster (1954, 20) sees the personification of the sun (or at least the mother of the sun) as conveying the notion of value. Gold is a very special metal (Hesiod used gold as the primary metal in his identification of the ages of mankind) and it has always been a symbol of light and beauty, and the invulnerability and immortality of the gods. (O. Betz, 1995, 20). Phoebus Apollo, unlike other Olympians, was blond.

SECTION 9: COMMENTARY and NOTES

55. (9. 388 E) With “But what is this to Apollo?” Plutarch is playing on the phrase, τί ταῦτα πρὸς τὸν Διόνυσον; (what is this to Dionysus?) and Young Plutarch is using it, a procatalepsis, to forestall questions from his audience about how he got from the pentad (and the E) back to Apollo.

Athenian tragedy developed out of the cult practices of the worship of Dionysus; but when two early poets, Phrynichus and Aeschylus, began to move away from Dionysus and to treat other myths, their efforts were greeted with the quip, “But what has that to do with Dionysus?” (Pickard- Cambridge 1927, 80; Obsieger 2013, 199). Since that time, the Bonmot (to quote Obsieger) had been used to signal doubt about the relevance of a remark, or to mark a digression. The phrase must have been well worn by Plutarch’s time. Plutarch uses the figure to good effect in the first of his QC (1 1 5. 615 A), “Whether philosophy is a fitting topic for conversation at a drinking-party”.

56. (9. 388 E) The presence of other deities besides Apollo at Delphi is well known. Apollo, bringing his mother and sister, Leto and Artemis, arrived at Delphi long after Gaia but before Athena joined the celestial deities who were worshipped side by side with the Chthonians. The temple of Athena, in front of that of Apollo, was one of the group of four temples seen by Pausanias on his entrance into Delphi (Paus 10.2.1). Even as late as Plutarch’s time there was a temple to Gaia near the temenos of Apollo; and the Chthonian Dionysus shared with Apollo the worship in his innermost sanctuary (Middleton 1888, 282).

57. (9. 388 E) LSJ defines θεόλογος (“theologian”) by example: “one who discourses of the gods, used of poets such as Hesiod and Orpheus.” Heraclitus, who would be one of these authors, was mentioned in section 8 precisely on the phenomenon of cyclical flow. Young Plutarch may perhaps be relying on these authorities.

58. (9. 388 E) Young Plutarch makes it clear that this god is Apollo, although in the manic and manifold phase of his cycle he is called Dionysus. This duality is vehemently denied later by Ammonius when he introduces the daimones.

59. (9. 389 A) Dionysus, Zagreus, Nyctelius, and Isodaetes are all names associated with Dionysus. Ammonius has already etymologized five of Apollo’s epithets (2. 385 B), and he will analyse “Apollo”, “Phoebus” and “Ieius” later, in section 20. 393 C.

Zagreus, the son of Zeus and Persephone (or perhaps Hades and Persephone) was sometimes identified with Dionysus. Although the name does not appear in the extant Orphic fragments, he is sometimes identified with the Orphic Dionysus. Flacelière (1941, 84,) called the name Isodaetes “une épithète fort rare”, defining it as “that which is divided equally”. He believed that it might be a ritual name for Dionysus. Obsieger (2013, 207), on the other hand, states that he has not seen an explicit link between Dionysus and Isodaetes, although Pluto, with whom Dionysus is identified, is sometimes called Isodaetes. Pickard-Cambridge (1927, 81-82) comments:

The contrast between the dithyramb and the paean… dates from a time long after the fusion of Dionysus with Zagreus and the development of the mysteries in Greece. Plutarch is perhaps somewhat fanciful when he tries to prove the appropriateness of the distracted music (evidently that of the later dithyramb) with the experiences attributed to the later deity. There is no hint elsewhere of any association of the dithyramb with any of the mystic cults referred to.

60. (9. 389 B) This fragment from Aeschylus can be found at Nauck 1889, Aeschylus frag. 355.

61. (9. 389 B) Plutarch also uses the phrase “Dionysus of the orgiastic cry” in De exil. 607 C and QC, 667 C. Compare Bergk 3.730.

62. (9. 389 C) In Heraclitean cosmogony, κόρος (satiety) corresponds to διακόσμησις, the orderly arrangement of the universe, especially in the Pythagorean system, while χρησμοσύνη (need, want, poverty) to the time of the ecpyrosis. Fairbanks (1897, 41) sees these as Heraclitean catchwords, while Kahn (1979, 276) believes that their links to Heraclitus are confirmed by independent citations in Plutarch (here), Philo (Allegorical Interpretation, 3.7) and Hippolytus (Refutatio Omnium Haeresium 9.10.7), see also Marcovich (1967, 292, 296). The Stoics interpreted these as successive stages in the cosmic cycle. (See Bywater 24, Diels 65; Marcovich 55, Kahn 120).

63. (9. 389 C) Since the ratio of three months to the year is one to four, the “relation of the period of orderly disposition to that of fiery destruction”is three to one. Kirk comments that, while Plutarch is obviously drawing on a Stoic source; “the ratio of 3 to 1 for the length of ecpyrosis and cosmogony may be his own, rather than a Stoic, invention – it rests on the three-month tenure of Dionysus at Delphi as compared with the nine-month tenure of Apollo” (Kirk 1962, 358).

SECTION 10: COMMENTARY and NOTES

Young Plutarch’s interpretation is, in my opinion, a reductive and mechanical approach to music theory, since he is more interested in developing an application of the number five than in improving his listeners’ (or his own) understanding of music. On the same note, Goodwin in the first footnote to his translation of Pseudo-Plutarch’s De mus. introduces the caution: No one will attempt to study [italics in the original] this treatise on music, without some previous knowledge of the principles of Greek music, with its various moods, scales, and combinations of tetrachords…. An elementary explanation of the ordinary scale and of the names of the notes (which are here retained without any attempt at translation) may be of use to the reader. (Plutarch’s Morals 1874, vol 1)

The section is both terse, and technical, so that it requires at least a few comments on ancient music and harmony before beginning. It contains music theory no less difficult than that in De mus. but it is shorter, merely underlining the importance of the number five in yet another field of study. The reader can accept that point without a deep understanding of Greek music theory. Here I have relied on both West (1994) and Barker (2012). The following three terms are difficult to translate, although their transliterations are transparent (the definitions are from LSJ, s.v. “μουσική” and so on). First, μουσική, more general than “music”, is derived from the name of the Muses, and denoted any art over which the Muses presided

but it evolved into the name of a particular art – music. The masculine μουσικός is a votary of the Muses, a man of letters and accomplishments, or a scholar, and finally a practitioner of music – a musician. The word has much in common with τέχνη (techne) an art, skill, or craft; a technique, principle, or method by which something is achieved or created, and as a product of this, a work of art, also known as a μουσικὴ τέχνη. Second, the noun ἁρμονία from the verb ἁρμόζω (to join or fasten), is a joining, a joint or fastening. The goddess Harmonia, born of the adulterous affair between Aphrodite and Ares (Hesiod Theogony, 933-37), was the goddess of harmony and concord, and as such presided over both marital harmony, soothing strife and discord, and martial harmony, governing the array and deployment of soldiers. In this abstract sense, harmony lies in the regularity contained in notions of rank and order. Implicit in the meaning of harmony is the idea of limits and constraints in contrast to the licence in mere pleasure. In English the notion of carpentry or handiwork appears in such words as joiner and joinery (compare the memorable phrase, “that hideous piece of female joinery, a patch-work counterpane”, Mary Russell Mitford, 1824). The English expression can describe either the physical (his nose is out of joint) or the metaphysical (the time is out of joint). For the Pythagoreans, its most important application was for the explanation of the cosmos and the doctrine of music (understood as harmony or order of the spheres). Compare Plato’s Republic (531 b) where the theory of music corresponds exactly to the theory of astronomy: “for the numbers they [astronomers] seek are those found in these heard concords” (ἀστρονομίᾳ: τοὺς γὰρ ἐν ταύταις ταῖς συμφωνίαις ταῖς ἀκουομέναις ἀριθμοὺς ζητοῦσιν). Harmonia’s involvement in warfare should not be discounted, and we can see the relation between the notion of rank and order in στίχος (row, line, rank or file, the first word, in fact, in De E). Health, both physical and spiritual, is a result of a balance and proportion, for if one element dominates then order and harmony disappear, causing illness in the human body, anarchy in society, disorder in the cosmos and a descent into chaos. Late Greek and Roman writers sometimes portrayed Harmonia in the abstract – a deity who presides over cosmic balance. Heraclitus, too, explored the themes of cosmic balance and the place of war within that balance. His beautifully designed (Kahn 1978, 202) aphorism, “ἁρμονίη ἀφανὴς φανερῆς κρείττων“ is celebrated for its own proportion and linguistic balance. It serves as an epigraph for this thesis. Finally the third, συμφωνία (concord or unison of sound, musical concord, accord, such as the fourth, fifth, and octave) means, metaphorically, harmony or agreement. Practitioners and teachers of music developed theories of music; these included those who analysed interval ratios mathematically

and those who analysed them “by ear”, that is, perceptually or through the senses. The latter, the harmonikoi, were regarded much like other professional intellectuals: Theophrastus, in his thumbnail sketch of the obsequious man, represents him as owning a little sports-court that he lends out to philosophers, sophists, arms- instructors and harmonikoi for their lectures. After the fourth century, we hear little of these oral expositors [of music], but written treatises continue to multiply. In the end, Antiquity was destined to leave us far more musical theory than music. (West 1994, 218):

Nevertheless, the two groups, the empiricists and the analysts, went their different ways. The name harmonikoi came to be associated with the empiricists. Aristoxenus (born circa 375 BC), an empiricist, nevertheless constructed an axiomatic system of scales that, he claimed, reflected natural melody. He based his system on intervals measured in tones and fractions of tones, defining a fourth as equal to two and a half tones. The calculation of harmonic ratios, on the other hand, was associated with the Pythagoreans, as Goodwin explains in his introduction:

The harmonic intervals, discovered by Pythagoras, are the Octave (διὰ πασῶν,) with its ratio of 2:1; the Fifth (διὰ πέντε), with its ratio of 3: 2 (λόγος ἡμιόλιος or Sesquialter); the Fourth (διὰ τεσσάρων), with its ratio of 4: 3 (λόγος ἐπίτριτος or Sesquilerce); and the Tone (τόνος), with its ratio of 9: 8 (λόγος ἐπόγδοος or Sesquioctave). (Plutarch’s Morals 1874)

An alternative derivation of these ratios lies in the triangular array of the tetractys (see appendix C). The significance of the tetractys for both the Pythagoreans and for Delphi is epitomised in the Pythagorean catechism: “What is the Oracle at Delphi? – the tetractys, which is the octave (harmonia) which has the Sirens in it.” West (1994, 235) quotes this from the list of Pythagorean catechisms given by Iamblichus (De Vita Pythagorica 82.47).

64. (10. 389 C) Surely the comment “reasonable proportion” is wordplay on the new subject, harmonic theory.

65. (10. 389 C) The working of harmony is, in a word, concord—these concords are based on the ratios between numbers.

66. (10. 389 D) The ratios of the five intervals, that is 2:1, 3:1, 4:1, 4:3, and 3:2, are all pairs of the four integers belonging to the tetractys. The only other possible pair is 4:2, which is equivalent to 2:1. Hence, all the possible intervals, and the only possible intervals, are represented in the tetractys. I have used simple mathematical notation to describe these intervals (as does Babbitt). Older

translations (for example, those of Amyot, Holland, Ricard and Goodwin) often use transliterations of the Greek. Consider Goodwin’s translation of this sentence:

For all these accords take their original in proportions of number; and the proportion of the symphony diatessaron is sesquitertial, of diapente sesquialter, of diapason duple, of diapason with diapente triple, and of disdiapason quadruple. These terms are now archaisms in English (as described by the OED, which has no citations beyond 1900). Some modern musicians and historians of music may still understand them, but their interpretation as mathematical ratios may better suit the modern reader.

67. (10. 389 E) I have simply transliterated harmonikoi, although “experts in harmony” would work. Plutarch has a particular group in mind – early musical theorists who adopted an empirical rather than mathematical approach to harmony. Aristoxenus saw these as his intellectual forebears, contrasting them with those who “stray into alien territory and dismiss perception as inaccurate, devising theoretical explanations and saying that it is in certain ratios of numbers and relative speeds that high and low pitch consist…” (Barker 2007, 37, quoting Aristoxenus, Elementa harmonicae, 32. 20-31).

68. (10. 389 E) The ratio of the diapason with diatessaron, that is, an octave with a fourth, is the numerical ratio 8:3 (that is 2/1 x 4/3). This ratio clearly cannot be derived from the tetractys.

69 (10. 389 E) The five stops of the tetrachord form a sequence of four notes separated by three intervals jointly spanning a perfect fourth (that is, the first and fourth notes span five semitones). The system of two octaves contains a continuous sequence of such tetrachords. Some are linked in conjunction, others are disjunctive (that is, they are separated by a tone).

70. (10. 389 E) Young Plutarch’s use of “the first five ‘modes’ or ‘keys’ or ‘scales’, whatever their right name is” suggests that even in Plutarch’s time these words were multivalent. Babbitt and Goodwin simply transliterate the Greek, using “tropes”, “tones”, and “harmonies”. Barker (2007, 55) gives a similar definition for the word::

The topic of tonoi is probably the thorniest of all those involved in Greek harmonics. For present purposes we can envisage them as roughly analogous to the ‘keys’ of modern musical discourse, that is, as a set of identically formed scales placed at different levels of pitch. They become important, in a scientific or theoretical context, when the structural basis of a sequence used by musicians cannot be located in a single, recognisable scale, but can be construed as shifting (‘modulating’) between differently pitched instances of the same scale-pattern. (Barker 2007, 55)

His use of tropoi is consistent with the uses of harmoniai and tonoi. The noun τροπός is. “like ἁρμονία, a particular mode … but more generally a ‘style’” (LSJ, s.v. “τροπός”). Barker describes the different styles of composers as different tropoi (2007, 248). The noun τροπός bears another similarity to harmonia, and that is its cosmological meaning of turning point, or the thong that was used as an oarlock. It appears in a fragment of Heraclitus, “The reversals of fire: first sea ; but of sea half is earth, half lightning storm” (Diels 31). The tropics of Cancer and Capricorn mark the turning points of the sun, and the limits of its movement above and below the equator.

71. (10. 389 F)…This is clearly a response to the empiricists, who were interested in the smallest interval distinguishable to the human ear, that is, the limit of human powers of perception, not the limit of theoretical possibility.

SECTION 11: COMMENTARY and NOTES

72. (11. 389 F) Not to belabour the point, but the two personal pronouns “I” in this sentence do not refer to the same person. Only one pronoun, ἐγὼ, appears in the Greek so the contradiction is not as obvious there as it is in the English. Young Plutarch uses the first, referring to himself, and Plutarch the second, referring to his younger self. These two uses recur during Young Plutarch’s speech. To use a self-referential “I” for an earlier version of oneself is common-place and idiomatic; to do otherwise would be pedantic. This use emphasises the notion that despite the changes we experience there is some core or kernel of us, which we could call the soul, the spirit, the ego, or the seat of our being, that endures and survives these changes.

73. (11. 389 F) That there could be other worlds besides ours, and they could be up to to five in number appears in Timaeus, 55 C-D. Cleombrotus provides a full explanation

You well remember that he [Plato] summarily decided against an infinite number of worlds, but had doubts about a limited number; and up to five he conceded a reasonable probability to those who postulated one world to correspond to each element, but, for himself, he kept to one. This seems to be peculiar to Plato, for the other philosophers conceived a fear of plurality, feeling that if they did not limit matter to one world, but went beyond one, an unlimited and embarrassing infinity would at once fasten itself upon them. (De def. 22. 422 A, trans. Babbittreptition of ) Aristotle, who voiced precisely such fears (De Caelo, 1. 8), must count amongst “other philosophers”.

74. (11. 389 F) Young Plutarch, immediately after giving another example of the importance of the number five, embarks on a digression about Aristotle’s assertion that there is a unique world. Young Plutarch attempts to reconcile this assertion with Plato’s view that there could be up to five by

by invoking Aristotle’s identification of the five solids with earth, water, fire, air and the quintessence. Young Plutarch’s use of “even if” (κἂν) is concessionary and he uses it to suggest that although Aristotle says that there is only one world he could also mean that there are five parts to that one world. For a discussion of Arsitotle’s assertion (De Caelo 278a26-279a6) that there is one unique world please see endote 130, page 78.

75. (11. 390 A) The repetition of the prefix συν (“with” or together”) in the phrase συγκείμενον κόσμων καὶ συνηρμοσμένον (“composed and conjoined from five worlds”) nicely mirrors the one in the Greek. This may not be, strictly speaking, hendiadys, but it is another example of Plutarch’s fondness for balanced repetition.

