plutarch's 'de e apud delphos': translation and commentary

University of Calgary

PRISM University of Calgarys Digital Repository

Graduate Studies The Vault Electronic Theses and Dissertations

2018-11-19

Plutarchs De E apud Delphos Translation and

Commentary

Alexander Judith Anne

Alexander J A (2018) Plutarchs De E apud Delphos Translation and Commentary

(Unpublished masters thesis) University of Calgary Calgary AB doi1011575PRISM34516

httphdlhandlenet1880109187

master thesis

University of Calgary graduate students retain copyright ownership and moral rights for their

thesis You may use this material in any way that is permitted by the Copyright Act or through

licensing that has been assigned to the document For uses that are not allowable under

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UNIVERSITY OF CALGARY

Plutarchrsquos De E apud Delphos Translation and Commentary

by

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

copy Judith Anne Alexander 2018

ii

ABSTRACT

Plutarchrsquos Parallel Lives are well known less so the essays and dialogues grouped into his

omnibus Moralia One of these essays De E apud Delphos (ldquoDe Erdquo) 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)

Plutarchrsquos 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

masterrsquos 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


iv

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

v

DEDICATION

To John and to Lisa Friedland

ΧΑΡΙΣΤΗΡΙΑ

vi

TABLE OF CONTENTS

ABSTRACTii

PREFACEiii

ACKNOWLEDGMENTSiv

DEDICATIONhellipv

TABLE OF CONTENTSvi

LIST OF FIGURESvii

LIST OF ABBREVIATIONSviii

EPIGRAPH1

INTRODUCTION2

NOTES ON THIS TRANSLATION10

SCHEMA STRUCTURE OF THE DIALOGUE15

TRANSLATIONhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip16

COMMENTARYhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip41

APPENDIX A PLUTARCH AND HERACLITUS81

APPENDIX B FREE INDIRECT DISCOURSEhelliphelliphelliphelliphelliphellip 99

APPENDIX C THE TETRACTYShelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip116

BIBLIOGRAPHYhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip130

vii

LIST OF FIGURES

All figures appear in Appendix C

Figure 1 The Pythagorean tetractys118

Figure 2 The Platonic Lambda121

Figure 3 The ldquofilled inrdquo Platonic Lambda122

Figure 4 The tetractys of Franceso Giorgi124

Figure 5 Nested Platonic Lambdashelliphelliphelliphelliphelliphellip124

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-OrsquoNeil W C Helmbold and Edward N OrsquoNeil Plutarchrsquos 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

OrsquoNeil E N OrsquoNeil 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 httpsplatostanfordedu

SVF Hendrick von Arnim Stoicorum Veterum Fragmenta (3 vols) Leipzig

1903-5

Wehrli Fritz Wehrli Die Schule des Aristoteles Basel-Stuttgart Schwabe

1945

ix

TITLES OF THE ldquoMORALIArdquo 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

1

EPIGRAPH

αρμονίη αφανης φανερης κρείττων

mdash 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 endeard

Pipe to the spirit ditties of no tone

ldquoOde on a Grecian Urnrdquo

mdash John Keats (1795-1821)

2

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

exchange1it 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

ldquofly from the uttermost ends of the earth towards its centrerdquo2 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 (Pausaniasrsquos 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 Plutarchrsquos 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 populous3 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

ldquohands onrdquo responsibilities of a civic-minded young man and later the ldquoleading by examplerdquo

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 place4

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 Plutarchrsquos

contemporary who may have asked Plutarch for advice about retiring from public life

4

ldquoportents coincidences history a little philosophy and anecdotes of Croesus Battus

Lysander and Battusrdquo (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 ldquoifrdquo the hypethical syllogism or the

second person singular of the verb to be ldquoYou arerdquo5

Plutarch (46 ndash 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 Plutarchrsquos life after his studies in Athens He left Chaeronea to study travelled

5 For those who would appreciate an overview of Plutarchrsquos life and work (and the Moralia) see

Babbittrsquos introduction in volume 1 of the Loeb editionLCL Moralia (1927 pp 9-33)and the

introduction in volume 1 of the Budeacute 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 Paludesrsquo 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 ldquothe smartest move of his careerrdquo6 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 Plutarchrsquos 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 Plutarchrsquos other writings make

the acquaintance of Plutarchrsquos 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 McInerneyldquolsquoDo you see what I seersquo Plutarch and Pausanias at Delphirdquo In F de Blois

The Statesman in Plutarchs 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 panelrsquos 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 saintrsquos life The

Autobiography of the Archpriest Avvakum written by himself7

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 versehellip 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 ldquoliferdquo 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 Tsarrsquos

retinue he also wrote in and was comfortable with the Chancellery Russian used in the court The

most obvious sign of Avvakumrsquos 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 Heaneyrsquos

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 ldquoliteralrdquo or ldquocloserdquo 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-orsquo-the-wisp that changes

from one passage to another within a work as the speaker or subject changes Often there is

no clear ldquobestrdquo 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 Δικαίαρχοςhellipοἴεται could have been

translated as ldquowhich Dichaearchus thinksrdquo 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 ldquoaccording to Dicaearchusrdquo 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 first8

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 ldquokeep a learned eye on himrdquo and that although the professorrsquos

comments ldquoinformed by scholarship and a lifetime of experience of teaching the poemrdquo were

invaluable nevertheless he was often reluctant to follow his advice and ldquopersisted many

times in what we both knew were erroneous waysrdquo

Although less than a century has passed since Babbitt and Flaceliegravere 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 Archilochusrsquo poetry This was published in 1974 (the ldquoCologne Epoderdquo) 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

10

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 Flaceliegravere (1941 and 1974) Hendrik Obsieger (2013) and the electronic

version of Bernardakisrsquo text (1891) The Obsieger text is especially useful because on points

of difficulty he has almost invariably reviewed both the Flaceliegravere 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 Obsiegerrsquos 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 Bernardakisrsquo 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

11

There are few English translations of the complete Moralia10 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

ldquothe translator generall of his agerdquo11 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 Everymanrsquos

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 Hollandrsquos strengths as his ldquoaccurate and

thoroughrdquo translation and a ldquorare and consummaterdquo knowledge of his mother tongue

The Dryden translation (1684-94) made by ldquoforty 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 Goodwinrsquos translation was an improvement over

10 By my count there have been four complete editions of the Moralia (Holland the Dryden edition

[ldquoby several handsrdquo] 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 Beacutetelaud and the Budeacute 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) 279ndash303

12

the earlier effort which Emerson found ldquocareless 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 Theseusrsquo ship since various parts have

been removed and new parts substituted Both the Teubner and Budeacute publishing houses work

with the same model

The collection by C W King (1908) contains the Pythian dialogues and several other

dialogues with religious themes12 King defines theosophy as ldquoknowledge of the things

pertaining to Godrdquo and recommends that these essays be read by ldquoevery religious disputantrdquo

In his introduction he acknowledges his debt to his ldquoancient brother-fellow the indefatigable

Philemon Hollandrdquo The translation of A O Prickard (1918) is difficult to find but does

appear on the Thomas Brownersquos Miscellany (1864) website for the University of Chicago

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

Robert Flaceliegravere (1941 1976) Jacques Amyot (1572) Dominique Ricard (1784)

Freacutedeacuterique 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 Babbittrsquos own adaptation while the Greek text on the Perseus site is from

Bernardakisrsquo Teubner edition Furthermore the Goodwin translation (1874) also available on

12 C W King Plutarchrsquos Morals Theosophical Essays London 1908

13

the Perseus website is a revision and modernisation of the much earlier translation by

ldquoseveral handsrdquo (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 Estiennersquos 1572 edition of the Moralia

are given throughout Estienne had originally introduced these numbers in his edition of

Platos complete works and they rapidly became standard notation On the formatting of these

numbers I have followed the contemporary style of Babbitt Flaceliegravere and Obsieger who

use exclusively the capital letter that is either 123A or 123 A I follow Obsiegerrsquos 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

Wyttenbachrsquos 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 Flaceliegravere and Obsieger use different translations

for them Babbittrsquos proper names often seem old fashioned (for example Heracleitus or

14

Archilauumls) 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

ndash Plutarch the narrator and his much younger self ndash I have differentiated them by calling the

latter ldquoYoung Plutarchrdquo There is also Plutarch the author and when he appears in the

commentary or the appendices I call him ldquoPlutarch the authorrdquo or simply ldquothe authorrdquo

For classical references other than to the Moralia I have used the authorrsquos name for

the first appearance and later a shorthand Thus later references to Pausaniasrsquo 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 ldquoHeraclitusrdquo or ldquoHerodotusrdquo for the obvious reason

Finally on the orthography of the epsilon This appears in Greek texts sometimes as

an E EI or ει There has been controversy amongst editors over the form of the letter in the

Greek text ndash how Plutarch wrote it and how it appeared in the pronaos of the temple Both

Babbitt and Paton maintained ει although Babbitt wrote ldquoErdquo in his English translation The

compiler of the Lamprias Catalogue used an ldquoErdquo I have used an ldquoErdquo in the title and in the

dialogue except where it is to be interpreted as something such as ldquoyou arerdquo or ldquoifrdquo 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

Gardner1885) Some archeologists and numismatists have claimed a link through Plutarchrsquos

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 - Brsquo) The second part is bookended by Ammoniusrsquo

opening and closing remarks Within it two sub-parts are devoted to the interpretation of the

meaning of the E

A Plutarchrsquos 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 ldquoErdquo (Section 2)

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

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

Brsquo 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 ndash 21)

Plutarch writes to Sarapion that the dialogue is ldquoaboutrdquo 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

16

TRANSLATION

SECTION 1 (384 D ndash 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 Sarapion1 were

according to Dicaearchus2 said by Euripides to Archelaus3

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 servile4 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 deliberations5 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

itself6 I recalled that long ago at the time when Nero visited the temple7 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 ndash 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)

18

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 ldquoPythianrdquo to

those who are just beginning to learn and to ask questions the ldquoPhaneausrdquo and the ldquoDelianrdquo to

those to whom some part of the truth has been revealed and is becoming clearer the

ldquoIsmenianrdquo to those who have gained wisdom and understanding and the ldquoLeschenorianrdquo to

those who are able to engage in and enjoy dialogue and philosophical conversation with

others8

ldquoForrdquo he said ldquothe 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 lsquowhyrsquo 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 incense10 statues of only two of the Fates stand here while

everywhere else three is customary11 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 lsquoKnow yourselfrsquo and lsquoNothing in excessrsquo have set in

motion philosophical researches and a veritable crowd of discussions has sprung from each

one as from a seed13 And in my opinion our topic of discussion is no less fruitful than any

one of theserdquo

SECTION 3 (385 E ndash 385 F)

Lamprias responds that the explanation he has heard is quite straightforward ndash 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 ldquoIn 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 number14 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 lsquosagersquo They

then disseminated and broadcast throughout Greece maxims and aphorisms which resembled

some of the sayings of the original five15 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

ldquoSo 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

ldquoTo convince yourself that their account is on the mark it is sufficient to listen to the

explanation of those connected to the sanctuary16 They describe the golden E as the E of

Livia the wife of Caesar17 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 commonrdquo

20

SECTION 4 (386 ndash 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 earlier18 that there are seven vowel sounds

amongst the letters19 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 sun20 ldquoBut all these ideasrdquo

he concluded ldquocome from star books and the rumours chattered about at the gates of the

sanctuaryrdquo21

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 guides22 that it is neither the form nor the

sound of the letter but only its name that carries symbolic significance23

SECTION 5 (386 C ndash 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 ldquoifrdquo 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 ndash to express a wish

ldquoFor as the Delphians understand itrdquo said Nicander the priest speaking on their behalf24 ldquoit

[ει] 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 counsel25 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 home26 The god in his wisdom gives short

shrift to those dialecticians who think that nothing comes from the inclusion of the

conjunction lsquoifrsquo in an expression and that it makes no real contribution to the meaning27 for

he considers all questions attached to that conjunction as realities and he welcomes the

questions

ldquoFurthermore 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 lsquoifrsquo is used to express a prayer or a wish no less than to pose a question lsquoIf only I

couldrsquo is the usual expression of a wish 28 For example Archilochus wrote lsquoIf only it might

be granted to me to touch the hand of Neobulersquo29 As for the phrase lsquoif onlyrsquo one can say that

the second word is not necessary30 just as lsquosurelyrsquo is hardly necessary in Sophronrsquos lsquoShe too

is surely desirous of childrenrsquo31 Or in Homerrsquos 32 lsquoAnd surely I will bring your strength to

naughtrsquo So as they say the optative force is quite clear in the lsquoifrsquordquo 33

SECTION 6 (386 D ndash 387 D)

Theon gives another interpretation of the E linking it through the conjunction ει

(ldquoifrdquo) to the syllogism used in dialectics and logic Almost the entire section is in

direct speech Theon defending dialectics claims that the conjunction ldquoifrdquo 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 Theon34 whom you know asked

Ammonius if Dialectic who had just been so roundly insulted was to be permitted to speak

freely in her turn35 When Ammonius encouraged him to speak for her and come to her aid

22

Theon said ldquoCertainly the god is a dialecticianrsquos 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 geometry36 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 lsquoifrsquo has the

greatest power [of all conjunctions] since this construction the syllogism is the most logical

of all propositions

ldquoFor 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 lsquoif it is day then there

must be lightrsquo37 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 demonstration38 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 lsquoifrsquo was consecrated by wise men to the god who is above all else a lover of the

truth

ldquoFurthermore 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 term39 Thus he who has the natural capacity to

connect causes and link them together also knows how to foretell lsquoall things that are the

things to come and the things that are in the pastrsquo 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 lsquoif an event occurs now then some other

has preceded itrsquo and again lsquoif an event occurs now then another will follow itrsquo In effect

skill and logic as has been said lie in the knowledge of consequences but the minor premise

is substantiated by perception

ldquoAlso 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 lyre41 should it astonish us then that through his love of dialectic

he finds the lsquoifrsquo which he sees philosophers use so freely and so often both agreeable and

charming

ldquoHercules 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 yokel42 disdaining dialectic and mocking reason with its lsquoif the antecedent is true

then so is the consequent alsorsquo43 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 dialecticrdquo44