76. (11. 390 A) With “the five most…fittingly associated each to each” Young Plutarch gives a condensed version of Plato’s description of the creation of the world from Timaeus 31 a: a product of the rational Demiurge, who imposes mathematical order on chaos to generate the cosmos. Donald Zeyl describes this as:

The governing explanatory principle of the account is teleological: the universe as a whole is so arranged as to produce a vast array of good effects. It strikes Plato strongly that this arrangement is not fortuitous, but the outcome of the deliberate intent of Intellect (nous), anthropomorphically represented by the figure of the Craftsman who plans and constructs a world that is as excellent as its nature permits it to be. (SEP, s.v. "Plato's Timaeus")

The polysemic φύσις occurred just one line above, where it was translated “by its own nature”. Instantiations of the polygon occur naturally (for example, honeycombs and tessellated pavements); the concept of a polygon does not. I have used universe to include both the physical and the ideal. The Platonic solids are forms of which, according to Plato, the first four provide analogues to the four elements – fire, earth, water, and air – and the fifth and last, the dodecahedron, which “God used to bedeck his universe” (ἐπὶ τὸ πᾶν ὁ θεὸς αὐτῇ κατεχρήσατο ἐκεῖνο διαζωγραφῶν, Timaeus, 55c). Plato used the existence of five, and no more than five, regular polygons to argue against a larger number of worlds and, by extension, an infinite number of them. Despite our name for them, some had been known to the Egyptians and the Pythagoreans (the tetrahedron, cube, and dodecahedron). That there are no more than five such polygons is not self-evident, but the Greeks solved this question quickly. Theaetetus of Athens (417-369? BC), a friend of Socrates and Plato, constructed the last two (the octahedron and icosahedron) and developed an elegant proof that there are exactly five regular polygons. He is the subject of Plato’s dialogue, Theaetatus, and his mathematical work is discussed in Euclid’s Elements, Book 13.

SECTION 12: COMMENTARY and NOTES

77. (12. 390 B) These philosophers follow Aristotle’s theory of the correspondence of the senses in De anima. (2.7-11). 78. (12. 390 B) Plato (Timaeus (45.b-d) discusses the theory of the dual mechanism of seeing by mixing of the light of day with light from the eye. Lernould (2005, 2) remarks on the “extreme brevity” of this section, but it is Plutarch’s signature style to tease us with brief allusions to abstruse theories. Lernould gives the history of the interpretation of the melding of the fire emitted by the eye with the exterior fire found in daylight. Another good discussion appears in Merker, La vision chez Platon et Aristote, 2003. SECTION 13: COMMENTARY and NOTES

79. (13. 390 C) Young Plutarch refers to the passage in the Iliad where Iris has delivered Zeus’ command to Poseidon that he should leave the fighting at Troy and go back to his home in the sea, to which Poseidon replies angrily:

… Since we are three brothers born by Rheia to Kronos, Zeus, and I, and the third is Hades, lord of the dead men. All was divided among us three ways, each given his domain. I when the lots were shaken drew the grey sea to live in forever; Hades drew the lot of the mists and the darkness, and Zeus was allotted the wide sky, in the cloud and the bright air. But earth and high Olympos are common to all three. (Iliad, 15. 187-193, trans. by Lattimore) Heracleon gives a similar description of the partition of the world in De def. 23. 422 E and also describes the five Platonic solids, which Young Plutarch mentioned in section 11.

80. (13. 390 C) This fragment of Euripides occurs within a cluster of fragments (Nauck 970- 972), all of which Nauck attributes to Plutarch. The remark is so anodyne and the reference so fragmentary that one tends to pass quickly over it. The reference and the theme of drifting from the subject at hand occurs often in the Moralia, perhaps because Plutarch often indulges in digressions.

Babut (1969) saw this as perhaps a sign of disorganization, “cette impression de désordre est renforcée par les allusions répétées des personnages, dans les trois [Pythian] dialogues, à des digressions qui les ont entraînés loin de leur sujet initial, et par des rappels insistants à ne pas perdre de vue ce sujet”. He lists other instances in De Pyth. (7. 397 D, and 17. 402 B) and in De def. (15. 418 C, 15. 420 E, and 38. 431 A). Whether these digressions constitute disorder or a studied lightness of style

is debatable. In this case Young Plutarch wants to step back from the pentad, and Homer, to review the properties of the tetrad. There are two digressions here, the first into Homer, and the second into the tetrad, neither one strictly necessary for Young Plutarch’s argument. A French version of this wandering from the subject at hand and then returning to the fold by some roundabout route, “revenons à nos moutons,” was a running joke in the medieval play, La Farce de Maître Pathelin, and is still in current use.

81. (13. 390 C) The crucial concept for the analysis of solid bodies is the nature of a point. For us a point is a figure without dimension; it has no length, breadth, or depth; in other words, it “is conceived as having position but no extent, magnitude, dimension, or direction (as the end of a line, the intersection of two lines, or an element of a topological space, OED s.v. “point”). It follows that a line having one dimension, with neither width nor depth, is associated with the number one, the plane of two dimensions, length and width, is associated with the number two, and a solid figure, with length width and depth, is associated with the number three. We speak casually of the three dimensions of our physical world and, backtracking through the three dimensions, we arrive at the point, which, having no dimensions, must be associated with zero.

In contrast, the Pythagoreans described the unit in arithmetic as “a point without position” (στιγμὴ ἄθετος) and the geometric point as a unit having position (μονὰς θέσιν ἔχουσα) (Heath 1931, 1 38). Extrapolating from the initial monad with position we can, by “stretching” that point, create a line (associated with the number two), then by stretching that line, create a plane (associated with the number three), and finally, by dragging down the plane create a solid. This, a solid comprising our three dimensions, isassociated for the Greeks with the number four. The absence of the number “zero” in the Greek conceptual system of algebra, and of the geometry of space, is the root cause of this distinction.

82. (13. 390 E) Every translation of, “ὀρφανὸν καὶ ἀτελὲς καὶ πρὸς οὐδ᾽ ὁτιοῦν”, that I have seen renders ὀρφανός as “orphan”. This cannot be right, since Young Plutarch has just finished telling us that Nature has constructed this inanimate thing, and inanimacy implies that there was neither father nor mother to lose. Both Chantraine and LSJ cite the reciprocal meaning, it can also be said of parents who have lost a child. Chantraine goes one step further, describing its metaphoric use as the adjective “deprived of”. He suggests, tentatively, that the name Orpheus might be from the same root as ὀρφανός, adding, “Orphée étant privé de son épouse [?]”.

83. (13. 390 E) The hegemony of the pentad had been recognized since the time of Pythagoras. Iamblichus, quoting Anatolius, explains how the number five dominates other numbers:

[T]he pentad is particularly comprehensive of the natural phenomena of the universe: it is a frequent assertion of ours that the whole universe is manifestly completed and enclosed by the decad, and seeded by the monad, and it gains movement thanks to the dyad and life thanks to the pentad, which is particularly and most appropriately and only a division of the decad, since the pentad necessarily entails equivalence, while the dyad entails ambivalence.(Waterfield 1988, 66).

84. (13. 390 E) These inanimate figures lack the fifth attribute that distinguishes animate beings from the inanimate. Having returned to consideration of the pentad after his excursion into the tetrad, Young Plutarch describes the five classes of animate beings and the five divisions of the soul. These five parts are listed in (De def. 429 E) as the vegetative part, the perceptive, the appetitive, fortitude, and reason (φυτικὸν, φυσικὸναἰσθητικὸν, ἐπιθυμητικὸν, θυμοειδὲς, and λογιστικόν). The five classes and five divisions are roughly comparable. The first part, the quality of nutrition or growth, is described in both lists as the least transparent of these qualities. See also Republic, 410 b, 440 e - 441 a; and Timaeus, 69-75).

SECTION 14: COMMENTARY and NOTES

85. (14. 391 A) Young Plutarch asserts that four is the “first square number”. This explains the digression into one as a square number, because if one is defined as square (since it is the number that results when it is multiplied by itself ), then four is not the first square. The monad is simultaneously the source of all number (but not a number), the first number, the first square number, and it is both even and odd.

86. (14. 391 A) Iamblichus, quoting Nicomachus, calls the monad the form of forms, since “it is creation thanks to its creativity and intellect thanks to its intelligence; this is adequately demonstrated in the mutual opposition of oblongs and squares” (Waterfield 1988, 36). The “ideal form” is the monad and “finite matter” is the tetrad, since “everything in the universe turns out to be completed in the natural progression up to the tetrad, as does everything numerical – in short everything, whatever its nature” (Waterfield 1988, 55). Furthermore all the numbers up to four give us the pentad, and are arrayed in the tetractys.

SECTION 15: COMMENTARY and NOTES

87. (15. 391 A) Young Plutarch is eliding Plato, the author, with Socrates, the character in the Cratylus who speaks these words. This helps us to understand later, in this rather ragged argument,

that an unattached pronoun “he” denotes Socrates, a character no longer in the Cratylus but in the Philebus.

At this point in the Cratylus, Hermogenes and Socrates move from the naming of the gods to the naming of celestial and other physical objects. Socrates begins by providing an etymology for the name of the moon (Σελήνη) from *Σελαενονεοάεια, a contraction of: σέλας-νέον-καὶ-ἕνον-ἔχει-ἀεί (“it always has light both new and old”). Some interpreters have found these etymologies not only ridiculous, but deliberately so. Ademollo comments:

read without prejudices of any sort, the etymologies qua etymologies may well strike you as delirious. Socrates goes on [at disproportionate length] to offer utterly implausible analyses, reaching bewildering results by reckless methodological anarchy. To the many examples we have already met I will only add the worst of the lot: the terrible ‘dithyrambic’ etymology of ‘moon’ or rather of the Doric variant Σελαναία (409a-c)”. (2011, 237) In the case of the etymology of the name of the moon, two examples support this opinion. The first is Fowler’s inspired translation of διθυραμβῶδες (dithyrhambic”) as “opera bouffe” (Plato: Loeb Classical Library 1926, 4.167). A second is Obsieger’s contention that just the mention of Anaxagoras from this section of the Cratylus would have signalled to Plutarch’s listeners (and later readers of De E) that a joke or “some sort of historical and philosophical illogicality” was in the offing. (Durch die Erwähnung des Kratylos werden die Zuhörer‚ Plutarchs und die Leser von De E gewarnt, daß eine philosophiehistorische Absurdität folgt [Obsieger 2013, 281].) On the more general question of the seriousness of the etymologies, Ademollo provides a measured assessment of Plato’s and Socrates’ attitudes towards them and towards etymologising, concluding that, for the most part, they thought the practice legitimate. He adds that, to his knowledge, no ancient interpreter of the Cratylus raised doubts about the etymologies and warns us against judging the Cratylus by the standards of modern linguistics, concluding that it is unlikely that the etymologies are a deliberate send up or anything else of that sort. (Ademollo 2011, 237-250)

In a nutshell, Socrates tells us that Anaxagoras’ finding is pre-empted by the longstanding folk etymology of the word “moon”, a word that developed from the two sources, new and old, of moonlight. This was exactly Anaxagoras’ theory. Young Plutarch’s argument follows the same path: the different artifacts of the E, displayed at Delphi for centuries, attested to the longstanding understanding of the importance of the number five, which Plato only belatedly discussed in his dialogues (without acknowledging his sources, a sin today but common practice then).

In the Cratylus, Socrates doggedly maintains his tomfoolery, concluding that borrowings of foreign words cannot be analysed with the usual linguistic tools. He admits frankly that his analysis is a contrivance (μηχανήν), all the while flummoxing Hermogenes. Young Plutarch is captivated, as we are, by this episode.

88. (15. 391 C) In The Sophist, Plato shows that there are five overarching classes (γένος, “race, kin, clan, family, or class”) and these classes group elements by their qualities, with each class containing elements embodying a like quality. The Stranger understands this when he replies to Theaetetus (The Sophist, 253 D):

Ξένος: οὐκοῦν ὅ γε τοῦτο δυνατὸς δρᾶν μίαν ἰδέαν διὰ πολλῶν, ἑνὸς ἑκάστου κειμένου χωρίς, πάντῃ διατεταμένην ἱκανῶς διαισθάνεται, καὶ πολλὰς ἑτέρας ἀλλήλων ὑπὸ μιᾶς ἔξωθεν περιεχομένας, καὶ μίαν αὖ δι᾽ ὅλων πολλῶν ἐν ἑνὶ συνημμένην, καὶ πολλὰς χωρὶς πάντῃ διωρισμένας. Then he who is able to do this [distinguish qualities, and place them in different classes] has a clear perception of one form or idea extending entirely through many individuals each of which lies apart, and of many forms differing from one another but included in one greater form, and again of one form evolved by the union of many wholes, and of many forms entirely apart and separate.(Trans. by Harold Fowler: 89. (15. 391 C) In other words, in The Philebus, Plato does not go beyond the four classes. See Meyer William Isenberg, 1940, 154-179.

90. (15. 391 C) There is a textual problem here in, “because he dedicated an E to the god”. Bernardakis has δύο Ε καθιέρωσε τῷ θεῷ; and Obsieger †δύο† εἶ καθιέρωσε τῷ θεῷ, signalling his doubts about δύο. Babbitt suggests, and uses, διὸ (because). Flacelière, writing soon after, follows suit but adds another word, διὸ εἶ καθιέρωσε τῷ θεῷ. Goodwin, translating using an earlier version of the text, produced the peculiar, “some one… consecrated to the God two E E”. If “two E E” is a misprint, it has survived in later editions of the translation. Amyot, three hundred years earlier must have faced the same version of the text, “Quelqu’un doncques … consecra deux E, au Dieu de ce temple”.

Obsieger provides an analysis of the emendations of Wyttenbach, Wilamowitz, Pohlenz, Babbitt, and Flacelière, and asserts (2013, 289) that the meaning of the sentence is clear: someone discovered before Plato did that there are exactly five general principles that appear again and again, and the E attests to that early discovery. Furthermore, the “δύο” given in the Bernardakis and earlier texts is illogical since, although the tradition was that there had been three different Es, there is no evidence that more than one E was on display at any given time. Obsieger agrees that Babbitt’s

generally accepted emendation, διὸ, is reasonable, and that Flacelière’s introduction of <τὸ> is “an obvious improvement”.

91. (15. 391 C) Socrates sings the verse, “In the sixth generation, bring to a stop the ritual of song” (‘ἕκτῃ δ᾽ ἐν γενεᾷ,’ φησὶν Ὀρφεύς, ‘καταπαύσατε κόσμον ἀοιδῆς’ Philebus 66c), identifying it as an Orphic verse (Kern, 87) and using it to bring this part of the discussion to a close. Young Plutarch jumps from Cratylus to the Sophist and then to the Philebus, where Socrates is quoting the Orphic verse, arguing that stopping before the sixth iteration of something is evidence of the importance of the number five.

SECTION 16: COMMENTARY and NOTES 92. (16. 391 D) The sixth day after the new moon was the day of the month dedicated to Artemis and Apollo. The conceptual link between this section and the last is the ordinal “the sixth”.

93. (16. 391 D) This sentence is notorious for its obscurity and corruption. Here, Goodwin permits himself, “I leave this corrupt passage as I find it in the old translation [i.e. by many hands]. The Greek cannot be tortured into any sense.” Babbitt cautions that the Greek text “is somewhat uncertain” I have followed Babbitt’s translation, with some editing. Not only are there textual problems but, no matter the amendments to the text, its meaning remains obscure, perhaps because we are faced with terse passage about an obscure religious practice. Given the context, and Nicander’s worried response, “the reason for it [the outcome of the casting] must not be divulged to others”, one cannot shake the suspicion that Plutarch’s original text could have been deliberately obfuscatory.

94. (16. 391 E) Plutarch is reporting in direct speech Young Plutarch’s response to Nicander. Young Plutarch speaks of the future, but he cannot know that he will become a priest at Delphi. Thus, I have stated this as a hypothetical, “if ever the time comes…”.

SECTION 17: COMMENTARY and NOTES

95. (17. 391 F) Ammonius first establishes his authority as the senior person in the group and then demonstrates his control over the material with his brief comments on the number seven.This number was mentioned in passing by the Chaldean and it resonates with collections of seven (virgins, virtues, vowels, lean and fat years, ages of man, days of the week, colours of the rainbow). According to Delatte, the Hebrew tradition of the mystical powers of the number seven found its way into the Christian tradition through the early Christian writers’ weakness for arithmology (“ils ont un faible pour l’arithmologie” Delatte 1915, 231). In a short essay, he describes Clement’s preoccupation with

reconciling Hebrew doctrine with the new Christian religion. He gives the example of Clement’s treatment of the third commandment (“do not take the name of the Lord in vain”) with the description of the Creator resting on the seventh day. The Lord’s injunction to mankind to rest on the seventh day is, in arithimological terms, consistent with the holiness of the number 7. The problem for Clement was that the Lord, being the Lord, has no need of rest, and that the Biblical report of creation was a purely symbolic and allegorical description. Clement’s explanation was that the Lord, while not needing the rest, was instructing and leading by example, so not to rest on the seventh day would be taking His name in vain. As Delatte says, “Dieu, étant naturellement infatigable, ignore le besoin du repos mais il est le modèle de celui que nous est commandé” (Delatte 1915, 232). There is much that Ammonius could have said about the seven, had he been interested in numbers.

96. (17. 391 F) Ammonius uses προεδρία (the privilege of front row seats), echoing Plutarch’s remark to Sarapion about the importance of the E (1. 385 A). The heptad is personified as a local worthy with the privilege of taking a front-row seat at the theatre. Our equivalent metaphor might be “ringside seat”. The metaphor of the front seats is particularly apt for Delphi, where the chief priests of Apollo and Dionysus would have taken their places in the front seats of the theatre.

97. (17. 392 B) The “long years of time”—must mean something like, “the weight of longstanding tradition” The citations is from Simonides of Crea (6th century BC). (Bergk 1, 522; and Simonides, 193)

SECTION 18: COMMENTARY and NOTES

98. (18. 392 B) Ammonius puts forward the premise that mortals living in a temporal and changing world cannot understand Being. He explains that mortal things are always in the process of change, “between coming into being and being destroyed” and are, for an instant, in both states simultaneously. He pursues this idea comparing each thing’s coming into being and its simultaneous destruction to “a vessel leaking birth and destruction” (ὥσπερ ἀγγεῖον φθορᾶς καὶ γενέσεως). This section uses variants of the words, γίγνομαι – to become, come into being, and φθείρω – to destroy. I have tried to reflect this vocabulary in my translation. 99. (18. 392 B) This is Plutarch’s second direct attribution to Heraclitus, given in direct speech by Ammonius, “…it is not possible to step twice into the same river”. I have taken only the words before “Heraclitus said” to be a direct quotation. There are two Heraclitean fragments concerning rivers, their interpretation is controversial but they were well known in Plutarch’s time. His version is unlikely to be in Heraclitus’ exact words, but simply a free rendering of “as they step into the same

rivers, other and still other waters flow upon them” (ποταμοῖσι τοῖσιν αυτοῖσιν ἐ̔μβαίνουσιν έ̔τερα καὶ ετερα ὑ̔́δατο ̔ἑπιρρεῖ Diels 12). Both versions were known to Plato (Cratylus. 402) and Aristotle (Met. 4. 1010a). It is now accepted that Plutarch was using an intermediate source that had probably developed from the work of Plato and Aristotle (and Cratylus). “It is obvious that [Plutarch’s] ποταμῷ … τῷ αὐτῷ reproduces the Aristotelian form of Plato’s paraphrase of the river statement and not (as Bywater, Diels, Kranz and others believed) the original words of Heraclitus” (See Kahn 1979, 168; Marcovich 1967, 206; and Kirk 1962, 374-381).

100. (18. 392 B) The assertion, “One cannot step into the same river twice” does not entail that the individual elements that make up the river – the drops of water – change their composition or state, they are just different drops of water (Obsieger 2013, 318). This linear flux or flow can be contrasted with the Heraclitean notion of circular flow introduced in section 8.

101. (18. 392 B) The phrase, “it disperses and gathers” is perhaps a fragment from Heraclitus (Diels, 91). Bernardakis and Babbitt construe this phrase as a continuation of the river fragment but this has been challenged. Fairbanks did not see it as a literal quotation but as another “catchword” phrase, a shorthand to denote early philosophical doctrines, where a word or two of the original has been preserved, although not the meaning (Fairbanks 1897, 79). Fairbanks’s view is now the professional consenus. Given that Young Plutarch has just been quoting Plato, Kahn’s comment that these pairs of antithetical verbs are reminiscent of Heraclitean “style” is intriguing. He suggests that this pair could well be a “Plutarchean interpolation” inspired by the Stranger’s contrast (at Sophist 242 D-E) between the Ionian (Heraclitus) and Sicilian (Empedocles) philosophers (Kahn 1979, 130)

102. (18. 392 C) The phrase, “the death of fire is birth for air and the death of air is birth for water”, is the third fragment that Plutarch attributes directly to Heraclitus. Fairbanks notes that it seems to be given accurately by Maximus Tyr. (41.4): “Fire lives the death of earth and air lives the death of fire; water lives the death of air, earth that of water”. But note that Maximus is the only writer to use the word “life”. Plutarch has given this allusion twice (Mor. 392 C, and Mor. 949 A), in two slightly different forms. The form in 949 A is:

φθειρομένων εἰς τοὐναντίον ἑκάστῳ, σκοπῶμεν εἰ καλῶς εἴρηται τὸ πυρὸς θάνατος ἀέρος γένεσις. Since corruption is the alteration of those things that are corrupted into their opposites, let us see whether the saying holds good that, “The death of fire is the generation of air.”

Nevertheless, Kahn is right to note the use of the words “birth” and “death” for the transformations of the elements. This vocabulary (which may be metaphoric) allows Ammonius to make the logical leap to animate being in “and it is clearer still in ourselves”. That is, the changes we undergo are little births and deaths, where, for us, neither birth nor death is a metaphor.

Ammonius then presents an elaborate excursus on the ages of man. Plutarch himself may not have been entirely in agreement with this analysis, since there is a lost dialogue, entitled “As to our not remaining the same, while being is always in flux,” attributed to him in an anonymous note (Classical Review 32 [1918]: 150-153), but I have been unable to find it mentioned elsewhere. Plutarch presents the opposite view (speaking as himself) in another dialogue that also took place at Delphi. The point at issue is whether a delay in divine retribution brings encouragement to wrong doers and distress to their victims, who do not see their aggressors duly punished. Plutarch describes a city as an organism having a continuous life and a stable and integrated unity, so that its moral responsibility outlasts the lives of its individual inhabitants. He compares the life of the city with its core identity to the life of a man, and ends his argument with an acerbic allusion to Heraclitus:

ἀλλ᾽ ἄνθρωπός τε λέγεται μέχρι τέλους εἷς ἀπὸ γενέσεως, πόλιν τε τὴν αὐτὴν ὡσαύτως διαμένουσαν ἐνέχεσθαι τοῖς ὀνείδεσι τῶν προγόνων ἀξιοῦμεν, ᾧ δικαίῳ μέτεστιν αὐτῇ δόξης τε τῆς ἐκείνων καὶ δυνάμεως: ἢ λήσομεν εἰς τὸν Ἡρακλείτειον ἅπαντα πράγματα ποταμὸν ἐμβαλόντες, εἰς ὃν οὔ φησι δὶς ἐμβῆναι τῷ πάντα κινεῖν καὶ ἑτεροιοῦν τὴν φύσιν μεταβάλλουσαν. Yet a man is called one and the same from birth to death; and we deem it only proper that a city, in like manner retaining its identity, should be involved in the disgraces of its forbears by the same title as it inherits their glory and power; else we shall find that we have unawares cast the whole of existence into the river of Heraclitus, into which he asserts no man can step twice, as nature in its changes shifts and alters everything. (De ser. num. 15. 559 C, trans. by Phillip H. De Lacy and Benedict Einarson.) Ildefonse (2006) draws out the implications. She comments, citing Sirinelli (2000, 423), that although these two passages contain the same fragment of Heraclitus, and compare it to the ages of man, the attitude of the two speakers is very different. She continues that the structure of De E contains three separate “Plutarchs” at different stages of his life, but the presiding intellect is that of one person, not a series of different entities. Hershbell (1977, 198) simply notes that Plutarch voices an opinion different from the one held by Ammonius in De E; Flacelière is more pointed (1941, 89, 11).

Ces idées n’expriment qu’un aspect de la réalité et comportement assurément une grande part d’exagération. Cf. Ricard dans sa note à ce passage [1884, 60 -61] «Les vicissitudes que nous éprouvons dans nos gouts, nos affections nos sentiments, et

même dans les traits de notre figure, ne détruisent ni l’unité de notre individu, ni la réalité de notre existence propre et individuelle ». These ideas express only one aspect of reality and certainly contain some exaggeration. See Ricard’s note to this passage [1884, 60-61]: "The vicissitudes we experience in our tastes, our affections our feelings, and even in our physical traits, destroy neither the unity of our personalities nor the reality of our own, individual existence”. Plutarch makes another reference to the river fragment in his discussion of the different nourishment for plants contained in rain-water and irrigation water.

Is the reason that Aristotle gives the true one, namely that the water that comes down as rain is fresh and new, while that of a marsh or pool is old and stale? The running waters of springs and rivers are fresh and new-born—you could not step into the same rivers twice, as Heraclitus says, because the waters that flow upon you are not the same—yet they, too, are less nourishing than rain-water. (QN, 912 A, trans. by F. H. Sandbach). This reference to Heraclitus is, in my opinion, no more than a rhetorical flourish. Despite its mention of “rivers”, it tells us little about the question of the actual words of Heraclitus and it seems to rely on Aristotle’s use of the aphorism. It also provides another example where “Heraclitus says” does not mean that the quotation is taken directly or accurately from its source.

The thirty-oared galley on which Theseus returned to Greece from Crete provides another example of the idea of constant change, but this time applied to an inanimate object (Theseus, 23. 1). Whittaker (1969, 190), calling the theme “evidently a Middle Platonic commonplace”, provides a similar example in Seneca’s letter to Lucius (On Being 58, 22).

103. (18. 392 D) A model in wax or plaster, from ἐκμάσσω “to mould or adapt oneself to”.

SECTION 19: COMMENTARY and NOTES

105. (19. 392 E) Time is mobile and immaterial, but discernible in conjunction with matter. So, true Being is outside time. Thus, the timeless existence of god as perfect and complete contrasts with the defective existence of individual mortal beings.

106. (19. 392 E) The description, “according to their connections with time”, might mean that each entity is somewhere between birth and death, and the place of each one is determined by its own circumstances.

SECTION 20: COMMENTARY and NOTES

107. (20. 393 A) The reading in Obsieger’s and Bernardakis’ Greek texts, and the English is in Goodwin’s translation is “ít must be said” (χρὴ φάναι). In contrast, Flacelière has the conditional, “if it needs to be said” (εἰ χρὴ φάναι), which appears as an interrogative in the French, “La divinité, elle, existe (est il nécessaire de le dire?)”. Babbitt, notes that εἰ does not appear in the manuscripts, but was added by Eusebius (Preparatio evangelica, 11.11), and followed by Cyril of Alexandria (Adv. Jul. 8). In any case, Babbitt uses “if there be need to say so”. The emphatic “it must be said” underlines the distinction that Ammonius is at great pains to make, that the god is not enmeshed in temporality. I have adopted Obsieger’s text.

108. (20. 393 A) Forever (αἰών) can mean a long space of time, an age (as our “eon”), “eternity”, or “ages” with no beginning or end. Here it is opposed to χρόνος, the same vocabulary pair that appears in Timaeus 37 c-38 C). The notion of “eternity” points us to Iamblichus (Waterfield 1988, 110) where the word is equivalent to the number of the decad. There are other resonances of Pythagoreanism in this section; they are Ammonius’ name, his background, the two appeals to “the ancients” ( possibly a reference to Neo-pythagorean doctrine) and the close relationship to Timaeus (Whittaker 1969, 188)

Whittaker asks if the Platonic Forms are eternal in the sense that they endure everlastingly, or if their eternity simply transcends duration. He concludes that the answer depends on the interpretation of αεí, as used by Plato – one referring to time and consequently involving duration, and the other referring to eternity that transcends duration. Mediaeval Latin distinguished between “eternal” (outside time) and “sempiternal” (lasting for endless eons).

109. (20. 393 A) ἀνέγκλιτον (from κλίνω, to make to lie back, to lean, to incline) meaning, “unchanging” and “orthogonal”, (LSJ). Plutarch also uses the word in the Life of Pericles (15):

ἀριστοκρατικὴν καὶ βασιλικὴν ἐντεινάμενος πολιτείαν, καὶ χρώμενος αὐτῇ πρὸς τὸ βέλτιστον ὀρθῇ καὶ ἀνεγκλίτῳ, he struck the high and clear note of an aristocratic and kingly statesmanship, and employing it for the best interests of all in a direct and undeviating fashion, Furthermore, the OED defines “to deviate” as “to turn aside from a course, method, or mode of action, a rule, or standard.” Hence, “to deviate” carries an extra nuance beyond “to change”, to include the notion of falling away from a standard. Similarly “orthogonal” can mean a standard or norm (it also means “right-angled”). A change can be for the worse or the better, but to deviate for the worse is a pleonasm and to deviate for the better a contradiction. Perrin has found the mot juste in her

translation, a translation that works just as well here. Then I discovered that Babbitt had used “deviate” in his translation. Nevertheless, like Plato and Anaxagoras, I shall bear my embarrassment and gratefully borrow the word from him.

110. (20. 393 A) The phrase “neither future nor past, neither older…” (οὐδὲ μέλλον οὐδὲ παρῳχημένον οὐδὲ πρεσβύτερον) appears only in Eusebius (see Obsieger, 346).

111. (20. 393 B) On the ancients, Whittaker (1969, 186) makes the link to “those coming to the shrine in search of wisdom” (τοὺς ἐν ἀρχῇ περὶ τὸν θεὸν φιλοσοφήσαντας, (De E 1. 385 A).

112. (20. 393 B) The word “god” appears in both the masculine (ὁ θεὸς) and the neuter (τὸ θεῖόν), which I translate a few lines below as “the divine is not manifold”. I have treated the masculine as a gendered being and the neuter as an analytic construct.

113. (20. 393 C) Obsieger (2013, 349) suggests that these ancients (who called all things chaste or pure “phoebus”) are Parmenides and Plato, referring us to Adv. Col. (13. 1114 C-F), where the doctrine underlying Ammonius’ argument – that true being remains always the same, but our world is fleeting and subject to change – also appears.

114. (20. 393 C) We have already seen these etymologies for Apollo as the not many and the one, and for Phoebus as the chaste (2. 388 F). Whittaker, identifying these as Pythagorean etymologies, gives instances in works by Clement of Alexandria, Plotinus, and Porphyry (Whittaker 1969, 187). He also links the name Ieius to the Pythagorean formula “the one and only” (εἷς καὶ μόνος, and sometimes ἔν καὶ μόνον) and sees it as derived from the epic adjective ἰός, ία, ἰόν (meaning εις, μια – one).

115. (20. 393 C) As Ildefonse says, the parallel to Homer (Iliad 4, 141 ff.) is loose, perhaps explaining Ammonius’ use of the qualifier πού. The conflating of the two meanings of μιαίνω (to “stain, colour, or dye” and to “stain, or sully”) may have been a commonplace in classical times (and perhaps today), but the Homeric simile does not introduce the resonances of μίγνυμι (to mix, mingle) that appear in Plutarch. Compare also QC 8.5.1. 725 C, where the question posed is “Why do sailors draw water from the Nile before daybreak?” The partial answer is that during the day riverwater is stirred up by animals and river traffic and hence polluted. This mixing “produces conflict, conflict produces change, and putrefaction is a kind of change

Serendipitously, English has an analogous pair of homonyms—die/dye—a doublet that has proved a fertile field for punning. Shakespeare has a simile in the same Homeric mode:

And, like a troop of jolly huntsmen come

Our lusty English, all with purple hands, Dyed in the dying slaughter of their foes. (King John II, 1 629)

SECTION 21: COMMENTARY and NOTES

116. (21. 393 E) The phrase “rapture and transformations” (ἐκστάσεις δ᾽ αὐτοῦ καὶ μεταβολὰς, repeated a few lines later as ἐκστάσεως καὶ μεταβολῆς) is another of Plutarch’s doublets, here combining two close synonyms. The first meaning of ἔκστασις is “displacement”, the second “standing aside and the third “entrancement, astonishment”. The Greek word can be transliterated as “ecstasy”, an English word closely related to one of the meanings of “rapture” (compare the OED: “ecstasy: an exalted state of feeling which engrosses the mind to the exclusion of thought; rapture, transport”). Ammonius is referring to the passage in section 9 where Young Plutarch uses the single word “transformation”:

For we hear the theologians, sometimes in verse, sometimes in prose, asserting and hymning that the god, by his nature, is deathless and immortal. Yet, as a result of the destined order of cosmos, he himself undergoes transformations [μεταβολαῖς]. Ammonius uses this doublet to emphasise that the phrase describes more than spatial displacement or uncomplicated change. He is also stressing that this change is not of Apollo’s volition, since everything in the cosmos is subject to a logos beyond human or divine control. The English word “rapture” captures the involuntary nature of these changes. The “Theologians” could certainly include Heraclitus, who wrote prose, but intricate and poetic prose.

Plutarch uses this doublet again in discussing the question “Whether it is possible for new diseases to come into being, and from what causes”, and whether qualitative changes in a substance can bring about a change into a new substance (a “substantial” change?). Plutarch comments that if this is not possible then there is no difference between vinegar and sour wine, or bitter and astringent, or wheat and darnel, or between one kind of mint and another. Yet all of these are very clearly qualitative losses of identity and transformations (καίτοι περιφανῶς ἐκστάσεις αὗται καὶ μεταβολαὶ ποιοτήτων εἰσίν, QC 8.9.3 732 B).

117. (21. 393 E) Those saying this are the Stoics, or the theologians in the passage from Section 9. Flacelière (1941, 84) suggests that the names of the two periods in the religious calendar where satiety or famine prevail, and the earlier passage in De E are related to Diels fragment 65 of Heraclitus.

118. (21. 393 F) For the simile comparing Apollo and his deadly destruction with a thoughtless little boy, see Homer Iliad, 15. 362.

119. (21. 394 A) Here we have a balance sheet contrasting the names of Apollo and Hades, and their attributes and predilections. Ammonius explores possible etymologies of these names, contrasting the one (A-pollo) with the many (Pluto, from πλέος - full, or perhaps from πλούτος - wealth). Ammonius does not mention α̉πόλλων (the future participle of α̉πόλλυμι, “to destroy”), whence, as Socrates explains, some people wrongly derive his name (Cratylus 405e-406a), since that abstract noun, signifies “destruction”, but not “destroyer”, the agent of that destruction. There are other epithets of Apollo that do entail havoc, if not destruction, for example the Homeric epithet “the far shooter” (Ἀπόλλων ἕκατος, Iliad 7.83).