24


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

ldquoLook how eagerly Theon defends logical argument all but donning the lion skin45 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 dear46 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 lsquocounting

by fivesrsquordquo47

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 ldquoNothing in excessrdquo just as soon as I became part of the Academy48

SECTION 8 (388 ndash 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 Eustrophusrsquo explanation had most gracefully resolved the difficulty with

Number49 ldquoForrdquo I continued ldquoall 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 lsquomarriagersquo 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

ldquoMoreover 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 lsquomarriagersquo because it is produced

from the union of the first masculine and the first feminine number

ldquoFive has sometimes been called lsquoNaturersquo 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 ndash wheat50 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 themselves51 Thus six times six is thirty-six

and five times five is twenty-five And again six does this only once52 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 whole53 For the first principle preserves the cosmos and then

out of the cosmos perfects itself lsquoAll things are exchanged for firersquo as Heraclitus said lsquoand

fire is exchanged for all things just as gold is for goods and goods for goldrsquo54 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 wholerdquo

SECTION 9 (388 E ndash 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

ldquoNow if someone were to ask what this has to do with Apollo55 we should reply that it

concerns not only him but also Dionysus56 who has a claim to Delphi no less important than

that of Apollo himself For we hear the theologians57 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

ldquoBut 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 Isodaetes59 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 says60

It is fitting that the dithyramb

should be present in Dionysusrsquo 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

hellip 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

ldquoBut the periods of these cycles are not the same the one that they call lsquosatietyrsquo is longer than

the one they call lsquocravingrsquo62 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 destructionrdquo63

SECTION 10 (389 C ndash 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

ldquoby earrdquo that is through the senses

28

ldquoBut this subject has been drawn out beyond all reasonable proportion64 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

ldquoAnd 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

concord65 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 43 of the fifth 32 of the octave 21 of the

octave plus a fifth 31 and of the double octave 4166

ldquoBut the concord composed of an octave and a fourth that the harmonikoi introduce in

addition to these ratios67 saying that it steps outside the measure cannot be accepted because

it privileges auditory perception over logic and is tantamount to being beyond logic68 Let us

not speak of the five stops of the tetrachord69 nor of the first five lsquomodesrsquo or lsquokeysrsquo or

lsquoscalesrsquo whatever their right name is70 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 ndash 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 melodyrdquo71

SECTION 11 (389 F ndash 390 A)

29

Young Plutarch continues his examples of the importance (and ubiquity) of the

pentad (and the E) with Platorsquos claim that by analogy to the Platonic solids there

can be no more than five worlds

ldquoThere are many other examples [of the pentad] that I shall put to one siderdquo I continued72

ldquoand 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 more73 On the other hand even if our

world is unique and the only one of its kind as Aristotle believes74 then it is in some way

composed and conjoined of five worlds75 one of earth another of water the third of fire the

fourth of air and the fifth of high heaven ndash which some call light some ether and some the

fifth substance ndash 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

ldquoAnd 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 eachrdquo76

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

ldquoFurthermore there are some who associate the powers of the different senses with the primal

elements77 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 lsquolightrsquo 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

fiverdquo78


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 ndash the five classes of animate beings

At that point I stopped and after a moment said ldquoEustrophus what has become of us that we

almost passed over Homer79 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

ldquoThe discussion must be taken further back as Euripides says80 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 fourfold81 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 deprived82 unfinished and not good for anything

whatsoever unless it has a soul using it appropriately

31

ldquoThus the balance and power of the five with greater force [than other numbers] has

not allowed animate beings to develop indiscriminately into unlimited kinds83 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

ldquoFurthermore 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 degreerdquo84


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

Plutarchrsquos argument is going

ldquoAnd 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

number85 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 pentad86 If

moreover as some rightly hold the monad is square ndash its power being itself and being

contained in itself ndash then the five engendered by the first two squares does not lack a noble

pedigreerdquo

SECTION 15 (391 A ndash 391 E)

32

In this disjointed section Young Plutarch first diverts us with the parallel between

Platorsquos and Anaxagorasrsquo 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

ldquoButrdquo I said ldquoI 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 Cratylusrdquo

ldquoCertainlyrdquo said Eustrophus ldquobut I do not see anything in that case analogous to our

ownrdquo87

ldquoNevertheless I presume you know that in the Sophist Plato shows that there are five

overarching classes88 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 about89 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

ldquoYou 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 universe90 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 lsquoIn the sixth generation bring to a

stop the ritual of songrsquordquo91

SECTION 16 (391 D ndash 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 ldquoFollowing up on what has been said to you I shall sing one short verse to the

wise men in Nicanderrsquos circle lsquoOn the sixth day after the new moonrsquo92 namely when you go

with the Pythia to the Prytaneum the first of your three lots is a five ndash she casts a three and

you a two each with reference to the otherrsquo93 Is that not sordquo

ldquoYes indeedrdquo said Nicander ldquobut the reason for it must not be divulged to othersrdquo

ldquoVery wellrdquo I said smiling ldquoif 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 fiverdquo94

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 ndash 392 A)

Ammonius responds to Young Plutarchrsquos paean to the pentad by observing that

every number displays remarkable qualities He then recalls Lampriasrsquo 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 ldquoyou arerdquo [ει] 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 ldquoIt 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

discussed95 Then too we should be claiming that the Sages were lsquoat warrsquo with usual practice

and lsquothe weight of longstanding traditionrsquo if we say that they ousted the heptad from its front-

row seat at the theatre96 and then dedicated as somehow more fitting the pentad to the god97

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 lsquoKnow yourselfrsquo

which means no less than lsquoHellorsquo We in our turn reply to the god lsquoYou arersquo which is the

truthful and truthfully spoken response and the only address proper to him only as Beingrdquo

SECTION 18 (392 B ndash 392 E)

Continuing his analysis of the E as a symbol for ldquoyou arerdquo 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 Timaeusrsquo asking about the difference between

that which is existent always and has no becoming and that which becomes and never is

(Timaeus 27 D)

35

ldquoFor we do not share in any real part of Being since every mortal nature is between coming

into being and being destroyed98 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 thingrsquos coming into being and

passing into destruction and then is unable to understand even one other thing that endures or

really exists

ldquolsquoIt is not possible to step twice into the same riverrsquo Heraclitus said99 Nor is it

possible to encounter a mortal being in one and the same state on two separate occasions100

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 lsquopresentrsquo and lsquoabsentrsquo101 Whence the thing coming

together does not reach being because it never stops or ceases from its formation

ldquoThis 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 lsquothe death of fire is birth for air and the death of air is birth for waterrsquo

and it is clearer still in ourselves102 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

todayrsquos person and todayrsquos is dying into tomorrowrsquos 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 mould103

ldquoOtherwise 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 isrdquo


Ammonius continues with the implications that follow from interpreting the E to

mean ldquoyou arerdquo Mortal substances were denied true Being in section 18 and here

Ammonius describes true Being ndash 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

ldquoThen what is it that Being really is It is everlasting without beginning indestructible

impervious to decay and no instant of time brings change to it104 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 destruction105 To say of time lsquothenrsquo or lsquobeforersquo or lsquoit will

bersquo or lsquoit has beenrsquo is an immediate admission of its non-being For to speak of what has not

yet happened as lsquobeingrsquo or of what has ceased to be as lsquoisrsquo 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 lsquoit has beenrsquo lsquoit is herersquo or lsquonowrsquo 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 time106 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

Beingrdquo

SECTION 20 (393 A ndash 393 D)

This section completes the interpretation of the E (as ldquoyou arerdquo) 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

ldquoBut the god107 it must be said is and he is for no particular time but forever108 a forever

that is motionless outside time and undeviating109 where there is neither before nor after

neither future nor past neither older nor younger110 But he being one has with one now

filled forever and only when lsquoBeingrsquo is as he is is it truly being It has neither become nor is it

about to become for lsquoBeingrsquo never did begin and it will never end So when we worship him

we must greet and address him in the same fashion lsquoYou arersquo or even by Zeus as some of

the ancients did111 with the address lsquoYou are onersquo

ldquoFor 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 together112 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

ldquoSo 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 lsquophoebusrsquo113

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 lsquofollowing the rule of Phoebusrsquo114 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

lsquodestructiversquo115 Surely then to be both one and unmixed befits the unsullied and

uncorruptedrdquo

SECTION 21 (393 D ndash 394 C)

Although Ammonius accepts the identification of Apollo with the sun he

categorically rejects Young Plutarchrsquos 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 ldquoKnow yourselfrdquo with the E the symbol for ldquoYou arerdquo and then reprising

and expanding the list of names for Apollo

ldquoAs 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 sunrsquos 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

godrsquos kindness and blessedness

ldquoBut as for his raptures and transformations when he sends out fire116 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

life117 to listen to such accounts is impious In these accounts he seems more lowly than the

poetrsquos 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 again118 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

ldquoIt seems to me that to address the god with the words lsquoYou arersquo 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 Aiumldoneus one Phoebus and the other

Scotios119 The Muses and Memory accompany the one Oblivion and Silence the other120

One is Theoros and Phanaeos the other lsquothe Lord of the dark night and sluggish sleeprsquo121 and

he is also lsquoof the gods the most hated by mortal menrsquo122 But Pindar sang not unpleasantly of

Apollo lsquoTowards mortals he has been judged the gentlestrsquo 123 and similarly Euripides quite

rightly spoke of

40

libations for the departed dead

and songs but not such as

golden-haired Apollo welcomes124

and even before him Stesichorus125

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 lsquoNeither the harp nor

the lyre is welcome for lamentsrsquo126 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

ldquoIt seems that in one way the E lsquoYou arersquo stands in opposition to the phrase lsquoKnow

yourselfrsquo 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 frailtyrdquo127

41

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 ldquoEuripides in Macedonrdquo Classical Quarterly 20 1926 1-19 and Scott

Scullion ldquoEuripides and Macedonrdquo 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-OrsquoNeil 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 goodshellip)

4 (1 384 E) The pair of phrases ldquoill-mannered and servile hellip generosity and beautyrdquo illustrates

Plutarchrsquos arguably best known stylistic device the doublet balanced repetition or ldquosemi-synonymrdquo

(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

ldquoKwanzaardquo into the English dictionary in 2009 the OED described it as the festival of the celebration

of the literal ldquofirst fruits of the harvestrdquo So the concept is still current and it still transcends parochial

42

interpretations The phrase is used again (απάρξασθαι τῷ θεῷ της φίλης μαθηματικης 7 387 E) and

appears in Plutarchrsquos De aud 640 B and Sept sap con 6 151 E

6 (I 385 B) Flaceliegravere (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 62 205) The priests at Delphi kept meticulous chronological records but Plutarch has not

given us a precise date


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

ldquoI inquirerdquo) is an analogy to the first steps of an initiate At the second level two names reflect

dawning understanding Apollo the ldquoDelianrdquo was born on the island of Delos and the epithet

allegorises the clarity (δηλος lsquolsquoclearrdquo) of new understanding and of dawning revelation which is also

captured in ldquoPhaneausrdquo (φαίνω ldquoI show I bring to lightrdquo) At the third level Apollo ldquoIsemniosrdquo

fathered the Boeotian river-god Ismenos (an inversion of the usual epithet ldquoson ofrdquo) which is

analogous to those at the third level who ldquoknowrdquo (ἴσmicroεν first person plural of the perfective of εἴδω ldquoI

have seenrdquo and the present of οἶδα ldquoI knowrdquo) Pindarrsquos first Hymn to Zeus opens with Melia ldquoof the

golden spindlerdquo 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 ldquoLeschenoriosrdquo from the Lesche a large

clubroom at Delphi built by the Knidians in 450 BC The stem appears in λεσχηνεύω (ldquoI converserdquo)

and as the second term in the compound ἕλλεσχος (ldquothat which provides material for conversationrdquo)

both suited to Ammoniusrsquo 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 ndash Ismenos Pythia

and Delosndashmay be no more than toponyms Babbitt comments on this section ldquoPlutarchrsquos attempt to

43

connect Ismenian with ἴδ (οἶδα) can hardly be rightrdquo (1936 203) On the same passage Flaceliegravere

calls the proposed etymologies ldquopurement fanatasistesrdquo (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 Socratesrsquo remarks on the name of the moon (15 391 B) Ammonius

returns to etymology in his final speech (21 394 A)

Babbittrsquos 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 ldquothe seeking of answersrdquo 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 ldquowonder is the feeling of a philosopher

and philosophy begins in wonderrdquo (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 1059) The pass of Tempe running from

Macedonia into Thessaly along the river Peneus was frequented by Apollo and the Muses (Herodotus

Histories 1173) 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 ldquobut in place of the third Fate there stand by their

side Zeus Guide of Fate and Apollo Guide of Faterdquo (Paus 10244) For the significance of the

substitution of Zeus and Apollo see Auguste Boucheacute-Leclercq (1879 121)

Pindar [522-443 BC] neacute dans un pays fertile en oracles eacutetait lrsquointerpregravete de lrsquooracle

apollinien de Delphes alors agrave lrsquoapogeacutee de son prestige et son influencehellip Dans le

temple de Delphes non loin du siegravege de fer ougrave Pindar srsquoessayait dit-on pour

chanter des hymnes en lrsquohonneur drsquoApollon on voyait un groupe de statues

repreacutesentant Zeus Mœragegravete et Apollon Mœragegravete associeacutes agrave deux Mœres et tenant

la place de la troisiegraveme La theacuteologie et lrsquoart symbolisait ainsi cette union intime de

la fataliteacute at la Providence dont la raison ne devait jamais parvenir agrave eacutelucider le

mystegravere

44

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 Boucheacute-Leclercq (1888 389 fn 2)

13 (2 385 C) The imperative used in ldquolook how these inscriptionshelliprdquo (ὅρα δὲ καὶ ταυτὶ τὰ

προγράμματαhellip) means more than simply ldquolookrdquo a spiritual understanding is implied (Obsieger

(2013 116) The same construction appears earlier at ldquobut see also thatrdquo (ὅρα δη ὅσον) (1 384 D)


14 (3 385 D) Ammonius as we see later is not persuaded by Lampriasrsquo 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 ldquoat least twice that numberrdquo attended Their

discussion of different forms of government conveys a pervasive ldquoanti-tyrannical biasrdquo (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 dinnerwhich was held near the shrine of Aphrodite

Plutarch discusses the sages (Life of Solon 12 4) noting that the group at Delphi ldquosummoned

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 listrdquo 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

ldquoonly 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 statesmenrdquo 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 113) 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)

45

Pausanias visited Delphi and commented on the wise men and their maxims but not on the E

He gives us the seven names on Platorsquos 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 ldquoKnow yourselfrdquo (γνῶθι σαυτόν Thales of Miletus) and ldquoNothing in excessrdquo

(μηδὲν ἄγαν Solon of Athens) (Paus 10241)

15 (3 385 D) Obsieger (2013 123) interprets Lampriasrsquo description of ldquomaxims and aphorismsrdquo

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) Flaceliegravere comments that those connected to the sanctuary were more likely to be

temple attendants (neacuteocores) or accredited guides (peacuterieacutegegravetes) than priests (1941 77 n 20)

17 (3 385 F) We can infer that ldquoLivia the wife of Caesarrdquo 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) ldquoChaldeanrdquo was not by Plutarchrsquos time a mark of

ethnicity but a term for astronomers and astrologers The province of Chaldea in the Achaemenid

Empire (539ndash330 BC) disappeared from the historical record during the time of the Roman Empire

19 (4 386 B) The ldquoseven sounds amongst the letters that make a complete sound by

themselvesrdquo 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

46

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 discussantsrsquo feet Lamprias has just

described the Wise Men as dedicating ldquothat one of the letters which is fifth in alphabetical order and

which stands for the number fiverdquo saying that the (rump of) the Wise Men used the E (which also

happens to be a vowel) because it represented their number ndash 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 ndash 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

Aratusrsquo Phaenomena a tract hugely popular in Imperial Rome in part because of Cicerorsquos 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 ldquo[they] come from star books and

the rumours chattered about at the gates of the sanctuaryrdquo 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 Plutarchrsquos favourite construction a doublet

47

Plutarch constructed this section by first describing in the indirect speech of unidentified

speaker the way the Chaldean spoke (he ldquospoke nonsenserdquo ldquoplayed the foolrdquo or ldquopratedrdquo) The

Chaldean used the imperfect tense suggesting that he might have gone on at length Next comes a

crescendo of the Chaldeanrsquos claims ndash 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 ldquoBut all of

these ideas come from star books and the rumours chattered about at the gates of the sanctuaryrdquo We

know what he means even if we cannot parse every word

There is a similar phrase denoting much the same thing ndashμετεωρολόγοι καὶ αδολέσχαι τινές

(ldquosky-watchers and chatterersrdquo or ldquohigh thinkers and great talkersrdquo) but with ambiguous connotations

The first term has a history of serious usage but in Aristophanesrsquo 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

Republicwhere a helmsman is accused by his crew of being a ldquostar-gazer and chattererrdquo 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 ldquohigh-talkingrdquo is required to attain a theoretical as well as a

practical understanding of onersquos craft

22 (4 386 B) Lamprias suggested earlier that his interpretation of the E could be supported by

listening to ldquothe explanations of those connected to the sanctuaryrdquo (γνοίη τις ἂν ακούσας τῶν κατὰ τὸ

ἱερὸν 3 385 F) Here Plutarch speaks specifically of ldquoguidesrdquo 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 Plutarchrsquos

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 ldquoWe seem my friend to be rather rudely depriving the guides of their

proper jobrdquo (αλλὰ καὶ νῦν ὦ παῖ δοκοῦμεν ἐπηρείᾳ τινὶ τοὺς περιηγητὰς αφαιρεῖσθαι τὸ οἰκεῖον

ἔργον 7397 E)

The guides that Pausanias might have had and those that Plutarch might have known were

ldquolocal informants who are able to hold their own in the company of lsquothe educatedrsquo and those

48

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 amateursrdquo (Jones 2001 36)

23 (4 386 C) The guides believe that the name ldquoειrdquo 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 ldquoειrdquo lies in its semantic meaning ldquoyou arerdquo


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 σχημα (ldquoform shape construction or figurerdquo) as ὄχημα (a

vehicle animal or mechanical for carrying freight including human beings) Obsieger prefers the

latter reading although Goodwin has produced the reasonable ldquoa conveyance and form of prayer to

the Godrdquo where ldquoconveyancerdquo means a grammatical structure Nevertheless the phrase ldquothe shape

and form of every prayer to the godrdquo has rhythm reflects the semi-synonyms ldquoσχημα καὶ μορφηrdquo and

avoids the possible hendiadys in ldquoa conveyance and form of prayerrdquo

26 (5 386 C) Nicander claims that ldquoifrdquo [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 Nicanderrsquos 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 απὸ τοῦ φίλου (if I am to receive what is owed me by a friend)

49

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 ldquoby whom and to whomrdquo 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 την

γυναῖκα αὐτοῦ μη συμφωνησαι νῦν τῷ πατρὶ α(ὐτοῦ) αλλὰ αντιλέγειν καὶ μη

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

α[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 ldquotell merdquo ldquoI askrdquo or ldquoNike asksrdquo The interrogative use of εἰ is derived from the conditional

where the protasis is elided thus ldquodo tell me whether you will save merdquo (σὺ δὲ φράσαι εἴ με σαώσεις)

This helps us to understand the next point about the identity of the dialecticians

27 (5 386 C) ldquoThose dialecticiansrdquowere 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 ldquoifrdquo 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) ldquoIf only I couldrsquo is the usual expression of a wishrdquo Despite its appearance here in

a verse from Archilochus the expression lsquoεἰ γὰρrsquo was used most often in the ldquoexalted style of tragedyrdquo

(GP 1959 93) and the εἰ in wishes was from Homer on seen as a conditional Nevertheless it can be

50

difficult to make a distinction between wish and condition as the variations in editorsrsquo punctuations

show ldquoThe difference between lsquoIf only James were here He would help mersquo and lsquoIf only James were

here he would help mersquo is merely the difference between an apodosis at first vaguely conceived and

then clearly defined and an apodosis clearly envisaged at the outsetrdquo (GP 1950 90) Nicander asserts

that γὰρ reinforces εἰ and turns ldquoifrdquo into ldquoif onlyrdquo just as θε does to εἴ in εἴθε

29 (5 386 D) We owe the fragment ldquoto touch the hand of Neobulerdquo to Plutarch (Bergk frag

402 Helmbold-OrsquoNeil frag 6) Almost nothing substantial written by Archilocus a lyric poet from

the seventh centurywas 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 Westrsquos] interpretation I think we

have to do with a fresh and naiumlve 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 ldquoifrdquo) 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 Plutarchrsquos time and place make it difficult to interpret this story in its recently

expanded context We may never completely understand this passage nor Nicanderrsquos choice of

examples

30 (5 386 D) I have chosen to translate ldquoκαὶ τοῦ lsquoεἴθεrsquo την δευτέραν συλλαβην παρέλκεσθαί

φασινrdquo with the paraphrase lsquoif onlyrsquo one can say that the second word is not necessaryrdquo using

51

ldquosecond wordrdquo instead of ldquosecond syllablerdquo (την δευτέραν συλλαβην) 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 ldquoso as they [the

Delians] say the optative force is quite clear in the lsquoifrsquordquo Considering the first use of ldquoifrdquo ndash εἰ γὰρ ndash he

argues that γὰρ is an intensifier that strengthens εἰ to the equivalent of the Latin ldquoutinamrdquo or the

English ldquoif onlyrdquo or ldquowould thatrdquo 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 ldquosurely nowrdquo 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


34 (6 386 E) Plutarchrsquos friend Theon (as opposed to another friend Theon a grammarian)

appears in QC 630 A and is probably the Theon of De Pythwho 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 Theonrsquos and Ammoniusrsquo personification of

ldquoDialecticrdquo 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

52

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 Socratesrsquos 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 Apollorsquos interest in geometry beyond Plato (Riginos

1976 145 Kouremenous 2011 349)

Plutarch reports another anecdote about Platorsquos (and Apollorsquos) interest in geometry He asks

the question ldquoWhat did Plato mean when he said that god always plays the geometerrdquo at a

symposium held to celebrate Platorsquos 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 ldquoif it is day then it must be lightrdquo was used in Stoic teaching of

elementary dialectics Flaceliegravere citing Sextus Empiricus (SVF 2 216 and 279) shows that this

example was part of the elementary curriculum Other examples of the ldquoif it is dayhelliprdquo 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 ldquoεἰ μη ἥλιοςrdquo φησίν ldquoἦν εὐφρόνη ἂν ἦνrdquo

For as Heraclitus says ldquoIf there were no sun it would be perpetual nightrdquo

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 OrsquoNeil (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 Plutarchrsquos

De soll anim (13 969 A) where Plutarch discusses Chrysippusrsquo theory of perception

53

39 (6 387 B) Here we recognise the Stoic theory of divination that all acts and events are

intimately linked and that ldquohe who has the natural capacity to connect causes and link them together

also knows how to foretellrdquo 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

(Boucheacute-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 ldquoall

things that are the things to come and the things that are in the pastrdquo (Iliad 1 70) The phrase ldquobird

interpreterrdquo resonates with the ldquowolves and dogs and birdsrdquo 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 ndash 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 swanrsquos 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 Apollorsquos 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 ldquoa regular yokelrdquo is literally ldquoa real Boeotianrdquo For the Athenians

ldquoBoeotianrdquo 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 Beacuteotie antique 1948 79-92) As to its

54

cause some blame the climate Cicero (De fato 4 71) observes ldquoAthens has a light atmosphere

whence the Athenians are thought to be more keenly intelligent Thebes a dense one and the Thebans

are fat-witted accordinglyrdquo By putting into Theonrsquos mouth lsquole preacutejugeacute habituel contre ses

compatriotesrsquo (Flaceliegravere 1941 81) Plutarch does not hesitate to laugh at his own origins

Nevertheless by not keeping the word ldquoBoeotianrdquo I may be missing the irony that Guillon sees (1948

85) in ldquoHercules a real Boeotian began by disdaining logicrdquo (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 Demetriusrsquo 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 questionshellipabout treasures or inheritances or unlawful marriages (αἰσχρῶν καὶ

αθέων ἐρωτημάτωνhellip 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 ldquoifrdquo and that the syllogism ldquoif the first then the

secondrdquo 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 ldquoif the first then the secondrdquo 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 ldquoquite Pascalian mannerrdquo 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


45 (7 387 E) By qualifying his introduction of Eustrophus with ldquoI thinkrdquo 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

55

46 (7 387 E) Notice Eustrophusrsquo repetition of Plutarchrsquos 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 ndash 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) ndash the number

of joints on the four fingers of one hand forgetting the thumb This is also the derivation of the term

ldquodactylic hexameterrdquo (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 personrsquos

education might have found Eustrophusrsquo views on mathematics (and even Young Plutarchrsquos) over

enthusiastic See appendix B for a discussion of free indirect discourse and its role in expressing

irony

In contrast to Wyttenbachrsquos τάχα δὲ μέλλων Obsieger follows Sieveking Flaceliegravere Cilento

and Babbitt in preferring τάχα δη 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 δη (ldquoverilyrdquo

ldquoactuallyrdquo or ldquoindeedrdquo) 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


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 ldquooften reads like little more than the written-up notes of a

studentrdquo (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 ldquohardrdquo 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

ldquoevery point on a cycle (or a circle) is simultaneously the beginning and the endrdquo (Ξυνόν γαρ αρχή και

56

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 ldquosix does this only once when it is squaredrdquo 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 3125hellip) 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 30hellip in the Greek it is

εʹ ιʹ ιεʹ κʹ κεʹ λʹ λεʹ μʹ μεʹ νʹ νεʹhellip 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 hellip represent the

tens

54 (8 388 E) The comparison ldquolike gold for goods and goods for goldrdquo 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 Obsiegerrsquos text has πυρός τε

ανταμείβεσθαι πάντα φησίν ο Ηράκλειτος καὶ πῦρ απάντων lsquoὅκωσπερ χρυσοῦ χρήματα καὶ

χρημάτων χρυσόςrsquo which is slightly different from Dielsrsquo πυρός τε ανταμοίβη τὰ πάντα καὶ πῦρ

απάντων ὅκωσπερ χρυσοῦ χρήματα καὶ χρημάτων χρυσός (Diels 90 Bywater 22 Kahn 40)

Bywaterrsquos 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 ανταμείβομαι (middle meaning ldquoto give or take in exchange to requite or punish

ie to give punishment in exchange for bad behaviourrdquo) 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

57

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 orsquoer 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


55 (9 388 E) With ldquoBut what is this to Apollordquo 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 ldquoBut what has that to do with Dionysusrdquo (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 Plutarchrsquos time Plutarch uses the figure to good effect in the first of his QC (1 1 5

615 A) ldquoWhether philosophy is a fitting topic for conversation at a drinking-partyrdquo

58

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 1021) Even as late as Plutarchrsquos 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 (ldquotheologianrdquo) by example ldquoone who discourses of the

gods used of poets such as Hesiod and Orpheusrdquo 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 Apollorsquos epithets (2 385 B) and he will

analyse ldquoApollordquo ldquoPhoebusrdquo and ldquoIeiusrdquo 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 Flaceliegravere (1941 84) called the name Isodaetes ldquoune

eacutepithegravete fort rarerdquo defining it as ldquothat which is divided equallyrdquo 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 paeanhellip 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