The name “Delian” describes someone born on the island of Delos, as Apollo was, but could also denote clarity (δῆλος - clear), which contrasts with Hades, or Aïdoneus, that which is hidden, in the dark, or invisible (in the Ionic dialect of Heraclitus the initial aspirate is missing and thus a-idēs means “invisible” (Khan. 1978, 257). Plutarch has already cited Cratylus and clearly enjoyed its anarchic approach to etymology, and he must surely have been aware of the passage in Cratylus where Socrates riffs on the names of the gods, “As for Pluto, he was so named as the giver of wealth (πλοῦτος), because wealth comes up from below out of the earth. And Hades – I fancy most people think that this is a name of the Invisible (ἀειδής), so they are afraid and call him Pluto” (Plato Cratylus, 403a). Indeed, the section in Cratylus on divine names brings up another resonance with Heraclitus. These etymologies (from 401d to 411b) are organized around the theme of the Heraclitean theory of flux (See Ademollo 2011, 201 ff.). We have already discussed the name Phoebus in (Section 2), which also means radiant or shiningand is clearly opposed to darkness, blindness, and Homer’s “darkness of death” (σκότιος). 120. (21. 394 A) Apollo, with his lyre and his interest in geometry, is easily linked with the Muses and memory, which is the polar opposite of oblivion.

Pausanias (10.24.4) describes a statue of Apollo Musagetes (leader of the Muses) at Delphi. Henry Middleton describes statues of Apollo, Artemis and Latona standing in the eastern pediment of the new temple built at Delphi after the fire of 548 BC. He speculates , “a well-known series of statues in the Vatican of Apollo Musagetes and the Muses, though rather feeble works of Imperial date, look as if they were partly copies of some much earlier pediment sculpture” (Middleton 1888, 289, see also footnote 11, 2. 385 C).

121. (21. 394 A) Theoros is an observer or one who contemplates and Phanaean one who reveals or who brings light (discussed in section 2). Phanaeos is also an epithet of Zeus. Both epithets contrast

nicely with “Lord of night and sleep” in the fragment that follows. This fragment, and indeed the whole passage, appears again in An recte. dict. (6. 1130 A). For the fragment itself, see Bergk, 3. 719, = Adespota, 92; = Edmonds 3 452.

122. (21. 394 A) For the phrase, “of the gods the most hated by mortal men”, see Homer (Iliad, 9. 158-9) :

Ἀΐδης τοι ἀμείλιχος ἠδ᾽ ἀδάμαστος, τοὔνεκα καί τε βροτοῖσι θεῶν ἔχθιστος ἁπάντων:

… For Hades gives not way and is pitiless, And therefore he amongst all the gods is most hateful to mortals. (Tr. Lattimore)

123. (21. 394 B) Wyttenbach (1830) established δὲ θνατοῖς in “towards mortals he has been judged the gentlest” (κατεκρίθη δὲ θνατοῖς ἀγανώτατος ἔμμεν) by comparison with De def. 7. 413 C, where this fragment appears word-for-word, and in Non pos. suav., again word-for-word except for δὲ.

124. (21. 394 A) The Suppliants: 975. a Chorus of Argive women, mourning their slain sons.

125. (21. 394 B) A fragment in Bergk, 3, p. 224, = Stesichorus no. 50 = Edmonds 2, 58

126. (21. 394 B) A fragment of Sophocles, Nauck no. 764.

127. Ammonius has linked the E, symbolising the expression “You are” and an offering from the seven Sages with the aphorism “Know yourself”. He has demonstrated the uncrossable chasm between mortal substance which is always becoming but never is, and the god who is neither coming into being nor passing into destruction. The words and the views given to Ammonius might have come from Plutarch himself. Since Plutarch is both a participant in the dialogue and its narrator, we could interpret the dialogue as a comparison of Plutarch’s views and understanding as a young man, and his views as a mature man and priest.

Lamprias reports that the original E was a gift from the seven Sages to Apollo, putting it on a par with their other well-known maxims. This report is accepted without question by the other participants. There is only one other passage (that we know of) where the Delphic E appears (in De def. 22. 422 F), just after Cleombrotus’ long description of the arguments for and against the existence of exactly one world, or a finite number of them. We hear of the wonderful universe of Petron of Himera, containing 183 separate dancing worlds arranged in a triangle enclosing the Plain of Truth. (This long digression brings to mind the glancing attention paid by Young Plutarch to the question of the number of possible worlds.) Not surprisingly Cleombrotus’ description of these

theories and of the extraordinary man who spent his days by the Persian Gulf consorting with nymphs and roving demigods, was met with thorough scepticism by the participants. Cleombrotus himself introduces one of his more outrageous anecdotes by asking where else would he find such kindly listeners to test out his stories. The participants in De def. set a low bar for acceptable and credible philosophical discourse, and were unanimous in agreeing that the question of possible worlds had hardly met their threshold test. Consequently, when Philip remarked to Lamprias that plumbing the controversy over the number of possible worlds was more important to him than understanding the meaning of the E, he banishes that dialogue (De E ,)in which Lamprias participated, to the remote bathybial regions of intellectual enquiry.

εἰ δὲ τὸν θεὸν ἐκβιβάζομεν ἑνὸς κόσμου, διὰ τί πέντε μόνων ποιοῦμεν οὐ πλειόνων δημιουργόν, καὶ τίς ἔστι τοῦ ἀριθμοῦ τούτου πρὸς τὸ πλῆθος λόγος, ἥδιον ἄν μοι δοκῶ μαθεῖν ἢ τῆς ἐνταῦθα τοῦ εἶ καθιερώσεως τὴν διάνοιαν. But if we rule out that the god made only one world, then the question is: why do we restrict the god to creating just five and no more? and then: what is the relation of the number five to the rest of the many numbers? Personally, I should rather understand this than discover the meaning of the E dedicated here [in the temple]. (De def. 31. 426 F) This is a turnaround from the enthusiasm with which the participants in De E carried out their discussion. We see that the characters in the dialogue have convincingly demonstrated the limits of the search for the truth, there have been a succession of clouded insights and the uncovering of half truths. And, as with the Delian problem, to search for the truth, however hopeless, is an ineluctable instruction from the god. The limits of human knowledge are encapsulated in maxims and proclamations from the god, including the two maxims that recur throughout the dialogue, “Know yourself” and “Nothing in excess”

Ammonius is of the same opinion as Philip. He responds by finding the truth by proclaiming the absolute transcendence of divinity and coining his own aphorism or, if you will, mantra, “You are”. As he says, these are the words that people use when they approach the god. We can see the parallel to Socrates’ solution to the Delian problem. The E symbolises divine transcendence and the phrase”You are”, which does not require logic, dialectic, philosophy, or even geometry to be understood. No mortal can cross the chasm from Becoming to Being, not even through profound diligence and learning, but mortals can, through faith and the mantra “You are”, apprehend the god. Thus Ammonius answers the riddle to those who seek answers through reason by saying that it is through faith. .The votive E turns us outward to contemplate god as Being and the aphorisms of the sages turn us inward to understand our own humanity. 81

APPENDIX A: PLUTARCH AND HERACLITUS

The history of electrical development begins long before the Christian era when Thales, Theophrastus and Pliny tell of the magic properties of electron—the precious substance we call amber—that came from the pure tears of the Heliades, sisters of Phaethon, the unfortunate youth who attempted to run the blazing chariot of Phoebus and nearly burned up the earth. Nikola Tesla, Manufacturer's Record September 9, 1915.

From the little we can guess from the fragments from his lost book, Heraclitus the Ephesian drew on the cosmology of the Milesians, wrote on theology and was probably what we now call a public intellectual, and in any case a visionary.1 That book no longer exists and all that remains of his philosophy is “a handful of polished aphorisms scattered across the eastern

Mediterranean” (Lowry 1974, 434). Quotations from his work were filtered and collected by

Theophrastus (in a work now lost), the Stoics, the Christian Fathers, Diogenes Laertius,

Plutarch, and others. We may admire his prose, but not so much the man.2 He wrote a scornful assessment of Hesiod, Pythagoras, Xenophanes and Hecataeus, and thought that Homer and

1. Diogenes Laertius gives us the title, On Nature, and adds that Heraclitus deposited the book in the Temple of Artemis in Ephesus (DL 9.5). Plutarch wrote a study (also lost) of Heraclitus, “On the Question of Heraclitus’ Beliefs”, listed as Lamprias 205 (Moralia LCL, Vol. 15).

2 Not everyone admires Heraclitus’ style. Lucretius (De Rerum Natura, 1.638 44), objecting to his extravagant imagery and sophomoric wordplay, lambasted him for his obscurity and chastised those who enjoyed his wordplay,“mistaking it” for cogent reasoning.

Archilochus should have been excluded from rhapsodic competitions at athletic games. On the other hand, he approved of Bias of Priene, apparently for his probity.3 Bias, one of the seven Sages, is known to us for his maxim “Most men are bad” (πλεῖστοι ἄνθρωποι κακοί), which Heraclitus himself borrowed. He excoriated his fellow Ephesians for their stupidity

(Diels 121),4 and perhaps all humankind, of whom (he said) most are bad and very few good

(Diels 104).

The “art” in the title of a collection of the fragments, The Art and Thought of

Heraclitus (Kahn 1979) is apt since in the aphorisms form is as important as substance, and often the form is the substance. The art in the aphorisms lies in their careful structure, their ambiguity, and their use of literary ornament. Consider, for example, the fragment used in the epigraph to this thesis, ἁρμονίη ἀφανὴς φανερῆς κρείττων (Diels 54), according to Kahn “the shortest and most beautifully designed of the fragments” (Kahn 1979, 202). The two central words are the same adjective, positive and privative, and their central position presents the opposition that holds the sentence together (and illustrates Heraclitus’ doctrine of the unity of opposites). Kahn speculates that by placing ἀφανὴς before φανερῆς, Heraclitus is affirming

3. Diogenes Laertius often seems to enjoy gossip and name-dropping. Kahn (1979, 10) calls Diogenes’ Life of Heraclitus “a tissue of Hellenistic anecdotes, most of them obviously fabricated on the basis of statements in the preserved fragments”.

4. The different numbering systems for identifying the fragments are distracting. In this appendix, the Diels number of a fragment is always given. Numbers from other systems are given when they may help the reader find a particular fragment in a particular text. It is possible to track through different systems by using some combination of the following concordances; in Kahn, a one way concordance (Diels/Kahn) and a triple one-way concordance (Kahn/Diels/Marcovich); in Marcovich a one way concordance(Diels/Marcovich) and a triple-one way concordance (Marcovich/Diels /Bywater). Diels cross references his fragments to Bywater. 83

that “the negative term is superior to the positive and he has expressed in a formal way the dialectical re-evaluation of the negative principle”, but this may be going too far. It is easy to understand what the fragment says, but it not so easy to know what it means. If we think of an ambiguity as any verbal nuance that leaves room for different reactions to the same syntagm

(Empson 1949, 1), then Heraclitus’ use of three polysemic words allows us to read it in several different ways. I chose Keats’s translation because he has given the fragment context, a poem with a title and a form (the ecphrasis) that nod towards classical Greek literature and plastic art, and then the oxymoron “unheard melodies”, with the noun suppressed, a direct homage to Heraclitus’ appositional structure. I like to think that Heraclitus would have enjoyed the bad pun in the third line. There is no “right” translation of the fragment, but Keats gives one that respects the thought living in the Greek, and the art and artifice that we can sense in Heraclitus.

Bywater attributes this fragment (Diels 54, Bywater 47) to Plutarch and translates it:

“Of the soul, however, nothing is pure and unmixed nor remains apart from the rest, for ‘the hidden harmony is better than the visible,’ in which the blending deity has sunk variations and differences.” Bywater, on the strength of Hippolytus, also connects it to “whatever concerns seeing hearing, and learning, I particularly honour” (Diels 55, Bywater 13). 5 Both these fragments are credited to Hippolytus, Bishop of Rome in the late second century AD. In his

5. The Greek version – ἁρμονίη ἀφανὴς φανερῆς κρείττων – as given in the epigraph to this thesis is consistent, almost without exception, across editions and quotations of the fragments. Bywater (47) has κρείσσων for κρείττων, which is neither here nor there; Plutarch inserts “γαρ” (ἁρμονίη γαρ ἀφανὴς φανερῆς κρείττων). The careful structure of poetry, with its rhythms and rhymes and other extra-semantic attributes, simplifies memorization, and protects against faulty recall. Aphorisms such as this one may be easier to recall and quote exactly than less dense prose structures. 84

treatise The Refutation of All the Heresies, he argues that the source of the Neotian heresy could be found in the teachings of Heraclitus. He is responsible for eighteen of our

Heraclitean frgaments. Here is his exegesis of this fragment:

Heraclitus honours in equal degree the seen and the unseen, as if the seen and the unseen were confessedly one. For what does he say? “A hidden harmony is better than a visible,” and “whatever concerns seeing hearing, and learning, I particularly honour”, having before particularly honoured the invisible. (Hippolytus Refutation of All the Heresies, 9.9.10) We could draw up a table of opposites to contrast Plutarch and Heraclitus, the one scabrous, rude, antisocial, and misogynistic, the other moderate in his views and in his expression of them, gentle in his humor, and a participant in and host of elegant symposia.

Their only similarities are their love of learning and writing. One wonders what affinity

Plutarch could find for this strange man who lived half a millennium before him.

Yet affinity there was, and it is reflected in Plutarch’s attention to Heraclitus’ philosophy and writings and his numerous allusions to him in his own work. According to the

Lamprias catalogue, of the 120 or so extant fragments of Heraclitus, Plutarch cites thirty-two, and he is our sole authority for seven. He has about fifty distinct citations of Heraclitus (some are repeated) and seventy if one counts references to the testimonia.6

Plutarch was known to his contemporaries for the breadth and depth of his reading, and to modern readers for the variety, frequency, and zest of his citations.7 There are about

6. The testimonia are listed in section A of Diels, and the quotations in section B. This paper discusses only the quotations, and I have dispensed with the designation B for them.

7. Annewies Van Den Hoek (1993), in her essay on Clement of Alexandria’s methods of citation, briefly discusses Plutarch, on whom Clement often relied. Discussing note taking by ancient authors, including Plutarch, she describes the three “bookworms” (her term) – Clement, Plutarch, and Eusebius

7000 identified quotations and borrowings, from 497 authors, in Plutarch’s extant works

(Helmbold-O’Neil). Even in one short piece such as De E the resonance of Plutarch’s quotations and allusions, and their fitness to the occasion, delight the reader. In De E, we see in almost every speaker’s contribution to the dialogue a mention of an interesting problem or story that receives no more than a glancing remark, accompanied by a succinct quotation or allusion.8 Plutarch’s three attributed fragments from Heraclitus in this dialogue are in this vein

– short, but a direct contribution to the development of the narrative arc of the dialogue. The first is Young Plutarch’s use of the notion of exchange to describe the regularity and periodicity of the pentad (Diels 90), and the second and third occur in Ammonius’ argument on the many and the one and the gulf between human-kind and the god (Diels 91 and 76).

These allusions to Heraclitus are not only an ornament to Plutarch’s prose but also a contribution to the development of his ideas. Before discussing these further, it is important to describe the structure and content of the fragments.

THE HERACLITEAN FRAGMENTS

Heraclitus’ reputation for obscurity has probably been enhanced by the fragmentary nature of his extant writings and by the filtering of those fragments through his different authorities, with their different agendas and points of view. One puzzle for compilers has been how to present the more than one hundred fragments (estimated to be about half of Heraclitus’

– writers who reportedly loved books and libraries and who seeded their written works with the harvest from their omnivorous reading and meticulous note-taking.

8 For the sake of some examples, consider the story of the seven Sages (3. 385 D), the Delian problem (6. 386 E), the number of worlds (11. 389 F), the divisions of the soul (13. 390 F), the source of the illumination of the moon (15. 391 A), and musical theory (10. 389 D). 86

original output) without imposing an extraneous ordering or logic upon them. This question arises in our attempt to confront Heraclitus through Plutarch’s presentation of him in De E. I do not discuss the testimonia, nor descriptions of Heraclitus, his life, or his teachings.

Ingram Bywater (Heracliti Ephesii Reliquiae, Oxford, 1877) produced a Greek-Latin version of the fragments with an extensive review of the work of German philologists. This was quickly translated into English by G. T. W. Patrick (Heraclitus of Ephesus on Nature.

Baltimore: N. Murray, 1889).9 Patrick presents Bywater’s compilation as the culmination of a century of scholarly study (mainly on the continent) beginning with the publication of

Friedrich Schleiermacher’s Herakleitos, der Dunkle von Ephesos (1807), followed by the

Heraclitea of Jakob Bernays (1848). Bywater’s work provides an excellent introduction to the work of Heraclitus, and Patrick’s translation made it available

to every man to read and judge for himself [the philosophy of Heraclitus]…. The increasing interest in early Greek philosophy, and particularly in Heraclitus, who is the one Greek thinker most in accord with the thought of our century, makes such a translation justifiable, and the excellent and timely edition of the Greek text by Mr. Bywater makes it practicable. Bywater’s specialist work has been overtaken by the more general studies of Diels and Kranz on the pre-Socratic philosophers; nevertheless, Bywater remains a reliable and lucid

9. The English title, Heraclitus of Ephesus on Nature, tells us as much about Bywater as it does about Heraclitus. Bywater, Regius Professor of Greek at Oxford, had a keen interest in the natural and biological sciences. He was instrumental in establishing a scholarship in biology at Exeter College, Oxford, in 1872, and was a corresponding member to the Academy of Sciences in Berlin. He was also one of the academics involved in the organisation of the “Challenger” oceanic expedition (1872-76), which circumnavigated the globe to gather information on the world’s oceans. His obituary appeared in Nature 94 (1914): 455.

introduction to the Heraclitean fragments. 10 To my knowledge, Arthur Fairbanks (1897) was the first to analyse the records of Plutarch’s quotations from the early philosophers.11 Using

Bywater’s compilation (that of Diels was not yet in print), Fairbanks reviewed 228 fragments from these philosophers.12 In the case of Heraclitus, he found forty-eight fragments cited by

Plutarch (of which seven are in De E).13 About half of these raised the suspicion of being taken at second hand, either from Plato and Aristotle, or from some Stoic source; others are single phrases that were current and familiar (one in De E). Fairbanks winnows to four the candidates that might have been quoted directly.14

Diels built on Bywater’s work, but re-ordered the fragments alphabetically by the name of the source (except for the first, which looks very like a preamble to a treatise).