59

61 (9 389 B) Plutarch also uses the phrase ldquoDionysus of the orgiastic cryrdquo in De exil 607 C and

QC 667 C Compare Bergk 3730

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 37) and Hippolytus (Refutatio Omnium

Haeresium 9107) 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 ldquorelation of the

period of orderly disposition to that of fiery destructionrdquois three to one Kirk comments that while

Plutarch is obviously drawing on a Stoic source ldquothe ratio of 3 to 1 for the length of ecpyrosis and

cosmogony may be his own rather than a Stoic invention ndash it rests on the three-month tenure of

Dionysus at Delphi as compared with the nine-month tenure of Apollordquo (Kirk 1962 358)


Young Plutarchrsquos 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 listenersrsquo (or his own) understanding of music On the same note Goodwin in the first footnote to

his translation of Pseudo-Plutarchrsquos 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 tetrachordshellip 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 (Plutarchrsquos 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 sv ldquoμουσικήrdquo and so on) First μουσική more general than

ldquomusicrdquo is derived from the name of the Muses and denoted any art over which the Muses presided

60

but it evolved into the name of a particular art ndash 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 ndash 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 μουσικη τέχνη

Second the noun αρμονία from the verb αρμόζω (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 ldquothat hideous piece of female joinery a patch-work

counterpanerdquo 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 Platorsquos Republic (531 b) where the theory of music

corresponds exactly to the theory of astronomy ldquofor the numbers they [astronomers] seek are those

found in these heard concordsrdquo (αστρονομίᾳ τοὺς γὰρ ἐν ταύταις ταῖς συμφωνίαις ταῖς ακουομέναις

αριθμοὺς ζητοῦσιν)

Harmoniarsquos 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 ndash 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 ldquoαρμονίη αφανης φανερης κρείττωνldquo 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

61

and those who analysed them ldquoby earrdquo 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 21 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) (Plutarchrsquos 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 ldquoWhat is the Oracle at Delphi ndash the tetractys which is the octave (harmonia)

which has the Sirens in itrdquo West (1994 235) quotes this from the list of Pythagorean catechisms given

by Iamblichus (De Vita Pythagorica 8247)

64 (10 389 C) Surely the comment ldquoreasonable proportionrdquo is wordplay on the new subject

harmonic theory

65 (10 389 C) The working of harmony is in a word concordmdashthese concords are based on the

ratios between numbers

66 (10 389 D) The ratios of the five intervals that is 21 31 41 43 and 32 are all pairs of

the four integers belonging to the tetractys The only other possible pair is 42 which is equivalent to

21 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

62

translations (for example those of Amyot Holland Ricard and Goodwin) often use transliterations of

the Greek Consider Goodwinrsquos 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 ldquoexperts in harmonyrdquo would

work Plutarch has a particular group in mind ndash 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 ldquostray 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 consisthelliprdquo (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 83 (that is 21 x 43) 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 Plutarchrsquos use of ldquothe first five lsquomodesrsquo or lsquokeysrsquo or lsquoscalesrsquo whatever

their right name isrdquo suggests that even in Plutarchrsquos time these words were multivalent Babbitt and

Goodwin simply transliterate the Greek using ldquotropesrdquo ldquotonesrdquo and ldquoharmoniesrdquo 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

lsquokeysrsquo 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

(lsquomodulatingrsquo) between differently pitched instances of the same scale-pattern

(Barker 2007 55)

63

His use of tropoi is consistent with the uses of harmoniai and tonoi The noun τροπός is ldquolike

αρμονία a particular mode hellip but more generally a lsquostylersquordquo (LSJ sv ldquoτροπόςrdquo) 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 ldquoThe reversals of fire first sea but of sea half is earth

half lightning stormrdquo (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)hellipThis 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


72 (11 389 F) Not to belabour the point but the two personal pronouns ldquoIrdquo 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 Plutarchrsquos speech To use

a self-referential ldquoIrdquo 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 ldquoother philosophersrdquo

74 (11 389 F) Young Plutarch immediately after giving another example of the importance of

the number five embarks on a digression about Aristotlersquos assertion that there is a unique world

Young Plutarch attempts to reconcile this assertion with Platorsquos view that there could be up to five by

64

by invoking Aristotlersquos identification of the five solids with earth water fire air and the quintessence

Young Plutarchrsquos use of ldquoeven ifrdquo (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 Arsitotlersquos 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 (ldquowithrdquo or togetherrdquo) in the phrase συγκείμενον

κόσμων καὶ συνηρμοσμένον (ldquocomposed and conjoined from five worldsrdquo) nicely mirrors the one in

the Greek This may not be strictly speaking hendiadys but it is another example of Plutarchrsquos

fondness for balanced repetition

76 (11 390 A) With ldquothe five mosthellipfittingly associated each to eachrdquo Young Plutarch gives a

condensed version of Platorsquos 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 sv Platos Timaeus)

The polysemic φύσις occurred just one line above where it was translated ldquoby its own naturerdquo

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 ndash fire earth water and air ndash and the fifth and last the dodecahedron which ldquoGod used to

bedeck his universerdquo (ἐπὶ τὸ πᾶν ο 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 Platorsquos dialogue Theaetatus and his

mathematical work is discussed in Euclidrsquos Elements Book 13

65


77 (12 390 B) These philosophers follow Aristotlersquos theory of the correspondence of the senses

in De anima (27-11)

78 (12 390 B) Plato (Timaeus (45b-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 ldquoextreme

brevityrdquo of this section but it is Plutarchrsquos 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


79 (13 390 C) Young Plutarch refers to the passage in the Iliad where Iris has delivered Zeusrsquo

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

hellip 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 ldquocette impression de deacutesordre est

renforceacutee par les allusions reacutepeacuteteacutees des personnages dans les trois [Pythian] dialogues agrave des

digressions qui les ont entraicircneacutes loin de leur sujet initial et par des rappels insistants agrave ne pas perdre de

vue ce sujetrdquo 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

66

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 Plutarchrsquos argument A French version of this

wandering from the subject at hand and then returning to the fold by some roundabout route

ldquorevenons agrave nos moutonsrdquo was a running joke in the medieval play La Farce de Maicirctre 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 ldquois 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 sv ldquopointrdquo) 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 ldquoa point without positionrdquo

(στιγμη 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 ldquostretchingrdquo 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 ldquozerordquo 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 ldquoὀρφανὸν καὶ ατελὲς καὶ πρὸς οὐδ᾽ οτιοῦνrdquo that I have seen

renders ὀρφανός as ldquoorphanrdquo 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

ldquodeprived ofrdquo He suggests tentatively that the name Orpheus might be from the same root as

ὀρφανός adding ldquoOrpheacutee eacutetant priveacute de son eacutepouse []rdquo

67

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)


85 (14 391 A) Young Plutarch asserts that four is the ldquofirst square numberrdquo 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 ldquoit is

creation thanks to its creativity and intellect thanks to its intelligence this is adequately demonstrated

in the mutual opposition of oblongs and squaresrdquo (Waterfield 1988 36) The ldquoideal formrdquo is the

monad and ldquofinite matterrdquo is the tetrad since ldquoeverything in the universe turns out to be completed in

the natural progression up to the tetrad as does everything numerical ndash in short everything whatever

its naturerdquo (Waterfield 1988 55) Furthermore all the numbers up to four give us the pentad and are

arrayed in the tetractys


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

68

that an unattached pronoun ldquoherdquo 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-αεί (ldquoit

always has light both new and oldrdquo) 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 lsquodithyrambicrsquo etymology of lsquomoonrsquo or rather of the Doric variant

Σελαναία (409a-c)rdquo (2011 237)

In the case of the etymology of the name of the moon two examples support this opinion The first is

Fowlerrsquos inspired translation of διθυραμβῶδες (dithyrhambicrdquo) as ldquoopera boufferdquo (Plato Loeb

Classical Library 1926 4167) A second is Obsiegerrsquos contention that just the mention of Anaxagoras

from this section of the Cratylus would have signalled to Plutarchrsquos listeners (and later readers of De

E) that a joke or ldquosome sort of historical and philosophical illogicalityrdquo was in the offing (Durch die

Erwaumlhnung des Kratylos werden die Zuhoumlrersbquo Plutarchs und die Leser von De E gewarnt daszlig eine

philosophiehistorische Absurditaumlt folgt [Obsieger 2013 281])

On the more general question of the seriousness of the etymologies Ademollo provides a

measured assessment of Platorsquos and Socratesrsquo 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 Anaxagorasrsquo finding is pre-empted by the longstanding folk

etymology of the word ldquomoonrdquo a word that developed from the two sources new and old of

moonlight This was exactly Anaxagorasrsquo theory Young Plutarchrsquos 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)

69

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 ldquorace

kin clan family or classrdquo) 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

αλλήλων 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 ldquobecause he dedicated an E to the godrdquo

Bernardakis has δύο Ε καθιέρωσε τῷ θεῷ and Obsieger daggerδύοdagger εἶ καθιέρωσε τῷ θεῷ signalling his

doubts about δύο Babbitt suggests and uses διὸ (because) Flaceliegravere writing soon after follows suit

but adds another word διὸ lttὸgt εἶ καθιέρωσε τῷ θεῷ Goodwin translating using an earlier version

of the text produced the peculiar ldquosome onehellip consecrated to the God two E Erdquo If ldquotwo E Erdquo 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 ldquoQuelqursquoun doncques hellip consecra deux E au Dieu de ce

templerdquo

Obsieger provides an analysis of the emendations of Wyttenbach Wilamowitz Pohlenz

Babbitt and Flaceliegravere 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 ldquoδύοrdquo 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 Babbittrsquos

70

generally accepted emendation διὸ is reasonable and that Flaceliegraverersquos introduction of ltτὸgt is ldquoan

obvious improvementrdquo

91 (15 391 C) Socrates sings the verse ldquoIn the sixth generation bring to a stop the ritual of

songrdquo (lsquoἕκτῃ δ᾽ ἐν γενεᾷrsquo φησὶν Ὀρφεύς lsquoκαταπαύσατε κόσμον αοιδηςrsquo 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


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 ldquothe sixthrdquo

93 (16 391 D) This sentence is notorious for its obscurity and corruption Here Goodwin

permits himself ldquoI leave this corrupt passage as I find it in the old translation [ie by many hands]

The Greek cannot be tortured into any senserdquo Babbitt cautions that the Greek text ldquois somewhat

uncertainrdquo I have followed Babbittrsquos 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 Nicanderrsquos

worried response ldquothe reason for it [the outcome of the casting] must not be divulged to othersrdquo one

cannot shake the suspicion that Plutarchrsquos original text could have been deliberately obfuscatory

94 (16 391 E) Plutarch is reporting in direct speech Young Plutarchrsquos 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 ldquoif ever the time comeshelliprdquo


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 sevenThis

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 writersrsquo weakness for arithmology (ldquoils ont un faible

pour lrsquoarithmologierdquo Delatte 1915 231) In a short essay he describes Clementrsquos preoccupation with

71

reconciling Hebrew doctrine with the new Christian religion He gives the example of Clementrsquos

treatment of the third commandment (ldquodo not take the name of the Lord in vainrdquo) with the description

of the Creator resting on the seventh day The Lordrsquos 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 Clementrsquos 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 ldquoDieu eacutetant naturellement infatigable ignore le besoin du

repos mais il est le modegravele de celui que nous est commandeacuterdquo (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 Plutarchrsquos

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

ldquoringside seatrdquo 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 ldquolong years of timerdquomdashmust mean something like ldquothe weight of

longstanding traditionrdquo The citations is from Simonides of Crea (6th century BC) (Bergk 1 522 and

Simonides 193)


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 ldquobetween coming into being and being destroyedrdquo and are for an instant in both states

simultaneously He pursues this idea comparing each thingrsquos coming into being and its simultaneous

destruction to ldquoa vessel leaking birth and destructionrdquo (ὥσπερ αγγεῖον φθορᾶς καὶ γενέσεως) This

section uses variants of the words γίγνομαι ndash to become come into being and φθείρω ndash to destroy I

have tried to reflect this vocabulary in my translation

99 (18 392 B) This is Plutarchrsquos second direct attribution to Heraclitus given in direct speech

by Ammonius ldquohellipit is not possible to step twice into the same riverrdquo I have taken only the words

before ldquoHeraclitus saidrdquo to be a direct quotation There are two Heraclitean fragments concerning

rivers their interpretation is controversial but they were well known in Plutarchrsquos time His version is

unlikely to be in Heraclitusrsquo exact words but simply a free rendering of ldquoas they step into the same

72

rivers other and still other waters flow upon themrdquo (ποταμοῖσι τοῖσιν αυτοῖσιν ἐμβαίνουσιν έτερα και

ετερα υδατο 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) ldquoIt is obvious that [Plutarchrsquos] ποταμῷ

hellip τῷ αὐτῷ reproduces the Aristotelian form of Platorsquos paraphrase of the river statement and not (as

Bywater Diels Kranz and others believed) the original words of Heraclitusrdquo (See Kahn 1979 168

Marcovich 1967 206 and Kirk 1962 374-381)

100 (18 392 B) The assertion ldquoOne cannot step into the same river twicerdquo does not entail that the

individual elements that make up the river ndash the drops of water ndash 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 ldquoit disperses and gathersrdquo 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 ldquocatchwordrdquo

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) Fairbanksrsquos view is now the

professional consenus Given that Young Plutarch has just been quoting Plato Kahnrsquos comment that

these pairs of antithetical verbs are reminiscent of Heraclitean ldquostylerdquo is intriguing He suggests that

this pair could well be a ldquoPlutarchean interpolationrdquo inspired by the Strangerrsquos contrast (at Sophist 242

D-E) between the Ionian (Heraclitus) and Sicilian (Empedocles) philosophers (Kahn 1979 130)

102 (18 392 C) The phrase ldquothe death of fire is birth for air and the death of air is birth for

waterrdquo is the third fragment that Plutarch attributes directly to Heraclitus Fairbanks notes that it

seems to be given accurately by Maximus Tyr (414) ldquoFire lives the death of earth and air lives the

death of fire water lives the death of air earth that of waterrdquo But note that Maximus is the only writer

to use the word ldquoliferdquo 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

αέρος γένεσις

Since corruption is the alteration of those things that are corrupted into their

opposites let us see whether the saying holds good that ldquoThe death of fire is the

generation of airrdquo

73

Nevertheless Kahn is right to note the use of the words ldquobirthrdquo and ldquodeathrdquo for the transformations of

the elements This vocabulary (which may be metaphoric) allows Ammonius to make the logical leap

to animate being in ldquoand it is clearer still in ourselvesrdquo 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 ldquoAs to our not

remaining the same while being is always in fluxrdquo 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

αλλ᾽ ἄνθρωπός τε λέγεται μέχρι τέλους εἷς απὸ γενέσεως πόλιν τε την αὐτην

ὡσαύτως διαμένουσαν ἐνέχεσθαι τοῖς ὀνείδεσι τῶν προγόνων αξιοῦμεν ᾧ δικαίῳ

μέτεστιν αὐτῇ δόξης τε της ἐκείνων καὶ δυνάμεως ἢ λήσομεν εἰς τὸν Ἡρακλείτειον

ἅπαντα πράγματα ποταμὸν ἐμβαλόντες εἰς ὃν οὔ φησι δὶς ἐμβηναι τῷ πάντα κινεῖν

καὶ ἑτεροιοῦν την 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 ldquoPlutarchsrdquo 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 Flaceliegravere is more pointed (1941 89 11)

Ces ideacutees nrsquoexpriment qursquoun aspect de la reacutealiteacute et comportement assureacutement une

grande part drsquoexageacuteration Cf Ricard dans sa note agrave ce passage [1884 60 -61] laquoLes

vicissitudes que nous eacuteprouvons dans nos gouts nos affections nos sentiments et

74

mecircme dans les traits de notre figure ne deacutetruisent ni lrsquouniteacute de notre individu ni la

reacutealiteacute de notre existence propre et individuelle raquo

These ideas express only one aspect of reality and certainly contain some

exaggeration See Ricardrsquos 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

existencerdquo

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-bornmdashyou could not step

into the same rivers twice as Heraclitus says because the waters that flow upon you

are not the samemdashyet 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 ldquoriversrdquo it tells us little about the question of the actual words of Heraclitus and it seems to rely on

Aristotlersquos use of the aphorism It also provides another example where ldquoHeraclitus saysrdquo 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 ldquoevidently a Middle Platonic commonplacerdquo provides a

similar example in Senecarsquos letter to Lucius (On Being 58 22)

103 (18 392 D) A model in wax or plaster from ἐκμάσσω ldquoto mould or adapt oneself tordquo


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 ldquoaccording to their connections with timerdquo might mean that

each entity is somewhere between birth and death and the place of each one is determined by its own

circumstances


75

107 (20 393 A) The reading in Obsiegerrsquos and Bernardakisrsquo Greek texts and the English is in

Goodwinrsquos translation is ldquoiacutet must be saidrdquo (χρη φάναι) In contrast Flaceliegravere has the conditional ldquoif it

needs to be saidrdquo (εἰ χρη φάναι) which appears as an interrogative in the French ldquoLa diviniteacute elle

existe (est il neacutecessaire de le dire)rdquo Babbitt notes that εἰ does not appear in the manuscripts but was

added by Eusebius (Preparatio evangelica 1111) and followed by Cyril of Alexandria (Adv Jul 8)

In any case Babbitt uses ldquoif there be need to say sordquo The emphatic ldquoit must be saidrdquo underlines the

distinction that Ammonius is at great pains to make that the god is not enmeshed in temporality I

have adopted Obsiegerrsquos text

108 (20 393 A) Forever (αἰών) can mean a long space of time an age (as our ldquoeonrdquo) ldquoeternityrdquo

or ldquoagesrdquo 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 ldquoeternityrdquo 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 Ammoniusrsquo name his background the two appeals to ldquothe

ancientsrdquo ( 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 αεiacute as used by Plato ndash one referring to time and consequently involving duration and the other

referring to eternity that transcends duration Mediaeval Latin distinguished between ldquoeternalrdquo (outside

time) and ldquosempiternalrdquo (lasting for endless eons)

109 (20 393 A) ἀνέγκλιτον (from κλίνω to make to lie back to lean to incline) meaning

ldquounchangingrdquo and ldquoorthogonalrdquo (LSJ) Plutarch also uses the word in the Life of Pericles (15)

αριστοκρατικην καὶ βασιλικην ἐντεινάμενος πολιτείαν καὶ χρώμενος αὐτῇ πρὸς τὸ

βέλτιστον ὀρθῇ καὶ ανεγκλίτῳ

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 ldquoto deviaterdquo as ldquoto turn aside from a course method or mode of action

a rule or standardrdquo Hence ldquoto deviaterdquo carries an extra nuance beyond ldquoto changerdquo to

include the notion of falling away from a standard Similarly ldquoorthogonalrdquo can mean a standard or

norm (it also means ldquoright-angledrdquo) 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

76

translation a translation that works just as well here Then I discovered that Babbitt had used

ldquodeviaterdquo 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 ldquoneither future nor past neither olderhelliprdquo (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 ldquothose coming to the

shrine in search of wisdomrdquo (τοὺς ἐν αρχῇ περὶ τὸν θεὸν φιλοσοφήσαντας (De E 1 385 A)

112 (20 393 B) The word ldquogodrdquo appears in both the masculine (ο θεὸς) and the neuter (τὸ θεῖόν)

which I translate a few lines below as ldquothe divine is not manifoldrdquo 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 ldquophoebusrdquo) are Parmenides and Plato referring us to Adv Col (13 1114 C-F) where the

doctrine underlying Ammoniusrsquo argument ndash that true being remains always the same but our world is

fleeting and subject to change ndash 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 ldquothe one and onlyrdquo (εἷς καὶ μόνος and sometimes

ἔν καὶ μόνον) and sees it as derived from the epic adjective ἰός ία ἰόν (meaning εις μια ndash one)

115 (20 393 C) As Ildefonse says the parallel to Homer (Iliad 4 141 ff) is loose perhaps

explaining Ammoniusrsquo use of the qualifier πού The conflating of the two meanings of μιαίνω (to

ldquostain colour or dyerdquo and to ldquostain or sullyrdquo) 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 851 725 C where the question posed is ldquoWhy do sailors

draw water from the Nile before daybreakrdquo The partial answer is that during the day riverwater is

stirred up by animals and river traffic and hence polluted This mixing ldquoproduces conflict conflict

produces change and putrefaction is a kind of change

Serendipitously English has an analogous pair of homonymsmdashdiedyemdasha 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

77

Our lusty English all with purple hands

Dyed in the dying slaughter of their foes (King John II 1 629)


116 (21 393 E) The phrase ldquorapture and transformationsrdquo (ἐκστάσεις δ᾽ αὐτοῦ καὶ μεταβολὰς

repeated a few lines later as ἐκστάσεως καὶ μεταβολης) is another of Plutarchrsquos doublets here

combining two close synonyms The first meaning of ἔκστασις is ldquodisplacementrdquo the second

ldquostanding aside and the third ldquoentrancement astonishmentrdquo The Greek word can be transliterated as

ldquoecstasyrdquo an English word closely related to one of the meanings of ldquorapturerdquo (compare the OED

ldquoecstasy an exalted state of feeling which engrosses the mind to the exclusion of thought rapture

transportrdquo) Ammonius is referring to the passage in section 9 where Young Plutarch uses the single

word ldquotransformationrdquo

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 Apollorsquos volition since

everything in the cosmos is subject to a logos beyond human or divine control The English word

ldquorapturerdquo captures the involuntary nature of these changes The ldquoTheologiansrdquo could certainly include

Heraclitus who wrote prose but intricate and poetic prose

Plutarch uses this doublet again in discussing the question ldquoWhether it is possible for new

diseases to come into being and from what causesrdquo and whether qualitative changes in a substance

can bring about a change into a new substance (a ldquosubstantialrdquo 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 893 732 B)

117 (21 393 E) Those saying this are the Stoics or the theologians in the passage from Section 9

Flaceliegravere (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

78

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 απόλλων (the future participle of απόλλυμι ldquoto destroyrdquo)

whence as Socrates explains some people wrongly derive his name (Cratylus 405e-406a) since that

abstract noun signifies ldquodestructionrdquo but not ldquodestroyerrdquo the agent of that destruction There are

other epithets of Apollo that do entail havoc if not destruction for example the Homeric epithet ldquothe

far shooterrdquo (Ἀπόλλων ἕκατος Iliad 783)

The name ldquoDelianrdquo describes someone born on the island of Delos as Apollo was but could

also denote clarity (δηλος - clear) which contrasts with Hades or Aiumldoneus 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 ldquoinvisiblerdquo (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 ldquoAs for Pluto he was so named as the giver of wealth

(πλοῦτος) because wealth comes up from below out of the earth And Hades ndash I fancy most people

think that this is a name of the Invisible (αειδής) so they are afraid and call him Plutordquo (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

Homerrsquos ldquodarkness of deathrdquo (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 (10244) 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 ldquoa 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 sculpturerdquo (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

79

nicely with ldquoLord of night and sleeprdquo 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 ldquoof the gods the most hated by mortal menrdquo see Homer (Iliad 9

158-9)

Ἀΐδης τοι αμείλιχος ἠδ᾽ αδάμαστος

τοὔνεκα καί τε βροτοῖσι θεῶν ἔχθιστος απάντων

hellip 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 ldquotowards mortals he has been

judged the gentlestrdquo (κατεκρίθη δὲ θνατοῖς αγανώτατος 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 ldquoYou arerdquo and an offering from the

seven Sages with the aphorism ldquoKnow yourselfrdquo 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 Plutarchrsquos 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 Cleombrotusrsquo 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 Cleombrotusrsquo description of these

80

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 αριθμοῦ τούτου πρὸς τὸ πληθος λόγος ἥδιον ἄν μοι

δοκῶ μαθεῖν ἢ της ἐνταῦθα τοῦ εἶ καθιερώσεως την 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 ldquoKnow

yourselfrdquo and ldquoNothing in excessrdquo

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 ldquoYou

arerdquo As he says these are the words that people use when they approach the god We can see the

parallel to Socratesrsquo solution to the Delian problem The E symbolises divine transcendence and the

phraserdquoYou arerdquo 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 ldquoYou arerdquo 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 electronmdashthe

precious substance we call ambermdashthat 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 Manufacturers 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 visionary1 That book no longer exists and all that

remains of his philosophy is ldquoa handful of polished aphorisms scattered across the eastern

Mediterraneanrdquo (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 man2 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 95) Plutarch wrote a study (also lost) of Heraclitus ldquoOn the

Question of Heraclitusrsquo Beliefsrdquo listed as Lamprias 205 (Moralia LCL Vol 15)

2 Not everyone admires Heraclitusrsquo style Lucretius (De Rerum Natura 1638 44) objecting to his

extravagant imagery and sophomoric wordplay lambasted him for his obscurity and chastised those

who enjoyed his wordplayldquomistaking itrdquo for cogent reasoning

82

Archilochus should have been excluded from rhapsodic competitions at athletic games On

the other hand he approved of Bias of Priene apparently for his probity3 Bias one of the

seven Sages is known to us for his maxim ldquoMost men are badrdquo (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 ldquoartrdquo 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 αρμονίη αφανης φανερης κρείττων (Diels 54) according to Kahn ldquothe

shortest and most beautifully designed of the fragmentsrdquo (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 Heraclitusrsquo doctrine of the unity of

opposites) Kahn speculates that by placing αφανης before φανερης Heraclitus is affirming

3 Diogenes Laertius often seems to enjoy gossip and name-dropping Kahn (1979 10) calls Diogenesrsquo

Life of Heraclitus ldquoa tissue of Hellenistic anecdotes most of them obviously fabricated on the basis of

statements in the preserved fragmentsrdquo

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

(DielsKahn) and a triple one-way concordance (KahnDielsMarcovich) in Marcovich a one way

concordance(DielsMarcovich) and a triple-one way concordance (MarcovichDiels Bywater) Diels

cross references his fragments to Bywater

83

that ldquothe negative term is superior to the positive and he has expressed in a formal way the

dialectical re-evaluation of the negative principlerdquo 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 Heraclitusrsquo use of three polysemic words allows us to read it in

several different ways I chose Keatsrsquos 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 ldquounheard melodiesrdquo with the noun suppressed a direct

homage to Heraclitusrsquo appositional structure I like to think that Heraclitus would have

enjoyed the bad pun in the third line There is no ldquorightrdquo 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

ldquoOf the soul however nothing is pure and unmixed nor remains apart from the rest for lsquothe

hidden harmony is better than the visiblersquo in which the blending deity has sunk variations and

differencesrdquo Bywater on the strength of Hippolytus also connects it to ldquowhatever concerns

seeing hearing and learning I particularly honourrdquo (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 ndash αρμονίη αφανης φανερης κρείττων ndash 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 ldquoγαρrdquo (αρμονίη γαρ

αφανης φανερης 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 ldquoA hidden harmony

is better than a visiblerdquo and ldquowhatever concerns seeing hearing and learning

I particularly honourrdquo having before particularly honoured the invisible

(Hippolytus Refutation of All the Heresies 9910)

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 Plutarchrsquos attention to Heraclitusrsquo

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 testimonia6

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 citations7 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 Alexandriarsquos methods of citation

briefly discusses Plutarch on whom Clement often relied Discussing note taking by ancient authors

including Plutarch she describes the three ldquobookwormsrdquo (her term) ndash Clement Plutarch and Eusebius

85

7000 identified quotations and borrowings from 497 authors in Plutarchrsquos extant works