Amongst Diels’s contemporaries, John Burnet (1930) and H. Gomperz (“Über

10. Kahn comments favorably on Bywater’s contribution, “in many respects [Bywater’s compilation] has remained the most useful edition of any detailed study of Heraclitus (“A new look at Heraclitus” 1979, 189). Kahn sees Bywater’s methodical arrangement of the fragments by topic as a valiant attempt to interpret Heraclitus’ work as a coherent narrative argument.

11. These were Heraclitus, Empedocles, Anaxagoras, Parmenides and Xenocrates. See Arthur Fairbanks, “On Plutarch's Quotations from the Early Greek Philosophers”, TAPA 28 (1897): 75-87.

12. The precise numbers are Heraclitus 48, Empedocles 99, Anaxagoras 42, Parmenides 21 and Xenocrates 18.The number 48 apparently includes citations that Diels later included in his list of the Testimonia. There are fourteen testimonia listed in Helmbold-O’Neil, which, with the 33 citations by Plutarch, sums (almost) to 48.

13. They can be found in De E: 8. 388 C, 8. 388 E, 9. 389 C, 18. 392 A, 18. 392 C, 18. 392 D, and 21. 393 E. Fairbanks counts seven allusions or quotations in De.E, while Helmbold-O’Neil restrict themselves to the three signalled by a phrase meaning “as Heraclitus said”.

14. The four are: fragments 11, 12, 130, and 126 in Bywater (93, 92, 127, and 128 in Diels). Plutarch quotes the first three, and Pseudo-Plutarch the last. None is in De E 88

dieürsprüngliche Reihenfolge einiger Bruchstücke Heraklits.” Hermes, 58 [1923, 20]) disputed Diels’s arrangement, while Hermann Fränkel argued persuasively that the care and artifice exhibited in the construction of the extant fragments presupposed some larger coherent composition. Some later compilers (including Marcovich and Kahn) have arranged the fragments by their personal conceptions of their subject matter. Kirk restricts his analysis to the “cosmic” fragments, those “describing the world rather than men in particular” (1968,

30), and included about half of the extant fragments. Kathleen Freeman provided a handbook to the whole of the Die Fragmente der Vorsokratiker, following the Diels ordering whilst allowing herself diversions back and forth to different fragments to suit her line of exposition.

Eugen Fink and Martin Heidegger (Heraclitus Seminar, 1979) taking a step away from the linear ordering, used the Diels numbering system to identify the fragments but eschewed any significance to the order implicit in the numbers. Thus, at the opening of the seminar,

Professor Fink, on his own motion and authority, simply declares, “without further preliminary considerations, we shall proceed directly to the midst of the matter, beginning our interpretation with Fr. 64 [τὰδὲ πάντα οἰακίζει κεραυνός]”.15 This free form approach leads to a stimulating, if discursive, meander through 162 pages and forty-six fragments (some visited more than once). Obviously, to be productive, this approach requires well prepared

15. The source for this fragment (Diels 64, Bywater 28, Kahn 119) is Refutation of All the Heresies, 9.10.7. Diels translates this into German as “Das Weltall aber steuert der Blitz“ (Diels 1906, 71), which Seibert translates as “lightning steers the universe”. John Burnet’s translation is “the thunderbolt steers all things”.

participants who are familiar with the fragments, as the participants in the Heraclitus Seminar seem to have been.16

Fink chose this fragment because it is a transparent expression, with little of the

“linguistic density” that appears in other fragments.17 It consists of three words (ignoring the particle δὲ): τὰ πάντα; οἰακίζει; and κεραυνός. The English counterparts are: “all things”;

“steers” or “guides”; and “lightning” or “thunderbolt”.18 Heidegger commented that the

16. Martin Heidegger and Eugen Fink conducted this seminar at the University of Freiburg during the school year 1966-67. The plan was to repeat the experiment, but that did not come to pass. We know neither the names of the participants nor their number. Heidegger himself described the procedure as “venturesome” and “hazardous”; nevertheless, reading the account of the seminar stimulates both the mind and the imagination.

17. Kahn describes two properties of the fragments: linguistic density, “the phenomenon by which a multiplicity of ideas is expressed in a single word or phrase”, and resonance, “the relationship between fragments by which a single verbal theme or image is echoed from one text to another [so that] the meaning of each is enriched when they are understood together” (1979, 89). Kahn does not say so, but resonance must depend on some metric of distance. The closer together two fragments are, the easier it is to “see” a relationship. Closeness means that they are next to each other, on the same page, or share common words or electronic links. Diels’s instincts were good when he tried to randomise the fragments.

18. Bywater gives the context: “And he [Heraclitus] says that a judgement of the world and all things in it will take place by fire, expressing it as follows, ‘Now lightning rules all’, that is, guides it rightly, meaning by lightning, everlasting fire.” The “context” for Bywater is the context given in the source. The source of this quotation is Refutation of All the Heresies, 9.10 (Patrick, Heraclitus on Nature. 24, 1888, 91). Hippolytus is responsible for eighteen fragments (Diels 50-67). Similarly, the twenty-seven fragments cited by Plutarch appear in fragments 85-101. This classification creates anomalies, for instance in fragment 65, “need and satiety”, which lies within the range of Hippolytus’ citations, but is also cited in De E (9. 389 C), and similarly fragment 47 is also quoted by Plutarch but attributed to Hippolytus. Plutarch died a few years before Hippolytus was born. Two factors might explain this

sentence makes good sense in that one knows what it says, but, since each of the words is multivalent, not necessarily what it means.19 The ship analogy in “steers” is a perennial favorite that has persisted up to the present. The notion of steering or governing resonates throughout the fragments. Lightning could be a transferred epithet for Zeus, as Heidegger commented; “I remember an afternoon during my journey in Aegina, I saw a single bolt of lightning, after which no more followed and my thought was: Zeus”. Finally, the equating of

“all things” and “the universe” is an adventurous but not an unreasonable or uncommon leap.

Heidegger concludes this first chapter by noting that the opposition of the one (the lightning) to the all, is an opposition that preoccupied Heraclitus. In Appendix C, we see the reconciliation of the one and the many in the tetractys, a single entity identified with the cosmos, which is at the same time a collection of the all – the first ten numbers.

Heidegger demonstrates how one can enter the maze of the fragments at any point, in this case, via fragment 64, and still profit from reading them. Kahn, in a neat homage to

Heraclitus (see Diels 50, “all things are one “and Diels 10, “from all things one and from one

anomaly: first, as Fairbanks points out, “need and satiety” appears to have been a catch-phrase, and one that Plutarch did not describe as coming from Heraclitus; and second, Hippolytus’ citations are contained in a span of 1000 words, from Refutation of All the Heresies, 9.9.1 to 9.10.8, and their very density within this passage would not spur a researcher to look for other earlier sources.

19. Kahn makes precisely this point about the fragment “the way up and the way down is one and the same”(Diels 60) which, he says, provides indirect evidence for a larger (coherent) structure since the statement cannot be interpreted in isolation. “The literal interpretation of this remark poses no difficulties, but taken in isolation it is so ambiguous as to be devoid of significance. Everything turns upon what kind of "way" is meant, and that we could only learn from the context – from the sentences that came before and after.”

thing all”), comments, “one might reasonably claim that all of Heraclitus’ fragments have only one single meaning, which in fact is the full semantic structure of his thought as a whole, of which any given phrase is but an incomplete fragment” (1979, 95). 20

CITATIONS FROM HERACLITUS IN DE E

Having been shown the way by Heidegger, we can enter the fragments with Plutarch’s first explicit quotation from Heraclitus. By giving Young Plutarch a quotation about circular flow, Plutarch is setting the stage for Ammonius’ excursus on the theory of flux (πάντα ῥεῖ, a slogan from Cratylus 402). In section 8, even before he refers to Heraclitus, Young Plutarch proposes the hegemony of the pentad by describing the life cycle of wheat from the seed to the plant and back to the seed, “so she [Nature] leads this work to its logical end, and at the end she displays its beginning – wheat” (Diels 103). He then compares this to the cycle of counting by fives, where each number ends in either five or zero (5, 10, 15, 20, 25…), and makes the imaginative analogical leap from these cycles to those of the cosmos being

20. We have mentioned Heraclitus’ syntax, and the patterns he creates in his aphorisms; these include parallelism, contrasts, analogies and pairings. Another is the pattern of the geometric mean, A/B = B/C, which, as the mean proportional, provides a method for solving the Delian problem. Fränkel in an elegant paper (“A Thought Pattern in Heraclitus.” AJP 1938) demonstrates that Heraclitus applied precisely this proportion to metaphysics. He suggests that perhaps Heraclitus had learned from the Pythagoreans about the correspondence between musical intervals and progressions in geometry and algebra.” There is another correspondence, to the Pythagorean tetractys. The interior numbers of the Platonic Lambda are the geometric means of the exterior numbers.

continually created and destroyed in alternation, and to the Heraclitean notion of balanced exchange:21

For the first principle preserves the cosmos, and then out of the cosmos perfects itself and, as Heraclitus says, “all things are exchanged for fire and fire is exchanged for all things,” just as “gold is for goods and goods for gold.” This contains two different ideas, one about the cosmos and the other about individual exchange. In quoting this, Young Plutarch gives a version of Heraclitean theory of change – a closed dynamic system, autonomously maintaining its equilibrium. This aphorism, memorable both for its content and for its artful chiasmus, aptly reflects its connotations – circularity, reciprocity and fungibility. Closed dynamic processes were explored much later in

European philosophy; we see the same ideas of circularity in the “invisible hand” in The

Wealth of Nations of Adam Smith (1776) and in the Tableau économique of François

Quesnay (1758). Even the quotidian balance sheets of modern commercial book-keeping reflect the idea.

There is an ambiguity here, whether “fire” is one of the things in “all things” and included in them, or something apart. The imagery suggests that fire possesses a unique and universal value and is worth all the rest. Kahn sees an echo of “from all things one and from one thing all” (Diels 10, Kahn 124) and links it to the cosmic cycle. “The universal exchange for fire is, in one sense, a fact of human experience: we see all sorts of things go up in flames… but the generation of all things from fire… is a pure requirement of theory and devoid of empirical support” (Kahn 1979, 150).

21. Plutarch has ‘πυρὸς τ᾽ ἀνταμείβεσθαι πάντα … ‘καὶ πῦρ ἁπάντων, ὅκωσπερ χρυσοῦ χρήματα καὶ χρημάτων χρυσός (Diels 90; Marcovich 54; Kahn 40; Kirk 103; Bywater 22). 93

Young Plutarch speaks of the oneness of the unchanging Apollo and the transformations of Dionysus, adding, “but the periods of these cycles are not the same, the one that they call ‘satiety’ is longer than the one they call ‘craving’” (Diels 65). Young

Plutarch ends his discussion by defining the proportionate lengths of these, “as three is to one, so is the relation of the period of orderly disposition to that of fiery destruction”. Young

Plutarch has linked Apollo and Dionysus to the cosmos, whose nature is one of underlying law and order:

[which] is not dependent on any divine purposeful will, but all is ruled by an inherent necessary “fate”. The elemental fire carries within itself the tendency toward change, and thus pursuing the way down, it enters the “strife” and war of opposites which condition the birth of the world (διαχόσμησις) and experience that hunger (χρησμoσύνη) which arises in a state where life is dependent upon nourishment, and where satiety (χόρος) is only again found when, in pursuit of the way up, opposites are annulled, and unity and peace again emerge in the pure original fire (έχπύρωσις). This impulse of Nature towards change is conceived now as “destiny”, “force”, “necessity”, “justice” or, when exhibited in definite forms of time and matter, as “intelligence”. [Patrick 1889, 39] Nevertheless, although the term ecpyrosis was not used by Heraclitus, it was adapted and elaborated by the Stoics in their theory of cyclical growth and destruction. Young

Plutarch appears to be giving a Stoicised version of the Heraclitean notion of constant cosmic change. This change is regular, confirming Heraclitus’ notion of measure and balance, as both

Tarrant and Kahn emphasise. Thus, we see evidence of the cyclical rhythm at both the macro and micro levels. We can leave this here and await Ammonius’ response when it is his turn to speak.

In section 18, Ammonius responds to Young Plutarch, but gives short shrift to the claim that the votary offering E is about numbers in general or the pentad. He then cites two fragments from Heraclitus, which serve to contrast flux with circular flow: 94

For, it is not possible to step twice into the same river, nor is it possible to encounter a mortal being in one and the same state on two separate occasions. For a being changes its state so suddenly and swiftly that it both disperses and comes together and disperses again, or rather not again or later, but all at once; it is instantaneously both coming together and departing, is both ‘present’ and ‘absent’”.

The authority for this quotation is Plutarch himself, and whether it should be interpreted as an accurate citation of Heraclitus or Plutarch’s own summary of a longer statement, we cannot say. The detail “you cannot step twice into the same river” is even more contentious.22 As I discuss in section 18, some assert that this is no more than a loose paraphrase of “as they step into the same rivers, other and still other waters flow upon them” (Diels 12). Nevertheless, the river is quickly left behind as the subject of the argument and the mortal being who is both coming together and departing and both present and absent, comes to the fore. Ammonius is closing in on the focus of his argument, the difference between mortal beings, always in the process of becoming, and the god who is. He has achieved this by disposing of the numbers and their powers and lobbing back Young Plutarch’s Heraclitean simile with one of his own.

Ammonius then takes Young Plutarch’s imagery of the seed, and turns it to his own advantage by describing the transformation of the seed as its “death” and the transformation into the embryo as a “birth”, whence it is but a short step to another fragment, a description of the cosmic cycle, “for as Heraclitus said, ‘the death of fire is birth for air and the death of air is birth for water’” (Diels 76), with the afterthought, “and it is clearer still in ourselves”.

22. The authenticity of the two river statements fragments (Diels 12 and 91) and their relationship to each other is controversial. There are three versions of Diels 12, Aristotle, Meta.,1010a10-15, Cratylus 402a and De E 18. 92 B. The statement probably goes back to Heraclitus, but Plato does not give it verbatim. Kahn (168) finds it ironic that the most celebrated saying of Heraclitus cannot be traced directly to him. Plutarch’s version appears to be derived from Aristotle and Plato.

I discuss the Greek for these fragments in the notes to section 18, it suffices here to note that “mortal substance” includes animate beings, and that in the second quotation we are given the metaphor of birth and death for changes in elements that we usually do not consider animate. It is not clear whether Ammonius means that the afterthought came from Heraclitus or from himself. He continues to describe the many deaths that we suffer during our lives.23

Ammonius' discussion leads up to the introduction of a god who, “being one, has with one now filled forever”, and he uses the sayings of Heraclitus to support his basic contention that nothing of this world participates in true being.

Ammonius treats the theories of cyclical change and flux as opposites, but the fragments do not bear this out. Human beings in their temporal world may experience flux from birth to death, but many of the Heraclitean fragments are concerned with larger matters

23. Flacelière, (1941, 89, fn. 111) comments:

Ces idées n’expriment qu’un aspect de la réalité et comportement assurément une grande part d’exagération. Cf. Ricard dans sa note à ce passage [1884. 60 -61] : « Les vicissitudes que nous éprouvons dans nos gouts, nos affections nos sentiments, et même dans les traits de notre figure, ne détruisent ni l’unité de notre individu, ni la réalité de notre existence propre et individuelle ».

Obsieger gives two other places where Plutarch explores this idea. In the first, (De ser. Num. 15. 559 C), climaxes his argument that both man and city maintain some core of sameness with the riposte, “else we shall throw everything before we know it into the river of Heraclitus, into which (he says) no one can step twice, since Nature by her changes is ever altering and transforming all things.”

In the second, The Life of Theseus (23.1) explores the meaning when the idea is applied to an inanimate object – in this case, the thirty-oared galley on which Theseus returned to Greece from Crete. Whittaker (1969, 190) provides a similar example in Seneca’s letter to Lucius, On Being (58 22), calling the theme of the ages of man “evidently a Middle Platonic commonplace”. 96

– seasonality and periodicity, starting with the cycle of human generations, the sun’s annual turnings between the tropics of Cancer and Capricorn, and the Great Year when the sun, moon and planets return to their original relative positions after a lapse of 10,800 years.

My purpose in this brief discussion was to demonstrate that citations from Heraclitus played a role in Plutarch’s construction of the dialogue. After the discursive presentations of the earlier speakers in De E, these three fragments serve to focus the debate and provide a comparison between the arguments of Young Plutarch and Ammonius. Whether Heraclitus meant to make the two sets of changes – circular flow and flux opposites, as Ammonius asserts, is debatable. It is certainly clear that Heraclitus was talking about cosmic order and change, not necessarily stages of a man’s life. Furthermore, Plutarch prefaces each of these quotations with “as Heraclitus said”, so that we are in no doubt as to their source.