(Helmbold-OrsquoNeil) Even in one short piece such as De E the resonance of Plutarchrsquos

quotations and allusions and their fitness to the occasion delight the reader In De E we see

in almost every speakerrsquos 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

allusion8 Plutarchrsquos three attributed fragments from Heraclitus in this dialogue are in this vein

ndash short but a direct contribution to the development of the narrative arc of the dialogue The

first is Young Plutarchrsquos use of the notion of exchange to describe the regularity and

periodicity of the pentad (Diels 90) and the second and third occur in Ammoniusrsquo 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 Plutarchrsquos 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

Heraclitusrsquo 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 Heraclitusrsquo

ndash 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 Plutarchrsquos 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 Bywaterrsquos compilation as the culmination of a

century of scholarly study (mainly on the continent) beginning with the publication of

Friedrich Schleiermacherrsquos Herakleitos der Dunkle von Ephesos (1807) followed by the

Heraclitea of Jakob Bernays (1848) Bywaterrsquos work provides an excellent introduction to the

work of Heraclitus and Patrickrsquos translation made it available

to every man to read and judge for himself [the philosophy of Heraclitus]hellip 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

Bywaterrsquos 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 ldquoChallengerrdquo oceanic expedition (1872-76)

which circumnavigated the globe to gather information on the worldrsquos oceans His obituary appeared

in Nature 94 (1914) 455

87

introduction to the Heraclitean fragments 10 To my knowledge Arthur Fairbanks (1897) was

the first to analyse the records of Plutarchrsquos quotations from the early philosophers11 Using

Bywaterrsquos compilation (that of Diels was not yet in print) Fairbanks reviewed 228 fragments

from these philosophers12 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 directly14

Diels built on Bywaterrsquos 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 Dielsrsquos contemporaries John Burnet (1930) and H Gomperz (ldquoUumlber

10 Kahn comments favorably on Bywaterrsquos contribution ldquoin many respects [Bywaterrsquos compilation]

has remained the most useful edition of any detailed study of Heraclitus (ldquoA new look at Heraclitusrdquo

1979 189) Kahn sees Bywaterrsquos methodical arrangement of the fragments by topic as a valiant

attempt to interpret Heraclitusrsquo work as a coherent narrative argument

11 These were Heraclitus Empedocles Anaxagoras Parmenides and Xenocrates See Arthur

Fairbanks ldquoOn Plutarchs Quotations from the Early Greek Philosophersrdquo TAPA 28 (1897) 75-87

12 The precise numbers are Heraclitus 48 Empedocles 99 Anaxagoras 42 Parmenides 21 and

Xenocrates 18The number 48 apparently includes citations that Diels later included in his list of the

Testimonia There are fourteen testimonia listed in Helmbold-OrsquoNeil 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 DeE while Helmbold-OrsquoNeil restrict

themselves to the three signalled by a phrase meaning ldquoas Heraclitus saidrdquo

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

dieuumlrspruumlngliche Reihenfolge einiger Bruchstuumlcke Heraklitsrdquo Hermes 58 [1923 20])

disputed Dielsrsquos arrangement while Hermann Fraumlnkel 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 ldquocosmicrdquo fragments those ldquodescribing the world rather than men in particularrdquo (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 ldquowithout further

preliminary considerations we shall proceed directly to the midst of the matter beginning our

interpretation with Fr 64 [τὰδὲ πάντα οἰακίζει κεραυνός]rdquo15 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

9107 Diels translates this into German as ldquoDas Weltall aber steuert der Blitzldquo (Diels 1906 71)

which Seibert translates as ldquolightning steers the universerdquo John Burnetrsquos translation is ldquothe

thunderbolt steers all thingsrdquo

89

participants who are familiar with the fragments as the participants in the Heraclitus Seminar

seem to have been16

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

ldquolinguistic densityrdquo that appears in other fragments17 It consists of three words (ignoring the

particle δὲ) τὰ πάντα οἰακίζει and κεραυνός The English counterparts are ldquoall thingsrdquo

ldquosteersrdquo or ldquoguidesrdquo and ldquolightningrdquo or ldquothunderboltrdquo18 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

ldquoventuresomerdquo and ldquohazardousrdquo nevertheless reading the account of the seminar stimulates both the

mind and the imagination

17 Kahn describes two properties of the fragments linguistic density ldquothe phenomenon by which a

multiplicity of ideas is expressed in a single word or phraserdquo and resonance ldquothe 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 togetherrdquo (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 ldquoseerdquo a relationship Closeness means that they are next to each other on the same page or share

common words or electronic links Dielsrsquos instincts were good when he tried to randomise the

fragments

18 Bywater gives the context ldquoAnd he [Heraclitus] says that a judgement of the world and all things

in it will take place by fire expressing it as follows lsquoNow lightning rules allrsquo that is guides it rightly

meaning by lightning everlasting firerdquo The ldquocontextrdquo for Bywater is the context given in the source

The source of this quotation is Refutation of All the Heresies 910 (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 ldquoneed and satietyrdquo which lies within the range of Hippolytusrsquo 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

90

sentence makes good sense in that one knows what it says but since each of the words is

multivalent not necessarily what it means19 The ship analogy in ldquosteersrdquo 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 ldquoI remember an afternoon during my journey in Aegina I saw a single bolt of

lightning after which no more followed and my thought was Zeusrdquo Finally the equating of

ldquoall thingsrdquo and ldquothe universerdquo 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 ndash 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 ldquoall things are one ldquoand Diels 10 ldquofrom all things one and from one

anomaly first as Fairbanks points out ldquoneed and satietyrdquo appears to have been a catch-phrase and

one that Plutarch did not describe as coming from Heraclitus and second Hippolytusrsquo citations are

contained in a span of 1000 words from Refutation of All the Heresies 991 to 9108 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 ldquothe way up and the way down is one and the

samerdquo(Diels 60) which he says provides indirect evidence for a larger (coherent) structure since the

statement cannot be interpreted in isolation ldquoThe 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 ndash from the sentences

that came before and afterrdquo

91

thing allrdquo) comments ldquoone might reasonably claim that all of Heraclitusrsquo 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 fragmentrdquo (1979 95) 20

CITATIONS FROM HERACLITUS IN DE E

Having been shown the way by Heidegger we can enter the fragments with Plutarchrsquos

first explicit quotation from Heraclitus By giving Young Plutarch a quotation about circular

flow Plutarch is setting the stage for Ammoniusrsquo 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 ldquoso she [Nature] leads this work to its logical end and at the

end she displays its beginning ndash wheatrdquo (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 25hellip) and

makes the imaginative analogical leap from these cycles to those of the cosmos being

20 We have mentioned Heraclitusrsquo syntax and the patterns he creates in his aphorisms these include

parallelism contrasts analogies and pairings Another is the pattern of the geometric mean

AB = BC which as the mean proportional provides a method for solving the Delian problem

Fraumlnkel in an elegant paper (ldquoA Thought Pattern in Heraclitusrdquo 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 algebrardquo

There is another correspondence to the Pythagorean tetractys The interior numbers of the

Platonic Lambda are the geometric means of the exterior numbers

92

continually created and destroyed in alternation and to the Heraclitean notion of balanced

exchange21

For the first principle preserves the cosmos and then out of the cosmos perfects

itself and as Heraclitus says ldquoall things are exchanged for fire and fire is exchanged

for all thingsrdquo just as ldquogold is for goods and goods for goldrdquo

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 ndash a

closed dynamic system autonomously maintaining its equilibrium This aphorism

memorable both for its content and for its artful chiasmus aptly reflects its connotations ndash

circularity reciprocity and fungibility Closed dynamic processes were explored much later in

European philosophy we see the same ideas of circularity in the ldquoinvisible handrdquo in The

Wealth of Nations of Adam Smith (1776) and in the Tableau eacuteconomique of Franccedilois

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

reflect the idea

There is an ambiguity here whether ldquofirerdquo is one of the things in ldquoall thingsrdquo 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 ldquofrom all things one and from

one thing allrdquo (Diels 10 Kahn 124) and links it to the cosmic cycle ldquoThe universal exchange

for fire is in one sense a fact of human experience we see all sorts of things go up in

flameshellip but the generation of all things from firehellip is a pure requirement of theory and

devoid of empirical supportrdquo (Kahn 1979 150)

21 Plutarch has lsquoπυρὸς τ᾽ ανταμείβεσθαι πάντα hellip lsquoκαὶ πῦρ απάντων 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 ldquobut the periods of these cycles are not the same the

one that they call lsquosatietyrsquo is longer than the one they call lsquocravingrsquordquo (Diels 65) Young

Plutarch ends his discussion by defining the proportionate lengths of these ldquoas three is to one

so is the relation of the period of orderly disposition to that of fiery destructionrdquo 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 ldquofaterdquo The elemental fire carries within itself the tendency

toward change and thus pursuing the way down it enters the ldquostriferdquo 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 ldquodestinyrdquo ldquoforcerdquo ldquonecessityrdquo ldquojusticerdquo or when exhibited in definite forms of

time and matter as ldquointelligencerdquo [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 Heraclitusrsquo 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 Ammoniusrsquo 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 lsquopresentrsquo and lsquoabsentrsquordquo

The authority for this quotation is Plutarch himself and whether it should be interpreted as an

accurate citation of Heraclitus or Plutarchrsquos own summary of a longer statement we cannot

say The detail ldquoyou cannot step twice into the same riverrdquo is even more contentious22 As I

discuss in section 18 some assert that this is no more than a loose paraphrase of ldquoas they step

into the same rivers other and still other waters flow upon themrdquo (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 Plutarchrsquos Heraclitean simile with one of his own

Ammonius then takes Young Plutarchrsquos imagery of the seed and turns it to his own

advantage by describing the transformation of the seed as its ldquodeathrdquo and the transformation

into the embryo as a ldquobirthrdquo whence it is but a short step to another fragment a description of

the cosmic cycle ldquofor as Heraclitus said lsquothe death of fire is birth for air and the death of air

is birth for waterrsquordquo (Diels 76) with the afterthought ldquoand it is clearer still in ourselvesrdquo

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 Meta1010a10-15 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 Plutarchrsquos version appears to be derived from Aristotle and Plato

95

I discuss the Greek for these fragments in the notes to section 18 it suffices here to

note that ldquomortal substancerdquo 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 lives23

Ammonius discussion leads up to the introduction of a god who ldquobeing one has with one

now filled foreverrdquo 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 Flaceliegravere (1941 89 fn 111) comments


grande part drsquoexageacuteration Cf Ricard dans sa note agrave ce passage [1884 60 -61] laquo

Les vicissitudes que nous eacuteprouvons dans nos gouts nos affections nos sentiments

et mecircme dans les traits de notre figure ne deacutetruisent ni lrsquouniteacute de notre individu ni

la reacutealiteacute de notre existence propre et individuelle raquo

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 ldquoelse 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 thingsrdquo

In the second The Life of Theseus (231) explores the meaning when the idea is applied to an

inanimate object ndash in this case the thirty-oared galley on which Theseus returned to Greece from

Crete Whittaker (1969 190) provides a similar example in Senecarsquos letter to Lucius On Being (58

22) calling the theme of the ages of man ldquoevidently a Middle Platonic commonplacerdquo

96

ndash seasonality and periodicity starting with the cycle of human generations the sunrsquos 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 10800 years

My purpose in this brief discussion was to demonstrate that citations from Heraclitus

played a role in Plutarchrsquos 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 ndash 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 manrsquos life Furthermore Plutarch prefaces each of these

quotations with ldquoas Heraclitus saidrdquo 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

Plutarchrsquos 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 Plutarchrsquos use of Heraclitus in the Pythian Dialogues or

even in the whole Moralia could lead to fascinating insights

Nevertheless Ammonius has not reconciled Young Plutarchrsquos (and Heraclitusrsquo) notion

of circularity with his own (and Heraclitusrsquo) 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 ldquoall thingsrdquo or a thing

97

that encompasses all things but not fire itself (Russellrsquos and the Liarrsquos 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 Heraclitusrsquo 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 ldquothe lightning steers all thingsrdquo 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-orderrdquo

Fink saw in the fragment ldquoThe lightning steers all thingsrdquo 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 ndash 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 catrsquos fur and silk They also knew of

the magical properties of amber Indeed in lightning we see another instantiation of

Heraclitusrsquo fragment ldquothe hidden connection is more powerful than the visiblerdquo 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 Seacutevigneacute (1626-1696)

In De E the transition from section 7 to section 8 contains an intriguing crux We have

reached the end of Eustrophusrsquo exposition on the E and are moving into Young Plutarchrsquos

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 ldquoNothing in excessrdquo just as soon as I became part of the Academy

Section 8 Then I said that Eustrophusrsquo explanation had most gracefully resolved the

difficulty with Number ldquoForrdquo I continuedhellip

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 ldquoIrdquo Plutarch the narrator is commenting on young Plutarchrsquos 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 ldquoIrdquo 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 (ldquousrdquo) 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 ldquosearching for an explanation of the unexplainablerdquo and that the dialogue

provides an engaging portrayal of the way in which a philosopher reacts when ldquoforced

unwillingly to face the unknowablerdquo 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 Plutarchrsquos 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 ldquoaboutrdquo1

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 ldquoNothing in excessrdquo just

as soon as he became part of the Academy

[Section 8] Then Young Plutarch said that Eustrophusrsquo explanation had most

gracefully resolved the difficulty with Number ldquoForrdquo he continued hellip

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 ldquous

ldquowith ldquothose presentrdquo 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 ndash the visits of Nero (1 385 C)

and Livia ldquothe wife of Caesarrdquo (3 386 A) ndash 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 ldquopresentrdquo where

Plutarch is writing to his friend Sarapion the second occurred ldquojust recentlyrdquo and involves

two of Plutarchrsquos 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 Flaceliegraverersquos 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 Flaceliegravere in his discussion of this

passage (7 413 C-D) recounts the contretemps with the Cynic Planetiades and comments

Mais il y a lagrave un proceacutedeacute litteacuteraire un kunstgriff [artifice] comme dit Wilamowitz

que nous avons deacutejagrave signaleacute agrave propos de Theacuteon personnage du De Pyth Plutarque

se substituant par moments lui-mecircme agrave son personnage comme par inadvertance et

sans preacutevenir le lecteur (Flaceliegravere 1974 86-87)

Leaving aside for the moment Flaceliegraverersquos reference to Theon this dialogue De def begins as

did De E ndash 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 ldquowerdquo joined their company and sat amongst them The careful

reader (or an adept at reading and decoding detective stories) will notice that the word ldquowerdquo

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 ldquoIrdquo attempts to calm Planetiades The narrative then

continues with ldquowhatever I had said worked he [Planetiades] turned and went out the door

without another wordrdquo (ἐγὼ μὲν οὖν ταῦτ᾽ εἰπὼν τοσοῦτο διεπραξάμην ὅσον απελθεῖν διὰ

θυρῶν σιωπῇ τὸν Πλανητιάδην) Section 8 continues the narrative with ldquoIt became quiet for a

momentrdquo (ἡσυχίας δὲ γενομένης ἐπ᾽ ὀλίγον) and Ammonius ldquoaddressing himself to merdquo (ἐμὲ

προσαγορεύσας) in direct speech said ldquoSee what it is that you are doing Lampriashelliprdquo Thus

Lamprias is revealed as the narrator

Aside from that incongruous ldquowerdquo until this moment we have probably surmised that

Plutarch himself is the narrator Flaceliegravere bases his opinion on the narratorrsquos 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-mecircme agrave son personnage) The wandering ldquoIrdquo 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 ndash first that Lampriasrsquo self reported comments were not effective

and that Planetiadesrsquo 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

Flaceliegravere refers us to Ulrich von Wilamowitzrsquos Der Glaube der Hellenen where

Wilamowitz too in precisely this passage identifies Plutarchrsquos tendency to blur the

boundaries between the narratorrsquos thoughts and words and those of his characters2 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 Plutarchrsquos 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 III3 In that

document written in Latin he again describes the phenomenon of Plutarchrsquos 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 (ie his charactersrsquo 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 deacutejagrave signaleacute agrave

propos de Theacuteon) Flaceliegravere 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 ldquoourrdquo administration speaks as if he were Plutarch

Flaceliegravere repeats almost word for word what he had said earlier about Plutarch and Lamprias

in De def

Cependant il nrsquoest pas impossible que lrsquoon doive identifier malgreacute tout ce Theacuteon agrave

lrsquoami de Plutarque agrave condition drsquoadmettre que Plutarque a utiliseacute ici comme

ailleurs ce singulier proceacutedeacute litteacuteraire par lequel comme par inadvertance et sans en

preacutevenir le lecteur il se substitue soudain lui-mecircme agrave lrsquoun des personnages qursquoil met

en scegravene (Flaceliegravere 1974 43)

Flaceliegravere 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 ldquosaid Diogenianusrdquo and ldquoTheon repliedrdquo and he turns into a participant

by using the pronoun ldquowerdquo ndash ldquowe urged him onhellip ldquowe accepted thisrdquo and so on Again

Plutarch is not listed amongst the dramatis personae so Flaceliegravere 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 (ldquowerdquo) conflates the narrator with a

character in the dialogue

Finally Frieda Klotz (2011) describes how Plutarch recounts autobiographical

details4

4 See Freida Klotz ldquoImagining the past Plutarchrsquos Play with timerdquo eds Frieda Klotz and

Katerina Oikonomopoulou The philosopherrsquos banquet Plutarchs Table Talk in the Intellectual

Culture of the Roman Empire (Oxford Oxford University Press 2011) and ldquoPortraits of the

106

He shuffles his youth and development into an unexpected a-chronological structure

and although he beginshellip 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 Diotima5 Klotzrsquos 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 ldquoGod isrdquo 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 authorrsquos 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 Ammoniusrsquo argument on the

difference between Being and Becoming Every mortal being is always in the process of

ldquocoming-into-beingrsquo so that we get instantiations such as Young Plutarch and his older self

This is a fine illustration of the implications of Ammoniusrsquo assertion

Philosopher Plutarchrsquos Self-Presentation in the lsquoQuaestiones Convivalesrsquordquo Classical Quarterly 57

(2007) 650-67

5 See Daniel Babut ldquoPeinture et deacutepassement de la reacutealiteacute dans le Banquet de Platonrdquo Revue des

Eacutetudes Anciennes 82 (1980) 5-29

107

Other examples where Plutarch inserts himself in the dialogue occur in De E at the

points where one speaker hands over to another6 where the transition is usually accomplished

through an intervention from the narrator In section 2 Plutarch gives a summary of

Ammoniusrsquo analysis of Apollorsquos 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 interruption7

Section 4 except for the last sentence is entirely in indirect discourse8

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 ldquomy friend Theon whom you knowrdquo 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 ndash 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 ldquoit was I think Eustrophus the

Athenianrdquo (Εὔστροφον Ἀθηναῖον οἶμαι) Both the hesitation contained in ldquoI thinkrdquo 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 ldquoIrdquo 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 ldquoNothing in excessrdquo

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 ο τῶν αριθμητικῶν καὶ ο τῶν μαθηματικῶν ἐγκωμίων

τοῦ Ε λόγος ὡς ἐγὼ μέμνημαι πέρας ἔσχεν

Section 17 ο δ᾽ Ἀμμώνιος ἅτε δη 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 endhellip

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

Ammoniusrsquo state of mind which can be interpreted also as an aside to Sarapion Thus the

109

referent of the ldquoIrdquo is Plutarch the letter writer and the sentence beginning section 17 is an

authorial intervention describing Ammoniusrsquo 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 Plutarchrsquos

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 Plutarchrsquos 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 ldquopresentrdquo of the letter to Sarapion and

the implied future of return gifts from him the ldquorecentrdquo encounter between Plutarch and his

sons and the recollections of the mature Plutarch on the ldquopastrdquo 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 dialoguersquos

first word στιχίδιον announces and describes the dialoguersquos 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 Flaceliegravere Wilamowitz and Klotz have commented on Plutarchrsquos

modes of speech and narration in the dialogues Their textual analyses suggest Plutarchrsquos skill

and sophistication but do not venture far into a literary analysis Only Klotz comments on the

fluid nature of time in much of Plutarchrsquos 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 characterrsquos 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 other9 In direct discourse a writer speaks in the person

of another assimilating his style to that persons 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

Lucianrsquos 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 (ldquoPerson lsquoPersonarsquo and Representation in Apuleiusrsquos Metamorphosesrdquo Materiali e

Discussioni per LrsquoAnalisi dei Testi Classici (25 [1990] 129-64) explores the distinction between the

historical author and his (or her) fictional persona using Lucianrsquos Metamorphoses See also Tim

Whitmarsh ldquoAn I for an I reading fictional autobiographyrdquo in The Authorrsquos Voice in Classical and

Late Antiquity by Anna Marmodoro and Jonathan Hill Oxford 2013

111

same end that we discovered when reading De E Lairdrsquos 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 Apuleiuss

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 ndash 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 ndash a

synthesis of two voices character and narrator which respectively epitomise our

two modes namely narrative and discourse The quotation of the characters words

is the property of narrative the expression of the narratorrsquos current sentiment is the

property of discourse

The ldquoexpression of the narratorrsquos current sentimentrdquo in De E is contained in those

parenthetical remarks that I have described as being directed to Sarapion to whom Plutarchrsquos

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 Plutarchrsquos dialogues as ldquofictionrdquo nor would they unhesitatingly call them

ldquodiscoursesrdquo 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 narrators

112

consciousness to the characterrsquos consciousness10 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 Plutarchrsquos 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 ldquoIt is a

truth universally acknowledged that a single man in possession of a good fortune must be in

want of a wiferdquo (Pride and Prejudice 1813) Austen has defined the clause ldquothat a single man

in possessionhelliprdquo as a ldquotruerdquo statement (ldquoa truth universally acknowledgedrdquo) even as she

undermines it by subordinating it The truncated statement ldquoa single man in possession of a

good fortune must be in want of a wiferdquo 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 laquo Le style indirect

libre et la moderniteacute raquo in Langages 73 (1984) 7-16 Norman Friedman has associated Socrates

three styles of poetry with modern telling and showingrdquo and Paul Hernadi explores the dual roles

of literature as representation (mimesis) and presentation (narration)

113

romance11 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 ldquouniversallyrdquo 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 Flaubertrsquos 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) ldquoElle deacuteclarait adorer les

enfants crsquoeacutetait sa consolation sa joie sa folie et elle accompagnait ses caresses

drsquoexpansions lyriques qui agrave drsquoautres qursquoagrave des Yonvillais eussent rappeleacute la Sachette de

Notre-Damerdquo As Ullmann tells us ldquoGrammatically lsquocrsquoeacutetait sa consolation sa joie sa folie

might be the authors 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 truthrdquo (Ullman 109) We know that it

cannot be the narrator who tells us that Emmas 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 ndash a devoted mother Ullmann does not quote the last part of the sentence where it is

not Emma who speaks but the narrator ldquoqui agrave drsquoautres qursquoagrave des Yonvillais eussent rappeleacute la

11 Laird cites this sentence saying ldquomoralizing such as we find in Jane Austen is discourse not

narrativerdquo (Laird ldquoPerson Personardquo 136)

114

Sachette de Notre-Damerdquo 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 (ie 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 Heideggerrsquos 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 Ammoniusrsquo 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 ldquoParticipantrdquo 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 μελετα

το πᾶν ldquoΙn care take the whole as a wholerdquo Another word that comes from him is

this φυσεως καταγορια Hinting at making nature visible

Heideggerrsquos concept of a philosophical dialogue could be Plutarchrsquos or Ammoniusrsquo The

approach to truth and true understanding proceeds through stages of conversation thinking

and learning

Plutarchrsquos 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

Ormdashif this will not serve their turnmdashsince all

Numbers are odd or even and they fall

First into five women may take us all

mdash ldquoThe Primroserdquo John Donne (1572-1631)

The word ldquotetractysrdquo 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 Plutarchrsquos 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 tetractys1 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

ldquothe rather disorderly and uncritical accounts in the few Hellenistic sources left to usrdquo leave those

questions unanswered These sources are Nicomachus of Gerasa Theology of Arithmetic (surviving

fragments in Photius Bibliothegraveque [cod 187] 40-48) Anatolius On the Decad and Iamblichus

Theology of Arithmetic (See ldquoMathematical Esotericism Some Perspectives on Renaissance

Arithmologyrdquo In Hermes in the Academy By Wouter J Hanegraaf and Joce Pijnenburg (eds)

Amsterdam University Press 2009 Pp 75-89

117

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 Hollandrsquos 1603 translation of

De Is where he transliterates the word and yokes it to its Latin translation ldquothat famous

quaternarie [of the Pythagoreans] named Tetractysrdquo In the same passage Babbitt contents

himself with ldquothe so-called sacred quaternionrdquo Perhaps through inadvertence Holland uses

quaternerie for tetractys in De an procr where tetractys again appears2 The notion of

ldquofournessrdquo comes through in lsquoquarternaryrsquo 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 ldquofourrdquo or a ldquoset of fourrdquo Figure 1 illustrates the notion of fourness in the tetractys and

its identification with the decad (and the universe) as the ldquofour is the tenrdquo 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 αριθμητικης

2 OED sv ldquotetractysrdquo 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 readerrsquos 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 ldquoThose who understand what Tetractysm

was to the Pythagoreans will comprehend what Triadism was to Baxterrdquo Baxterrsquos Nachleben also

includes several spots on YouTube See ldquoThe Signs amp Causes of Depression - Puritan Richard

Baxterrdquo httpswwwyoutubecomwatchv=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 Waterfieldrsquos translation of Iamblichusrsquo 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 Gerasa3 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 (fl100)

Plutarch (c 50-c 120) Anatolius of Alexandria (fl 269) Iamblichus (245 ndash c 325) Aetius (391-454)

On these dates it is not impossible that Plutarch knew of Nichomachusrsquo work but these dates may not

119

to Waterfieldrsquos translation quotes Aetius who relates Pythagorasrsquo description of numbers as

ldquothe first principlesrdquo and their interrelations as ldquoharmoniesrdquo (Waterfield 1988 9) Today we

might call such harmonies ldquothe structure of the number systemrdquo 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 ldquoarithmeticrdquo As to the coining of the

word ldquoarithmologyrdquo he adds4

It is found for the first time to my knowledge in a fragment of Codex Atheniensis

of the eighteenth centuryhellip Under the title Aριθμολγία ηθιχή (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 ldquoGod manifests in the mathematical laws that govern everything and the

understanding of these laws and simply doing mathematics could bring one closer to Godrdquo

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 Pythagorasrsquo 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 ndash too late to know Plutarch or for Plutarch to

know of him

4 My translation Delatte gives the reference for the codex (Bibliothegraveque 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 ldquoWhat you suppose is four is really ten and

a perfect triangle and our oath5 The word ldquotetractysrdquo 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 ldquofournessrdquo6

Plutarch wrote De an Procr (14 1027 E 1019 A-B) to help his teenage sons

understand Platorsquos 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 Eacutetudes sur la Litteacuterature Pythagoricienne (Paris Librairie ancienne Honoreacute

Champion 1915) 249-268

6Thirty-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 ErdősndashWoods 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)

Platorsquos Lambda (Timaeus 35b-c) can be presented as a type of tetractys one that still

displays ldquofournessrdquo but where numbers replace counters7

1

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 Platorsquos 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 Platorsquos 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 1218) sum to 36 as do the

three apexes of the triangle (1 8 27) Waterfield remarks that this diagram ldquonow contains all

the factors of 36 which as our author [Plato in Timaeus] says sum to 55rdquo 9 As we see in

section 10 this tetractys provides a calculator for analysing musical harmony

1

2 3

4 6 9

8 12 18 27

Figure 3 The ldquofilled inrdquo 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 ldquomarriagerdquo 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 ldquonestrdquo 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 six10