The more one reads of Heraclitus and rereads De E, the more one is struck by

Plutarch’s appreciation of Heraclitus, in so far as we can tell from such scant evidence. We can only speculate on how many other resonances and allusions we might have found in the complete works of Heraclitus (and the complete works of Plutarch). In footnote 13, I give the seven allusions to Heraclitus in De E identified by Fairbanks. The attentive reader will find other resonances in this dialogue and, of course, there are others scattered throughout the

Moralia. Expanding the focus to Plutarch’s use of Heraclitus in the Pythian Dialogues, or even in the whole Moralia could lead to fascinating insights.

Nevertheless, Ammonius has not reconciled Young Plutarch’s (and Heraclitus’) notion of circularity with his own (and Heraclitus’) notion of flux, which can be done, I believe by going beyond individual things (and goods) to the level of the cosmos. As we noted earlier

(8. 388 D), Heraclitus does not specify whether fire is a thing amongst “all things” or a thing 97

that encompasses all things but not fire itself (Russell’s and the Liar’s paradoxes). Ammonius may have seen the truth, but not the whole truth, which would include not only the fates of men and the gods, but also the other truth that Heraclitus sought, the truth about the cosmos.

Finally, I do not doubt that Heraclitus was a meteorologist and a cosmologist, in fact, a scientist. Kirk perceived the importance of this aspect of Heraclitus’ thinking when he confined himself to the cosmic fragments. Others have noticed this part of his philosophy and his interest in science. For example, David Wiggins (2009) has cited the possible scientific content of the fragment discussed earlier, “the lightning steers all things”. He compares fire, as Heraclitus conceived it, and energy, as conceived in eighteenth and nineteenth century physics:

Many plain men have scarcely any better idea of what energy is than Heraclitus had of what fire was. But most of us have some conception of energy. The common idea, and the idea that holds our conception of energy in place and holds Heraclitus' conception of fire in place, is the idea of whatever it is that is conserved and makes possible the continuance of the world-order”. Fink saw in the fragment, “The lightning steers all things”, a reference to the fire that lightning often engenders, and through that the idea of the fire that consumes all things. But that may be too literal an interpretation. Lightning may engender fire, but lightning s not fire but the manifestation of the release of a force, electrical energy. Nikola Tesla, another poet and visionary, saw in lightning one of the fundamental forces in our world – electricity or the power that resides in the electron. That force had been observed, if not understood, by the ancients. They knew of the static charge that develops in cat’s fur and silk. They also knew of the magical properties of amber. Indeed, in lightning we see another instantiation of

Heraclitus’ fragment, “the hidden connection is more powerful than the visible.” The other fundamental force still not understood is that of gravity. 98

In De E, Plutarch the priest of Apollo, writes of the golden-haired god who shares space with Zeus, Guide of Fate near the altar of Poseidon at Delphi. Apollo, god of the electron, flies with his musical swans, to the magical islands of the north, where amber grows on trees. Apollo, as Phoebus Apollo, is associated with the sun that burns with a heat greater than anything on earth, a heat generated, not by the electrical energy, but by another of the fundamental forces in our world, nuclear energy. In the myth, that is the heat that destroyed

Phaethon. 99

APPENDIX B: FREE INDIRECT DISCOURSE

Je ne suis pas toujours de mon avis. Madame de Sévigné (1626-1696) In De E, the transition from section 7 to section 8 contains an intriguing crux. We have reached the end of Eustrophus’ exposition on the E and are moving into Young Plutarch’s.

This is described in two sentences where Plutarch declares:

Eustrophus was not saying these things to us, in jest, but because I was at that time devoting myself enthusiastically to my mathematics. Nevertheless, I was to observe the maxim “Nothing in excess” just as soon as I became part of the Academy. Section 8 Then I said that Eustrophus’ explanation had most gracefully resolved the difficulty with Number. “For” I continued… Since the narrator (Plutarch) is also a character in the story, we must decide in each case of the use of a first-person pronoun whether he is communicating his present thoughts or those he had at the time of the event. There are two possible referents for the six first-person pronouns in these three English sentences, Plutarch, or Young Plutarch, and if it is Plutarch, he may be narrating the story, or as the author, be addressing parenthetical remarks to

Sarapion. For the first “I,” Plutarch the narrator is commenting on young Plutarch’s interest in mathematics. In other words, this is a self-reference to his younger self. In the second and third he is commenting in an aside on something that happened outside the time-frame of the dialogue. At the beginning of section 8, the last two pronouns “I” clearly refer to Young

Plutarch, first as speech reported by the narrator, then as the direct speech of Young Plutarch.

Finally, a first-person pronoun (“us”) appears as an indirect object in the first sentence, where it entails another self-reference to the narrator as part of the group. 100

This fussing over the grammar is not mere pedantry, but an attempt to understand the nature of the text that we are reading. Up to this point in the dialogue, we have seen a straightforward reporting of different interpretations of the meaning of the E. All seem to have had the same philosophical weight, all have been treated with mild scepticism by the listeners, and none has seemed persuasive. Babbitt makes the interesting comment that these first speakers are “searching for an explanation of the unexplainable” and that the dialogue provides an engaging portrayal of the way in which a philosopher reacts when “forced unwillingly to face the unknowable.” A reader who expected or believed that this dialogue was mere description or uncreative recounting of events that happened twenty years earlier should be disabused by this point. Plutarch’s self-referencing and shifting viewpoint suggests that we are not going to get an answer to the question of the meaning of the E but will have to settle for the insights into character and the intrinsic interest of the digressions into history and philosophy that Plutarch provides. Plutarch highlights the difficulty that the reader has in identifying exactly what the dialogue is “about”.1

Young Plutarch does not see the contradiction between his enthusiasm for mathematics and the motto of the Academy because for him there is no contradiction. The irony can be enjoyed by the narrator Plutarch, who surveys the whole timespan of the anecdote. To make this explicit, we could rewrite the sentence putting the original into reported speech and seeing that the irony has disappeared.

Eustrophus did not say these things to those present in jest, but because at that time Young Plutarch was devoting himself enthusiastically to his mathematics. But,

1. In contrast to this account, that given by Fink in The Heraclitus Seminar is a model of objective rapportage. No one could mistake that for a character study. 101

Sarapion, Young Plutarch did go on to observe the maxim, “Nothing in excess”, just as soon as he became part of the Academy. [Section 8] Then Young Plutarch said that Eustrophus’ explanation had most gracefully resolved the difficulty with Number. “For,” he continued, … In this version, the uninvolved narrator writes of all participants in the third person, since

Plutarch, as distinct from Young Plutarch, is no longer a participant, and he can replace “us

“with “those present”. Young Plutarch, a character in the narrative, knows only the present, not that he will one day join the Academy.

The technique of implicating the narrator in the story allows a character to appear in two (or more) incarnations. Both Young Plutarch and Plutarch appear within the same scene, and their simultaneous presence pulls us back to the present, where Plutarch is writing to

Sarapion. Thus, three time periods are telescoped into one scene. More generally time is fluid in the dialogue, where only two events in real time are given – the visits of Nero (1. 385 C) and Livia, “the wife of Caesar” (3. 386 A) – the first described by the narrator to Sarapion and the second (in direct speech) by Lamprias to the group. At the opening of the dialogue, the letter to Sarapion gives us three receding time periods. The first is the “present” where

Plutarch is writing to his friend Sarapion, the second occurred “just recently” and involves two of Plutarch’s teenage sons. The remembered encounter with his sons and his conversation about the E then conjures for Plutarch a meeting with Ammonius and several other friends.

This meeting took place even earlier, about twenty years ago and during the reign of Nero, we are told. Then, abruptly, we are in a dialogue, where Ammonius is introducing the subject to

Plutarch and his friends.

The observations that Plutarch, who as the author already has a presence, inserts himself into the narrative, and that he scrambles time are not original to me. I have seen three other instances where commentators make essentially the same observation. The first appears 102

in Flacelière’s translation of the Pythian Dialogues (1974). In his foreword to De def. he notes that the narrator in that dialogue has all the attributes of Plutarch, and appears to be Plutarch, although later, in section 8, he is identified as Lamprias. Flacelière, in his discussion of this passage (7. 413 C-D), recounts the contretemps with the Cynic Planetiades and comments:

Mais, il y a là un procédé littéraire, un kunstgriff [artifice] comme dit Wilamowitz, que nous avons déjà signalé à propos de Théon, personnage du De Pyth. Plutarque se substituant par moments lui-même à son personnage, comme par inadvertance et sans prévenir le lecteur. (Flacelière 1974, 86-87)

Leaving aside for the moment Flacelière’s reference to Theon, this dialogue, De def. begins as did De E – an unnamed narrator relates the substance of a discussion at Delphi to a friend.

The subject is the reason for the diminution and disappearance of many oracles in Greece.

There are seven participants: Lamprias, Ammonius, two eminent visitors, Cleombrotus and

Demetrios, and personnel from the temple, including Heracleon (but not Plutarch). In the first few sections, the narrator remains outside the conversation, relating the discussion between

Cleombrotus, Demetrius and Ammonius in the third person. These join another group, who invite them to join their philosophic discussion on which lambda, the first or the second, has been lost in constructing the future tense of βάλλω. At this point the narrator becomes part of the conversation, writing that “we” joined their company and sat amongst them. The careful reader (or an adept at reading and decoding detective stories) will notice that the word “we” eliminates Plutarch as the narrator, since he is not on the list of dramatis personae. It is only during the incident with the Cynic Didymus Planetiades that the name of the narrator is revealed.

The incident begins with the narrator explaining that Planetiades, incensed by the choice of the new topic for discussion (the disappearance of the oracles), claims (in indirect 103

speech) that there is so much evil in the world that Reverence (Αἰδὼς), and Divine Retribution

(Νέμεσις) have already fled the haunts of mankind, and that it is no wonder that Divine

Providence (πρόνοια θεῶν) has gathered up her skirts and oracles and followed suit. The narrator adds that Planetiades would have said more, but Heracleon intervened. The narrator, in direct speech and using the pronoun “I”, attempts to calm Planetiades. The narrative then continues, with “whatever I had said, worked; he [Planetiades] turned and went out the door without another word” (ἐγὼ μὲν οὖν ταῦτ᾽ εἰπὼν τοσοῦτο διεπραξάμην, ὅσον ἀπελθεῖν διὰ

θυρῶν σιωπῇ τὸν Πλανητιάδην). Section 8 continues the narrative with “It became quiet for a moment” (ἡσυχίας δὲ γενομένης ἐπ᾽ ὀλίγον), and Ammonius, “addressing himself to me” (ἐμὲ

προσαγορεύσας) in direct speech said, “See what it is that you are doing, Lamprias…” Thus,

Lamprias is revealed as the narrator.

Aside from that incongruous “we”, until this moment we have probably surmised that

Plutarch himself is the narrator. Flacelière bases his opinion on the narrator’s style, and a quotation from Pindar that appears three times in the Moralia. But there is another cogent reason for feeling that Plutarch may have inserted himself into the dialogue (se substituant par moments lui-même à son personnage). The wandering “I” allows the author (Plutarch) and

Lamprias (the narrator) to provide two different viewpoints. The description by the narrator that there was a moment of quiet, juxtaposed with the intervention of Ammonius that

Lamprias ought to concentrate on the matter at hand, suggests that the author sees a contradiction between these – first that Lamprias’ self reported comments were not effective and that Planetiades’ abrupt departure has shocked the other participants into silence. Plutarch the author, but not Lamprias himself, is aware of the pain to Planetiades that Lamprias has caused. 104

Flacelière refers us to Ulrich von Wilamowitz’s Der Glaube der Hellenen, where

Wilamowitz, too, in precisely this passage, identifies Plutarch’s tendency to blur the boundaries between the narrator’s thoughts and words and those of his characters.2 He does not go beyond identification to an analysis of this device or trick [Kunstgriff], but simply states that, at 413 D, the Cynic Planetiades is swiftly silenced by Plutarch’s brother Lamprias, whom Plutarch has made so much like himself that we might see Plutarch as the narrator of the dialogue. Wilamowitz then refers to his own Commentariolum Grammaticum III.3 In that document, written in Latin, he again describes the phenomenon of Plutarch’s appearing in his own writings where one might not expect him. He remarks on another example in De fac. where Lamprias is again one of the participants. None of this needs to detain us, except that in the first sentence in the opening paragraph of the analysis of that dialogue he writes (and we can see where he is going):

Sed redeo ad prosopopeian Plutarcheam. But back to Plutarchean personification. (i.e. his characters’ speeches) Although in German Wilamowitz uses the generic Kunstgriff, which could be a trick of any sort and not necessarily literary, in Latin he came up with the immensely appropriate Latin borrowing from the Greek, meaning mask, face, or personage, with theatrical and dramatic connotations.

To return to the second example, of Theon in De Pyth. (nous avons déjà signalé à propos de Théon): Flacelière claims that in that dialogue (409 B) Theon, when he discusses

2 Ulrich von Wilamowitz-Moellendorff Der Glaube der Hellenen. Berlin: Weidenmannshe, (1889 2, 499),

3. Ulrich von Wilamowitz-Moellendorff, Commentariolum Grammaticum. Gottingen: (1889 3, 27). 105

the rites at the temple and the leader of “our” administration, speaks as if he were Plutarch.

Flacelière repeats almost word for word what he had said earlier about Plutarch and Lamprias in De def.:

Cependant il n’est pas impossible que l’on doive identifier malgré tout ce Théon à l’ami de Plutarque, à condition d’admettre que Plutarque a utilisé ici, comme ailleurs, ce singulier procédé littéraire par lequel, comme par inadvertance et sans en prévenir le lecteur, il se substitue soudain lui-même à l’un des personnages qu’il met en scène. (Flacelière 1974, 43)

Flacelière is correct that this sounds much like a priest of Delphi speaking. This dialogue is structured differently from both De E and De def. As in the script of a drama, each passage is prefaced by the name of the speaker, and at first it seems that all information will be conveyed to us through the direct speech of the characters. But by section 4 the author comes into focus with remarks such as “said Diogenianus” and “Theon replied”, and he turns into a participant by using the pronoun “we” – “we urged him on…, “we accepted this”, and so on. Again,

Plutarch is not listed amongst the dramatis personae, so Flacelière is correct that Plutarch has once again inserted himself into the dialogue, which has evolved from a script into a narrative

(with a narrator). Again, the use of the first-person plural (“we”) conflates the narrator with a character in the dialogue.

Finally, Frieda Klotz (2011) describes how Plutarch recounts autobiographical details:4

4. See Freida Klotz, “Imagining the past: Plutarch’s Play with time.” eds. Frieda Klotz and Katerina Oikonomopoulou. The philosopher’s banquet: Plutarch's Table Talk in the Intellectual Culture of the Roman Empire. (Oxford: Oxford University Press, 2011.) and “Portraits of the

106

He shuffles his youth and development into an unexpected a-chronological structure, and although he begins… the book with scenes in which his own character is mature and authoritative, he ends with his teacher [Ammonius] playing the main role. This is also how Plato structures the Symposium, with Socrates eventually ceding pride of place to Diotima.5 Klotz’s assessment is also an accurate description of the structure of De E.

Plutarch follows the same scheme here, with young Plutarch as a character, and an Ammonius who takes the stage at the end of the dialogue for his master class in “God is”. Klotz focusses on the Table Talks, but much that she says applies to the dialogues, and it is certainly true in

De E that no one ever addresses Plutarch by his name. She claims that, this anonymity, rather than downplaying his importance, has the opposite effect. The unnamed shifting ego signifies

Plutarch as different from the other characters and draws our attention to him. Klotz does not make the connection to the use of personal pronouns and the author’s use of first person or third person narration, which is discussed below in the continuation of the analysis of the narration of De E.

In De E, the example given earlier on the transition from section 7 to section 8 is extraordinary in that we confront the two Plutarchs on the same page. The juxtaposition is not just a literary flourish since their simultaneous presence presages Ammonius’ argument on the difference between Being and Becoming. Every mortal being is always in the process of

“coming-into-being’, so that we get instantiations such as Young Plutarch and his older self.

This is a fine illustration of the implications of Ammonius’ assertion.

Philosopher: Plutarch’s Self-Presentation in the ‘Quaestiones Convivales’.” Classical Quarterly 57 (2007): 650-67.

5. See Daniel Babut, “Peinture et dépassement de la réalité dans le Banquet de Platon.” Revue des Études Anciennes. 82, (1980) : 5-29.

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Other examples where Plutarch inserts himself in the dialogue occur in De E at the points where one speaker hands over to another,6 where the transition is usually accomplished through an intervention from the narrator. In section 2, Plutarch gives a summary of

Ammonius’ analysis of Apollo’s names, and then allows Ammonius to continue without interruption in direct speech. Section 3 begins in the same way, Plutarch says that Ammonius has finished and introduces the next speaker, Lamprias, who continues without interruption.7

Section 4, except for the last sentence, is entirely in indirect discourse.8

A different authorial intervention occurs in sections 6 and 7. There, Plutarch introduces parenthetical remarks addressed to Sarapion, which serve to pull us out of the past and remind us that this dialogue is indeed being reported in a letter. In section 6, Plutarch introduces “my friend Theon, whom you know”. Theon is thus the friend of Young Plutarch,

Plutarch, and Sarapion, and we know that he has survived the intervening twenty or so years since the dialogue took place. We have returned to the present when the letter was written and

6. These points are set out in the Schema: Structure of the Dialogue, page 16.

7. The reader may have noticed that the section divisions track the changes of the speakers, and wonder why the section breaks do not provide sufficient sign-posting of the parts of the dialogue, and of the shift from one speaker to another. Surely the division into sections says it all. In answer, I do not believe that the section numbers are original to Plutarch, although I have been unable to determine their source. They may have been created by Wyttenbach, where they do appear. They do not appear in Amyot. The place to look for an answer would be in the Aldine collection in the Rylands Library in Manchester, England. If they did not exist then it is reasonable that Plutarch built in his own markers within the narrative that separates direct speeches. De Pyth. begins with a formal dialogue, with each speaker named at the beginning of his particular speech, but that soon evolved intothe system we have here.

8 See fn. 21 in section 4.?? 108

to Plutarch – the letter writer, who can be distinguished from the narrator of the dialogue when he addresses Sarapion directly (and us indirectly). This is confirmed at the beginning of section 7 where Plutarch introduces the next speaker with “it was, I think, Eustrophus the

Athenian” (Εὔστροφον Ἀθηναῖον οἶμαι). Both the hesitation contained in “I think” and the two pronouns require thought. The hesitation suggests that Plutarch the letter writer is not sure that his memory serves him (although he later repeats the name with confidence). So, the referent of the “I” is directing a parenthetical remark to his friend Sarapion, apparently to warn him that his memory may be faulty. On the other hand, the pronoun must include the narrator, the Plutarch of twenty years before who participated in the dialogue. As discussed earlier, at the end of section 7, Plutarch again makes a parenthetical remark about joining the

Academy to Sarapion, who, no doubt enjoyed the joke about “Nothing in excess”.

The contributions of both Young Plutarch and Ammonius (sections 8-21), are delivered almost entirely in direct speech. Logically enough, an intervention occurs at the point where Young Plutarch cedes the podium to Ammonius. The last sentence in section 16 and the first in section 17 read:

[Section 16] τοιοῦτο μὲν καὶ ὁ τῶν ἀριθμητικῶν καὶ ὁ τῶν μαθηματικῶν ἐγκωμίων τοῦ Ε λόγος, ὡς ἐγὼ μέμνημαι, πέρας ἔσχεν. Section 17 ὁ δ᾽ Ἀμμώνιος, ἅτε δὴ καὶ αὐτὸς οὐ τὸ φαυλότατον ἐν μαθηματικῇ φιλοσοφίας τιθέμενος, ἥσθη τε τοῖς λεγομένοις [Section 16] And that is, as I remember, how the discussion of the arithmetical and mathematical encomia to the letter E came to its end…. Section 17 Ammonius, in as much as he too believed that a not negligible part of philosophy is found in the study of mathematics, was pleased with the direction of the discussion.

The first sentence contains an aside to Sarapion and the second an authorial observation on

Ammonius’ state of mind, which can be interpreted also as an aside to Sarapion. Thus, the 109

referent of the “I” is Plutarch the letter writer, and the sentence beginning section 17 is an authorial intervention describing Ammonius’ state of mind.

ALThese interventions remind us of the temporal layers in the dialogue and its air of nostalgia, a nostalgia that is also obvious elsewhere in the Pythian dialogues. Plutarch’s references and allusions to thinkers of the past, Homer, the seven Sages, Hesiod, Heraclitus, and Pythagoras, add to the effect. In De E, when we listen to the conversation of those seated by the temple, we are taken back to these philosophers, who lived even before Cratylus, Plato and Aristotle. In the introduction, Plutarch describes to Sarapion the group at the temple at

Delphi and his own sons (1. 385 A), an image mirrored by the group surrounding Ammonius many years before (1. 385 B). Plutarch goes even further by seeking from Sarapion reports of similar discourses, which reflects the image of these discourses into the future. Plutarch’s self- referencing goes beyond his implication in his own story to the implication of his own story in a series of stories going back in time to the seven Sages, and potentially forward into the future. Plutarch gives us no markers to his own time, except for the references to Augustus and Nero, and we are lulled on gentle tides between the “present” of the letter to Sarapion and the implied future of return gifts from him; the “recent” encounter between Plutarch and his sons, and the recollections of the mature Plutarch on the “past” where Young Plutarch, his brother Lamprias and their friends cavort under the intellectual guidance of Ammonius. This returns us to the reciprocal and reflexive giving of gifts, described by the reversion from

Dichaearchus to Euripides to Archelaus in the opening lines of the dialogue. The dialogue’s first word, στιχίδιον, announces and describes the dialogue’s own structure. The word describes the whole, just as Plutarch describes his own self within the dialogue.

FLAUBERT AND AUSTEN : LE DISCOURS INDIRECT LIBRE 110

To my knowledge, only Flacelière, Wilamowitz and Klotz have commented on Plutarch’s modes of speech and narration in the dialogues. Their textual analyses suggest Plutarch’s skill and sophistication but do not venture far into a literary analysis. Only Klotz comments on the fluid nature of time in much of Plutarch’s work, which is, I believe, a direct result of his narrative style. The analysis of direct speech is straightforward; the text gives us what the character is supposed to have said, in the character’s own words. The only caution is, of course that it is Plutarch, the puppet-master, who is putting these words into their mouths.

Plato made a distinction between narration (diegesis) or authorial presentation on the one hand, and imitation (mimesis) on the other.9 In direct discourse, a writer speaks in the person of another, assimilating his style to that person's manner of speaking, just as an actor does when using voice and gesture; he imitates the person whose character he assumes. When a writer uses direct speech for his characters, it is the character who speaks to us, but in indirect discourse, our understanding of the character is filtered through the thoughts of the writer.

Lucian’s Metamorphoses has been analysed in much the same way by Andrew Laird.

He contrasts the use of the first-person voice in discourse and the third in narration. He finds that ancient theorists did not often recognise the differences between literary expression in the first and third persons. He then analyses several examples of free indirect discourse in the

Metamorphoses, which we need not go into, but he finds the first and third persons used to the

9 Modern writers have explored the use of mimesis and diegesis in classical biography and fiction. Andrew Laird, (“Person, ‘Persona’ and Representation in Apuleius’s Metamorphoses.” Materiali e Discussioni per L’Analisi dei Testi Classici (25 [1990]: 129-64) explores the distinction between the historical author and his (or her) fictional persona, using Lucian’s Metamorphoses. See also Tim Whitmarsh, “An I for an I: reading fictional autobiography” in The Author’s Voice in Classical and Late Antiquity, by Anna Marmodoro and Jonathan Hill, Oxford: 2013. 111

same end that we discovered when reading De E. Laird’s description and interpretation of free indirect discourse is like that which we saw in sections 7 and 8:

The interesting quality of [these] instances of free indirect discourse in Apuleius's narrative is that they could be quotations of articulate thoughts of Lucius the character made at the time described. Or they can be discursive utterances given by Lucius the narrator at the time of narration – probably this is how they would strike a listener: there are no declarative verbs of saying or thinking, and the exclamations are enclosed in pure narrative. But we must really entertain both possibilities – a synthesis of two voices, character and narrator, which respectively epitomise our two modes, namely, narrative and discourse. The quotation of the character's words is the property of narrative; the expression of the narrator’s current sentiment is the property of discourse. The “expression of the narrator’s current sentiment” in De E is contained in those parenthetical remarks that I have described as being directed to Sarapion, to whom Plutarch’s letter is addressed. Laird continues that the Metamorphoses combines elements of narrative and discursive genres, for its stylistic techniques such as apostrophe, occupatio, a specific type of free indirect discourse and self reference. He claims that none of these features were conspicuous in prose fiction, either Latin or Greek, before Apuleius. Laird may be right that

Apuleius was the first to use these figures so extensively. Plutarch also uses them, but no one would describe Plutarch’s dialogues as “fiction”, nor would they unhesitatingly call them

“discourses”. Plutarch writes in the first person, as he would in a discourse, but he also uses the figures emblematic of fiction given by Laird and uses them with skill and sophistication.

Narrative can also be varied by using correspondence, inserted quotations, and flashbacks, as well as changes in the scope of the voice of the narrator. It can also be varied by using free indirect discourse, where there is no abrupt jump the from narrator's 112

consciousness to the character’s consciousness.10 The two literary writers best known for their use of this style, and probably the most studied, are Jane Austen and Gustave Flaubert. This paper is not about them, but they must be mentioned. On the other hand, their work has been analysed so often and so exhaustively that it is difficult to say anything fresh. My only contribution is that one can see a family resemblance between Plutarch’s insinuation of his own persona into his writing, and the more developed technique of Flaubert and Austen, and much modern experimental literature. We can appreciate that even two millennia ago, writers such as Plato, Aristotle and Plutarch were interested in the techniques of writing.

Consider what is possibly the best known first sentence in an English novel. “It is a truth universally acknowledged, that a single man in possession of a good fortune must be in want of a wife” (Pride and Prejudice, 1813). Austen has defined the clause “that a single man in possession…” as a “true” statement (“a truth universally acknowledged”), even as she undermines it by subordinating it. The truncated statement, “a single man in possession of a good fortune must be in want of a wife,” as a complete sentence, gives a different impression.

If this were the opening sentence, one would expect a different novel, perhaps just a

10. I have consulted the following sources on the history and theory of discours indirect libre: P. Hernadi, "Dual Perspective: Free Indirect Discourse and Related Techniques." Comparative Literature (24 (1972): 32-43); Paul Hernadi, "Verbal Worlds between Action and Vision," College English (33 (1971):18-31); Norman Friedman, "Point of View in Fiction: The Development of a Critical Concept." (PMLA 70 5 (1955): 1160-184); and Yun Lee Too, The idea of ancient literary criticism (Oxford; New York: Clarendon Press, 1998); and Bernard Cerquiglini, « Le style indirect libre et la modernité », in Langages, 73 (1984) : 7-16. Norman Friedman has associated Socrates' "three styles" of poetry with modern "telling" and "showing”, and Paul Hernadi explores the dual roles of literature as representation (mimesis) and presentation (narration).

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romance.11 Similarly, at the end of section 7 in De E, the irony arises from the two different viewpoints contained in a compound sentence. The sentence sets up a tension between the narrator and those who might acknowledge the truth of the statement. We the readers are left to ponder the strength of “universally” and whether, even if some find the statement true, we can go so far as to say this its truth is acknowledged by all. Surely the author is taking too much upon herself with such a categorical statement.

Stephen Ullmann describes Flaubert’s mature use of indirect style in Madame Bovary in statistical terms. Flaubert has as many as five instances of the style to a page of the novel, more than Ullman has seen in other works. Certainly, the instances are more frequent than the three that I have found in De E (which is certainly shorter than Madame Bovary). I give the celebrated image of Emma as a good mother (1856 part ii, 4 147): “Elle déclarait adorer les enfants ; c’était sa consolation, sa joie, sa folie, et elle accompagnait ses caresses d’expansions lyriques, qui, à d’autres qu’à des Yonvillais, eussent rappelé la Sachette de

Notre-Dame.” As Ullmann tells us, “Grammatically, ‘c’était sa consolation, sa joie, sa folie' might be the author's own words, but the reader knows from the context that it is Emma, not

Flaubert, who is speaking, and that she is not telling the truth” (Ullman, 109). We know that it cannot be the narrator who tells us that Emma's little child was a joy and consolation for her.

Rather, reader and narrator share an ironic distance from the woman who tries to appear what she is not – a devoted mother. Ullmann does not quote the last part of the sentence, where it is not Emma who speaks but the narrator, “qui, à d’autres qu’à des Yonvillais, eussent rappelé la

11 Laird cites this sentence, saying, “moralizing such as we find in Jane Austen is discourse, not narrative”. (Laird “Person, Persona.”, 136) 114

Sachette de Notre-Dame.” Here, Flaubert uses an extravagant comparison to Sachette (from

The Hunchback of Notre Dame, who idolised her baby daughter Esmeralda, unfortunately stolen by gypsies) to tell us that those who did not know Emma (i.e. those who did not live in

Yonville), might well be persuaded to see her as another doting mother. Thus, after letting

Emma convict herself out of her own mouth, the narrator then steps into the minds of those who do not know her, and hypothesises on their reactions to her words, if they could have heard them. A fine and intricate mixture of authorial commentary.

The precise genre of De E has been the subject of debate, some seeing it as a didactic piece, or as a discourse on religious themes. By coincidence, Appendix A led us to read and consider Fink and Heidegger’s Heraclitus Seminar.(1970), whose declared purpose was to explore the thinking of Heraclitus:

Our seminar is not concerned with a spectacular business. It is however concerned with a serious-minded work. Our common attempt at reflection will not be free from certain disappointments and defeats. Nevertheless, reading the attempts of an ancient thinker, we make the attempt to come into the spiritual movement that releases us that releases us to the matter that merits being named the manner of thinking. There are echoes here of Ammonius’ introduction to the interpretation of the E, given two millennia ago. Plutarch is also engaged with a serious-minded work, but not one that is spectacular or portentous. The subject of the E is not a showy or pressing philosophical problem, but it could through collegial debate and discussion lead to intellectually satisfying ideas and conclusions. The Heraclitus Seminar then proceeds into a dialogue on the fragments, just as De E proceeds into different interpretations of the E. But there the similarity ends, the narrative style of the two seminars differs.

The Heraclitus Seminar is written entirely in direct speech with each speaker identified (as De Pyth. began in the first two sections), although only Fink and Heidegger are 115

identified by name. The other participants are called, generically, “Participant”. Fink,

Heidegger, and the participants are all on the same plane, equal partners in the dialogue.

There is no authorial presence and we could imagine that the report of the seminar is a transcript by a court reporter, or a transcript of a sound recording of the meeting. The whole thing is quite bloodless. Professor Heidegger has the last word:

At the close, I would like the Greeks to be honoured, and I return to the seven Sages. From Periander of Corinth we have the sentence he spoke in a premonition: μελἕτα τὸ πᾶν. “Ιn care, take the whole as a whole”. Another word that comes from him is this: φὕσεως καταγορἵα. Hinting at making nature visible. Heidegger’s concept of a philosophical dialogue could be Plutarch’s, or Ammonius.’ The approach to truth and true understanding proceeds through stages of conversation, thinking and learning.

Plutarch’s procedure is different. He uses his literary skills to embellish his prose with literary devices, character sketches, indirect discourse, and through authorial interventions that scramble discourse with narrative. This makes for a richer mix than Heidegger gives us in his exemplary but plain style. We come away from Heraclitus Seminar with questions and comments about the philosophy of Heraclitus, but none about the comportment or personalities of the participants at the seminar. Whether one believes that questions such as who Theon was, is a disfigurement or an embellishment to the basic question of the meaning of the E, is entirely personal. It suffices here to say that Plutarch has chosen to write a dialogue that is more than a bare-bones discourse on a philosophical problem. 116

APPENDIX C: THE TETRACTYS

Live, primrose, then, and thrive With thy true number five; And, woman, whom this flower doth represent, With this mysterious number be content; Ten is the farthest number; if half ten Belongs to each woman, then Each woman may take half us men; Or—if this will not serve their turn—since all Numbers are odd, or even, and they fall First into five, women may take us all. — “The Primrose” John Donne (1572-1631)

The word “tetractys” is not used in De E, but its meaning is implicit in almost every discussion of numbers there, especially in sections 8 and 10. Young Plutarch’s exposition of arithmology in section 8 focusses on the number five, the pentad, but the context is the decad, the system of the numbers between one and ten, represented by the tetractys.1 In section 10,

1. Waterfield (1988, 23) distinguishes arithmology from the hard science of mathematics (for example, Euclid). Jean-Pierre Brach asks how the two types of arithmetic, mathematical and the analogical, are related, and how such a relation can be justified philosophically and conceptually. He finds that the “the rather disorderly and uncritical accounts in the few Hellenistic sources left to us” leave those questions unanswered. These sources are Nicomachus of Gerasa, Theology of Arithmetic (surviving fragments in Photius, Bibliothèque [cod. 187], 40-48); Anatolius, On the Decad; and Iamblichus, Theology of Arithmetic. (See “Mathematical Esotericism: Some Perspectives on Renaissance Arithmology.” In Hermes in the Academy. By Wouter J. Hanegraaf and Joce Pijnenburg (eds) Amsterdam University Press, 2009 Pp 75-89

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he advocates the highly mathematical approach to musical harmony developed by the

Pythagoreans, where we recognize the commonality of the tetractys with the tetrachord.

The OED dates the first use of the word to Dr. Philemon Holland’s 1603 translation of

De Is., where he transliterates the word, and yokes it to its Latin translation: “that famous quaternarie [of the Pythagoreans], named Tetractys”. In the same passage, Babbitt contents himself with “the so-called sacred quaternion”. Perhaps through inadvertence, Holland uses quaternerie for tetractys in De an. procr. where tetractys again appears.2 The notion of

“fourness” comes through in ‘quarternary’, but the Pythagorean understanding of the tetractys is so foreign to our modern intuition of arithmetic that the similarly foreign looking Greek word is probably preferable to the Latin, then we can remember that it means something more than “four” or a “set of four”. Figure 1 illustrates the notion of fourness in the tetractys, and its identification with the decad (and the universe), as the “four is the ten”, according to

Pythagorean lore.

Jean-PieRRe BRacHyancient arithmological writings, including principally those of Varro, Philo, Nicomachus, Theon of Smyrna, Anatolius, the compilator of the Theologumena Arithmeticae, Chalcidius, Macrobius, Martianus Capella, Favonius Eulogius, and Johannes Laurentius Lydus. Θεολογούμενα ἀριθμητικῆς

2. OED, s.v. “tetractys”. The word has four entries, all associated with either Pythagoras or Plato. The 1846 entry is a convoluted joke that will etch forever the meaning of the word in the reader’s mind. In the foreword to a collection of four works by Richard Baxter (an English Puritan, church leader, poet, hymnodist, and theologian), Professor T. W. Jenkyn writes, “Those who understand what Tetractysm was to the Pythagoreans will comprehend what Triadism was to Baxter.” Baxter’s Nachleben also includes several spots on YouTube. See: “The Signs & Causes of Depression - Puritan Richard Baxter”: https://www.youtube.com/watch?v=WJLd3vsVpc 118

● ● ● ● ● ● ● ● ● ●

Figure 1. The Pythagorean tetractys

This triangular figure, in its completeness, represents the unity of the decad and of the cosmos. It contains ten elements representing the first ten integers and four rows representing the first four numbers. In modern arithmetic we represent this as:

1 +2+3 +4 = 10

It is not obvious from this equation that ten is a triangular number, but it follows from the arithmetic definition, the sum of the first four integers. Triangular numbers are formed from the sum of a set of consecutive integers, starting from one. The first six triangular numbers are: 3, 6, 10, 15, 21, 28, 36.

This appendix relies heavily on Waterfield’s translation of Iamblichus’ Theology of

Arithmetic (τa θεολογουμενα της αριθμητικής), written after Plutarch lived and centuries after the Pythagoreans were philosophising and arithmetising. The manuscript was first edited in

1817. Thought to have been compiled by Iamblichus; its chief sources are Anatolius and the

Theologoumena Arithmeticae of Nicomachus of Gerasa.3 Keith Critchlow, in his introduction

3 These names appear above in rough reverse chronological order. For greater clarity I give their generally accepted dates in chronological order: Pythagoras (fl. 540 BC); Nichomachus (fl.100); Plutarch (c. 50-c. 120); Anatolius of Alexandria (fl. 269); Iamblichus (245 – c. 325); Aetius (391-454). On these dates, it is not impossible that Plutarch knew of Nichomachus’ work, but these dates may not

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to Waterfield’s translation, quotes Aetius, who relates Pythagoras’ description of numbers as

“the first principles” and their interrelations as “harmonies” (Waterfield 1988, 9). Today, we might call such harmonies “the structure of the number system”. Furthermore, these numbers were not generated by a succession or a progression, but rather represent a unity with ten different qualities. This structure is beautiful, and harmony is indeed an apt description of it.

Armand Delatte notes that in antiquity there was a pseudo-science of the numbers and their properties that today we could not decently call “arithmetic”. As to the coining of the word “arithmology”, he adds:4

It is found for the first time, to my knowledge, in a fragment of Codex Atheniensis of the eighteenth century…. Under the title ̉Aριθμολγία η̉θιχή (ethical arithmology), the author has grouped series of numbers describing actions honest or dishonest, pious or impious, found in the sacred writings of the Old Testament (Solomon, Sirach, etc.). (1915, 139)

Waterfield has similar reservations about the enterprise of Pythagorean number theory. For the Pythagoreans, “God manifests in the mathematical laws that govern everything, and the understanding of these laws, and simply doing mathematics could bring one closer to God”

be right. There is a story that Nichomachus was born a generation and a half later than the date given above, based on the belief that the cycle of Pythagoras’ regular reincarnations was 216 years.

The story goes that Proclus the Neoplatonist (born 412) had a dream that he was a successor of Pythagoras, and hence his immediate predecessor must have died in the year 196. J. M. Dillon ("A Date for the Death of Nicomachus of Gerasa?" Classical Review 19, (1969): 274-75.) traces out the argument that led to identifying this person as Nicomachus of Gerasa. Dillon then argues that Nicomachus could have been born no earlier than 120 – too late to know Plutarch, or for Plutarch to know of him.

4. My translation. Delatte gives the reference for the codex: (Bibliothèque de la Chambre, n. 65), f08 198a sq. 120

(Waterfield, 1988, 24). Thus, the name arithmology designates remarks on the structure and importance of the first ten numbers, where sober scientific thought and religious and philosophical conjectures are mixed together.

The Pythagorean tetractys contains the four basic musical intervals, the fourth, fifth, octave, and double octave; also, the Platonic point, line plane and solid; it reflects the understanding that the Greeks (and many) barbarians counted from one to ten and then started again at one. Pythagoras is said to have remarked “What you suppose is four is really ten, and a perfect triangle, and our oath.5 The word “tetractys” appears in two essays in the Moralia,

De Is. and several times in De an. Procr.

In De Is. Plutarch is describing Egyptian religion to his friend, Clea, a priestess at

Delphi, explaining that the Egyptians link the names of their kings to the numbers. This reminds him of similar properties in number theory, where the Pythagoreans gave numbers and geometric figures the names of the gods. The number 36 (the sum of the first four odd numbers and the first four even numbers) was called the holy tetractys and used for the most sacred of oaths. This number, too, resonates with the notion of “fourness”.6

Plutarch wrote De an. Procr. (14. 1027 E; 1019 A-B) to help his teenage sons understand Plato’s Timaeus. Given its purpose, Plutarch is not breaking new ground, but providing a teaching tool. We are interested only in his construction of the third tectractys, the

Platonic Lambda (see figure 3). Plutarch begins by paraphrasing Timaeus (35b 4), and then

5. Armand Delatte, Études sur la Littérature Pythagoricienne (Paris: Librairie ancienne Honoré Champion, 1915), 249-268.

6.Thirty-six is also a triangular number (the sum of the first eight numbers), a square number, a perfect number, and the product of two square numbers (4 x 9). It is also an Erdős–Woods number 121

explains the seven numbers, the advantages of placing them in a lambda formation, rather than a straight line, and finally how they are used in the composition of the soul (the last is not pursued here).

Plato’s Lambda (Timaeus 35b-c) can be presented as a type of tetractys, one that still displays “fourness” but where numbers replace counters.7

2 3

4 9

8 27

Figure 2. The Platonic Lambda

At the apex is the monad, the non-spatial source of all number. Moving down the rows, the two planar numbers, (2 and 3) can be represented by dots in the shapes of plane figures, an oblong and a triangle), they are followed by two square numbers (4 and 9); and then two cubic numbers (8 and 27).8 The sum of these is 54. Plato used these seven numbers in the

Timaeus to describe the creation of the world from the monad through the point, the plane,

7. Probably called lambda by Crantor of Soli, one of Plato’s students and an interpreter of the Timaeus, who contributed to the discussion of the world-soul, interpreting its base number as 384, and arranging its harmonic divisions in a lambda-shaped diagram rather than a straight line. (See Harold Tarrant, Plato’s First Interpreters (Ithaca, New York: Cornell University Press, 2000: 53-55). 8. In Timaeus these numbers are presented in the sequence: 1, 2, 3, 4, 9, 8, 27. The placement of the nine before the eight may seem odd, but when the numbers are placed in a lambda, the oddness disappears, the numbers are ordered down each leg of the lambda and numbers are not compared across the horizontal. 122

and then the third dimension. The two legs represent the opposition between even (difference) and odd (sameness) and the progression through the powers from the point to the square to the cube.

We then fill in the Lambda to make a Platonic tetractys, using the patterning on each of the arms: 2 x 3 =6 and 2 x 6 = 12; similarly, 3 x 2 = 6 and 3 x 6 = 18. Furthermore, the central number 6 serves to harmonise the odd and the even, it is the geometric mean of (4, 9),

(2, 18) and (3, 12)). Critchlow adds that these new numbers (6, 12,18) sum to 36, as do the three apexes of the triangle (1, 8, 27). Waterfield remarks that this diagram “now contains all the factors of 36, which, as our author [Plato in Timaeus] says, sum to 55”. 9 As we see in section 10, this tetractys provides a calculator for analysing musical harmony.

2 3

4 6 9

8 12 18 27

Figure 3. The “filled in” Platonic Lambda, or numbered Pythagorean tetractys

Plutarch notes that the three new numbers filling in the open positions in the Lambda turn the figure into another tetractys, that is another triangle (summing to another triangular number), still representing unity, but no longer the decad. Waterfield adds:

9. The sum of the two separate legs of the Lambda is also 55. Some numbers are perfect, in that they are equal to the sum of their factors. One that we have already met is 6 (with factors 1, 2, 3), others are 28, 496, and 8, 128. The number 36 is not perfect (under the strict definition given above). 123

Even if Plato himself did not suggest the lambda form in the Timaeus, yet because of the convention of triangular numbering and the image of the tetraktys in four lines of dots were completely familiar to the Pythagoreans of the day, it would be inevitable that they would make the comparison. The idea of doing so is not new; the pattern we are about to investigate was, in fact, published by the Pythagorean Nicomachus of Gerasa in the second century AD The Pythagorean tetractys contains the first ten integers, displayed with ten counters; this tetrad contains, in its ten integers, all the integers from one to ninety, which can be produced by judicious addition of the ten numbers in the tetractys. The Platonic Lambda has several attributes involving the number 6 the “marriage” number in Pythagorean theory (Waterfield

1988, 29). The sum of each of the three geometric means is 36 (that is 6x6), and all eight of the factors of 36 appear in the triangle. Most fascinating of all, if we “nest” these geometric means inside the Platonic Lambda, we can continue to create as many new lambdas and tetractyses as we please.

First consider the tetractys created by Critchlow, following the work of the Franciscan friar, Francesco Giorgi (1466-1540). Critchlow creates a new tetrad with the central number

36 by multiplying all the numbers in the tetractys in figure 3 by six.10

10. This figure corresponds to Critchlow’s figure 14, see Critchlow (Waterfield 1988, 18). For more information on Giorgio and his work, Critchlow (an architect himself) directs us to R. Wittkowa, Architectural Principles in an Age of Humanism (W. W. Norton, New York: 1971). Another source is Chapter Four, “The Cabalist Friar of Venice: Francesco Giorgi,” in Yates (1979, 33-42). 124

12 18

24 36 54

48 72 108 162

Figure 4. The tetractys of Francesco Giorgi

I offer an alternative derivation (which I have not seen elsewhere), relying on the generation of the numbers in the Platonic tetractys from the two original numbers. This motivates the construction of Critchlow’s figures while staying true to the methods of the Pythagoreans. I give below a diagram of “nested” Platonic Lambdas, all derived for the source of all number, the monad.

1 2 3 4 6 9 8 12 18 27 24 36 54 48 72 108 162 144 216 324 288 432 648 972

Figure 5. Nested Platonic Lambdas. The figure shows a sequence of stacked lambdas (or inverted Vs). At the top of the stack is the familiar Platonic Lambda (in bold). Below it lies a lambda (un-bolded) containing Critchlow’s numbers.

At the apex of the pyramid is the monad, or 20·30. The identity n0 = 1 is consistent with, and sympathetic to, the Greek understanding that the source of all number is the monad, and it vindicates the procedure of taking powers of the first two numbers (2 and 3) to generate the 125

table.11 This table provides all the integers that have the numbers 2 and 3 as factors, and it is a limited application of the fundamental theorem of arithmetic (or the unique factorization theorem). This theorem states that every integer greater than 1 is either is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, except for the order of the factors. This application is limited because it uses only the first two prime numbers.12 he family resemblance between this table, Pascal’s triangle, and the binomial theorem is unmistakable.

Keith Critchlow generates two tetractyses and asserts that one can build more, for which I have provided a template. Theon of Smyrna may be the originator of this idea; he certainly understood it. Asked how many tetractyses there are, and what they signified, he replied first giving the Pythagorean oath: “I swear by the one who has bestowed the tetractys, the source of eternal nature, upon coming generations and into our souls;” and then listed eleven tetractyses. After the first and second tetractyses (the Pythagorean and Platonic), he drifted into arithmology, and I give only the last two: the tenth is that of the seasons of the year – spring, summer, autumn and winter, and the eleventh is that of the ages: childhood,

11. Nested lambdas (and tetractyses) have an additional advantage, the computational ease of constructing new elements and new tetractyses.

12. Gauss provides a statement and proof of the theorem using modular arithmetic (Disquisitiones Arithmeticae, 1801). Euclid set out the basic notion of the theorem in Elements, Book VII, propositions 30, 31 and 32, and continues the discussion in Elements, Book IX, proposition 14.

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adolescence, maturity and old age.13 All his constructions break into four parts, but aside from the first two, they do not have the arithmetical inter-connectedness of the Pythagorean and

Platonic tetractyses. The examples that he gives are often seen in arithmological discussion of the properties of the tetrad (Waterfield 1988, 55-63). His recital is like Young Plutarch’s recital of the appearances of the pentad.

Nested lambdas have an additional advantage, the computational ease in constructing them. Professor Critchlow went to considerable trouble to demonstrate, through their properties as arithmetic, geometric and harmonic means, that 6, 12, and 18 were the “right numbers” to fill out the Platonic tetractys. In the schema shown in figure 5, the pattern of the powers of the two basic numbers (2 and 3) allows us to simply follow the progression in the earlier rows and columns. After the initial two rows, a pattern is established of alternating rows containing three and four elements. In each row the sum of the powers of the two basic numbers is constant, and that constant increases by one is each successive row. For example, the next (and ninth) row in the table will have three elements and the powers will sum to eight. The three elements will be: 25·33, 24·34, and 23·35, and a quick calculation gives the numbers: 864, 1296, and 1944.

Other important numbers drop out of the tetractys. I mention three: the life span of the hamadryads, the number of the Great Year, and Plato’s number (5040).

13. See Theon, of Smyrna: Mathematics useful for understanding Plato; translated from the 1892 Greek/French edition of J. Dupuis by Robert and Deborah Lawlor (San Diego: Wizards Bookshelf, 1979).

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In De def. or. (11. 415 F and 416 B), Lamprias (now grown up) reports on an old riddle from Hesiod, on calculating the lifespan of the hamadryads. The discussion, a “witches’ brew of erudition and speculation” (Kahn 1979, 155), invokes many of the usual authorities:

Zoroaster, Homer, Orpheus, Plato, Pindar, Hesiod, and Heraclitus. The tetractys is not mentioned but, when Demetrios argues that fifty-four is the limit of the middle years of a vigorous man’s life and explaining that fifty-four is the sum of “the first number, the first two plane surfaces, two squares and two cubes”, we know that we are in Pythagorean territory.

These are the seven numbers in Plato’s Lambda. The interested reader can check that the lifespans of crows, stags, vigorous men, ravens, phoenixes, and hamadryads, all the beings in

Hesiod’s riddle, appear in figure 5.

The Great Year comes every 10,800 years, when the sun, the moon, and the planets, having completed an integral (but different) number of revolutions, return to the positions that they were in at the beginning of this great cycle (Timaeus 39). Then, according to the Stoics, the cycle culminates in the conflagration, destruction, and renewal of the cosmos. One derivation of the number 10,800 is: four seasons of three months each, with 30 days in a month yields the year (4 x 3x 30 =360); treating each day of the year as a human generation of 30 years yields gives the Great Year (30 x 360=10,800). This recalls the Heraclitean fragment (Diels A 13).

There is a great year whose winter is a great flood and whose summer is a world conflagration. In these alternating periods the world is now going up in flames, now turning into water. This cycle consists of 10,800 years. (Censorinus, De Die Natali 18.11)

The careful reader will have noticed that 10,800 does not appear in figure 5 although both 108 and 432 do (both factors of 10,800). Not every interesting number in classical philosophy can 128

be computed from the Pythagorean and Platonic tetractyses. The two tables are limited in that they contain powers of only the first odd and the first even numbers. The next step would be to construct tables containing the next prime numbers (3 and 5). Then the number of the Great

Year can be computed from either of the two numbers shown in figure 5:

432 x 25 = 432 x 5 x 5 = 10,800

108 x 100 = 108 x 4 x 25 = 10,800

Similarly, to calculate Plato’s number (Laws 737e1-3), from figure 5, we need the next prime number, seven. The number can then be derived from 144 in the second last row in

Figure 5: 5040 = 7 x 5 x 144

The number 5,040 has many beguiling properties, one of which is its appearance in Srinivas

Ramanujan’s list of highly composite numbers, and it is indeed a “superior highly composite number”.14

The real charm, of these numbers is that, the world has come around, at least in the last two hundred years, to the serious study of numbers and to a re-examination of ancient number theory. Many of the numbers that the ancients found pretty, or intriguing are showing

14. Benjamin Jowett comments, “Writing under Pythagorean influences, he [Plato] seems really to have supposed that the well-being of the city depended almost as much on the number 5040 as on justice and moderation”, (Plato’s Laws, translated by Benjamin Jowett, 1871).

The number 5040 is a factorial (7!) and one less than the square 5041, making (7, 71) a Brown number pair (and the largest of the three known pairs); a superior highly composite number, a colossally abundant number, the number of permutations of four items out of ten choices (10 x 9 x 8 x 7 = 5040), and the sum of forty-two consecutive primes starting with the number 23. Given Plutarch’s interest in the number 36, it is worth looking at the factors of 5040. We can write it as 36 x 2 x 70, which leads us back into the second row of figure 5. 129

up in advanced mathematics. Who could have imagined that, after two and a half millennia, we would see the names of two of the modern greats in number theory, Srinivas Ramanujan and Paul Erdős, appearing in the same paragraph as Plato and Pythagoras (the latter at least implicitly)? For example, Jean-Pierre Kahane (2015) writes in his remembrance of Paul

Erdős:

Jean-Louis Nicholas collaborated with Paul and wrote beautiful papers about him. As a detail let me mention their common interest in highly composite numbers, a term coined by Ramanujan for numbers like 60 or 5040 that have more divisors than any smaller number. My own interest was in the implicit occurrence of the notion in Plato’s Utopia: 5040 is the best number of citizens in a city because it is highly divisible (Laws, 771c). . 130

BIBLIOGRAPHY

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131

Flacelière, Robert, ed. and trans. Plutarque sur l’E de Delphes. Paris: Les Belles Lettres, 1941.

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132

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