10 This figure corresponds to Critchlowrsquos 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 ldquoThe Cabalist Friar of Venice Francesco Giorgirdquo in Yates (1979 33-42)

124

6

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 Critchlowrsquos figures while staying true to the methods of the Pythagoreans I

give below a diagram of ldquonestedrdquo 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 Critchlowrsquos numbers

At the apex of the pyramid is the monad or 20middot30 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

table11 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 numbers12

he family resemblance between this table Pascalrsquos 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 ldquoI swear by the one who has bestowed the tetractys

the source of eternal nature upon coming generations and into our soulsrdquo 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 ndash 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

126

adolescence maturity and old age13 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 Plutarchrsquos

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 ldquoright

numbersrdquo 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 25middot33 24middot34 and 23middot35 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 Platorsquos number (5040)

13 See Theon of Smyrna Mathematics useful for understanding Plato translated from the 1892

GreekFrench edition of J Dupuis by Robert and Deborah Lawlor (San Diego Wizards Bookshelf

1979)

127

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 ldquowitchesrsquo

brew of erudition and speculationrdquo (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 manrsquos life and explaining that fifty-four is the sum of ldquothe first number the first two

plane surfaces two squares and two cubesrdquo we know that we are in Pythagorean territory

These are the seven numbers in Platorsquos Lambda The interested reader can check that the

lifespans of crows stags vigorous men ravens phoenixes and hamadryads all the beings in

Hesiodrsquos riddle appear in figure 5

The Great Year comes every 10800 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 10800 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=10800) 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 10800 years (Censorinus De Die

Natali 1811)

The careful reader will have noticed that 10800 does not appear in figure 5 although both 108

and 432 do (both factors of 10800) 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 = 10800

108 x 100 = 108 x 4 x 25 = 10800

Similarly to calculate Platorsquos 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 5040 has many beguiling properties one of which is its appearance in Srinivas

Ramanujanrsquos list of highly composite numbers and it is indeed a ldquosuperior highly composite

numberrdquo14

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 ldquoWriting 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 moderationrdquo (Platorsquos 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 Plutarchrsquos

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

Platorsquos Utopia 5040 is the best number of citizens in a city because it is highly

divisible (Laws 771c)

130

BIBLIOGRAPHY

EDITIONS AND TRANSLATIONS OF PLUTARCHrsquoS ldquoMORALIArdquo

This list includes both complete collections of the Moralia and editions of selected essays

that include De E Other selections without De E appear in the Select Bibliography below

For example Philemon Hollandrsquos 1603 translation of the complete works appears here but

not the reprint Plutarchs ldquoMoraliardquo Twenty Essays

Amyot Jacques Oeuvres morales et mesleacutees de Plutarque Paris Chez Barthelemy Maceacute au

mont S Hilaire agrave lEscu de Bretaigne 1572

Babbitt F C ed and trans ldquoThe E at Delphirdquo in Plutarchrsquos Moralia in Sixteen Volumes

Loeb Classical Library Vol 5 London and Cambridge Mass Harvard University

Press 1927-2004

Bernardakis G N ed and trans Plutarchi Chaeronensi Vol 3 Leipzig Teubner 1894

Bernardakis Panagiotes D and Henricus Gerardus Ingenkamp eds Plutarchi Chaeronensis

Moralia recognovit Gregorius N Bernardakis Editionem Maiorem Vols 1-7

Athens Academy of Athens 2008-2013

Dryden John ed Plutarchs Morals Translated from the Greek by several hands London

1684-94

Ducas Demetrios ed Plutarch Moralia Venice Aldus Manutius and Andreas Torresanus

1509

Estienne Henri [Henricus Stephanus] Plutarchi Chaeronensis Ethica sive Moralia Opera

Geneva 1572

131

Flaceliegravere Robert ed and trans Plutarque sur lrsquoE de Delphes Paris Les Belles Lettres

1941

mdashmdashmdash ed and trans Plutarque œuvres morales Dialogues Pythiques Vol 4 Paris Les

Belles Lettres 1974

Goodwin W W ed and trans Plutarchs Morals Translated from the Greek by several

hands with an Introduction by Ralph Waldo Emerson 5 vols Cambridge Little

Brown and Company 1878

Holland Philemon trans Plutarch The Philosophy Commonly Called the Morals 1603

Revised Corrected and Printed by George Sawbridge at the Sign of the Bible on

Ludgate-Hill 1657

Ildefonse Freacutedeacuterique trans Dialogues Pythiques Paris Flammarion 2006

Obsieger Hendrik De E apud Delphos Uumlber das Epsilon am Apolltempel in Delphi

Einfuumlhrung Ausgabe und Kommentar Stuttgart Franz Steiner Verlag 2013

Paton W R ed Plutarchi Pythici dialogi tres Berlin Weidmann 1893

Plutarchrsquos Moralia in Sixteen Volumes LCL with an English translation London and

Cambridge MA Harvard University Press 1927-2004

Plutarchi Moralia recensuerent et emendaverunt W Nachstaumldt W Sieveking and

J B Titchener Leipsig Teubner 1985

Prickard A O trans Selected Essays of Plutarch Vol 2 Oxford Clarendon 1918

Ricard Dominique trans Oeuvres morales de Plutarque Paris Lefegravevre 1844

Stephanus Henricus See Estienne Henri

Wyttenbach Daniel ed and trans Plutarchi Chaeronensis Moralia id est opera exceptis

vitis reliqua Graeca emendavit notationem emendationem et Latinam Xylandri

interpretationem castigatam subiunxit animadversiones explicandis rebus ac verbis

item indices copiosos adiecit D Wyttenbach Editio nova annotatione et indice aucta

tomi II pars II Leipzig 1828 (Reprinted in eight volumes in 1962 by Georg Olms

Verlag Hildesheim The last two volumes contain the Greek lexicon)

132

SELECT BIBILIOGRAPHY

This list is not a complete record of all the works and sources I have consulted It includes

most references found in the commentary and in the introductory material and appendices A

few references on topics that are of only passing interest for the dialogue appear with full

bibliographic information in the introductory material and appendices

Aalders G J D ldquoPolitical Thought in Plutarchs lsquoConvivium Septum Sapientiumrsquordquo

Mnemosyne 30 1 (1977) 28-39

Acerbi F ldquoOn the Shoulders of Hipparchus A Reappraisal of Ancient Greek

Combinatoricsrdquo Archive for History of Exact Sciences 57 (September 2003) 465-502

Ademollo Francesco The Cratylus of Plato A Commentary Cambridge Cambridge

University Press 2011

Afonasin E V John M Dillon and John F Finamore eds Iamblichus and the Foundations

of Late Platonism Leiden Boston Brill 2012

Alcock Susan E John F Cherry and Jas Elsner eds Pausanias travel and memory in

Roman Greece New York Oxford University Press 2001

Amandry Pierre La Mantique Apollinienne agrave Delphes Essai sur le fonctionnement de

lOracle Paris Arno Press 1950

Aulotte Robert Amyot et Plutarque La Tradition des ldquoMoraliardquo au XVIe siegravecle Genegraveve

Librairie Droz 1965

Babut Daniel ldquoPlutarque et le Stoiumlcismerdquo Paris Presses universitaires de France 1969

mdashmdashmdash ldquoPeinture et deacutepassement de la reacutealiteacute dans le Banquet de Platonrdquo Revue des Eacutetudes

Anciennes 82 (1980) 5-29

mdashmdashmdashBabut Daniel ldquoLa composition des Dialogues pythiques de Plutarque et le problegraveme

de leur uniteacuterdquo Journal des savants 2 (1992) 187-234

Balmer Josephine Piecing Together the Fragments Translating Classical Verse Creating

Contemporary Poetry Oxford Oxford University Press 2013

133

Barker Andrew ldquoEarly Timaeus Commentaries and Hellenistic Musicologyrdquo Bulletin of the

Institute of Classical Studies 46 (2003) 73-87

mdashmdashmdash The Science of Harmonics in Classical Greece Cambridge Cambridge University

Press 2007

Barrow R H Plutarch and his Times London Chatto and Windus 1967

Bastide Georges and Victor Goldschmidt ldquoLe paradigme dans la dialectique platoniciennerdquo

Revue des Eacutetudes Anciennes 50 (1948) 371

Baxter Timothy M S The Cratylus Platorsquos Critique of Naming Leiden New York Koumlln

Brill 1992

Stanford William Bedell Ambiguity in Greek Literature Studies in Theory and Practice

Oxford Basil Blackwell 1939

Berman K and L A Losada ldquoThe mysterious E at Delphi a solutionrdquo Z Papyrologie

Epigraphik 17 (1975) 115

Betz O ldquoConsiderations on the Real and the Symbolic Value of Goldrdquo In Prehistoric Gold

in Europe eds G Morteani and J P Northover 19-30 NATO ASI (Series E Applied

Sciences) vol 280 Dordrecht Springer 1995

Betz H D and Edgar W Smith Jr ldquoContributions to the Corpus Hellenisticum Novi

Testamenti Plutarch lsquoDe E apud Delphosrsquordquo Novum Testamentum 13 (1971) 217-

235

Boucheacute-Leclercq Auguste ldquoLe fonctionnement de lrsquooracle de Delphesrdquo Annales de lrsquoEacutecole

des Hautes Eacutetudes de Gand II (1938) 82-84

mdashmdashmdash Histoire de la Divination dans LAntiquiteacute 4 vols Paris Ernest Leroux 1879-1892

Bowie Ewen ldquoPlutarchrsquos Habits of Citation Aspects of Differencerdquo in The Unity of

Plutarchrsquos Work lsquoMoraliarsquo Themes in the lsquoLives Features of the Lives in the

Moralia ed Anastasios G Nikolaidis 143-158 Berlin New York Walter de

Gruyter 2008

mdashmdashmdash ldquoSage and Emperor Plutarch and Literary Activity in Achaea AD 107-117rdquo in

Plutarch Greek Intellectuals and Roman Power in the Time of Trajan eds

134

Philip A Stadter and L Van der Stockt 98-117 Leuven Leuven University Press

2002

Boyanceacute P ldquoNote sur la Teacutetractysrdquo Lantiquiteacute classique 20 (1951) 421-425

mdashmdashmdash ldquoSur la vie pythagoriciennerdquo Revue des Eacutetudes Grecques 52 (1939) 36-50

Brenk Frederick E In Mist Apparelled Religious Themes in Plutarchs Moralia Leiden

Brill 1997

mdashmdashmdash ldquoPlutarchrsquos Middle-Platonic God about to enter (or remake) the Academyrdquo in Gott

Und Die Gotter Bei Plutarch ed Rainer Hirsch Luipold 27-50 New York Berlin

Walter de Gruyter 2005

Brouillette Xavier and Angelo Giavatto Les Dialogues Platoniciens chez Plutarque

Strateacutegies et Meacutethodes Exeacutegeacutetiques Leuven Leuven University Press Ancient and

Medieval Philosophy ndash Series 1 43 2010-2011

Brouillette Xavier La Philosophie Delphique de Plutarque Lrsquoitineacuteraire des Dialogues

pythiques Paris Les Belles Lettres 2014

Brumbaugh Robert S Platorsquos Mathematical Imagination Bloomington Indiana University

Press 1977

Burkert Walter Lore and Science in Ancient Pythagoreanism trans Edwin L Minar Jr

Cambridge Mass Harvard University Press 1972

Burnet John Early Greek Philosophy 4th ed London A and C Black 1930

Chappell M ldquoDelphi and the Homeric Hymn to Apollordquo Classical Quarterly 56 (2006) 331-

348

Cherniss H ldquoThe Characteristics and Effects of Presocratic Philosophyrdquo JHI 2 (I951) 319-

355

mdashmdashmdash ldquoThe Sources of Evil according to Platordquo Proc Am Phil Soc 98 (1954) 23-30

Chlup Radek ldquoPlutarchs Dualism and the Delphic Cultrdquo Phronesis 45 (2000) 138-158

Dalimier C Platon-Cratyle traduction ineacutedite introduction notes bibliographie et index

Paris Flammarion 1998

135

De Falco V ed Iamblichus Theologoumena Arithmeticae additions and corrections by

U Klein Stuttgart Teubner 1975

mdashmdashmdash Iamblichus Theologoumena Arithmeticae Leipzig Teubner 1922

De Wet B X ldquoPlutarchrsquos Use of the Poetsrdquo Acta Classica 31 (1988) 13-25

Delatte Armand Eacutetudes sur la litteacuterature pythagoricienne Geneva Slatkine 1974

Des Places Eacutedouard ldquoChronique de la philosophie religieuse des Grecs (1987-1991)rdquo

Bulletin de lAssociation Guillaume Budeacute Lettres dhumaniteacute 50 (1991) 414-429

Di Benedetto V 1990 ldquoAt the Origins of Greek Grammarrdquo Glotta 68 1 (1990) 19-39

Dillon John ldquoPlutarch and Platonist Orthodoxyrdquo Illinois Classical studies 13 (1988)

357-364

mdashmdashmdash ldquoPlutarch and God Theodicy and Cosmogony in the Thought of Plutarchrdquo in

Traditions of Theology Studies in Hellenistic Theology Its Background and

Aftermath ed Dorothea Frede and Andreacute Laks Leiden Boston Cologne Brill 2002

Dobson Marcia ldquoHerodotus 1471 and the Hymn to Hermes A Solution to the Test

Oraclerdquo AJP 100 (1979) 349-359

DOoge Martin Luther trans Nicomachus of Gerasa Introduction to Arithmetic Ann Arbor

University of Michigan Humanistic Series 16 London Macmillan 1926

Edmonds Radcliffe G III Redefining Ancient Orphism A Study in Greek Religion

Cambridge Cambridge University Press 2013

Einarson B and P de Lacy ldquoThe Manuscript Tradition of Plutarchrsquos Moralia 548A-612Brdquo

Classical Philology 46 (1951) 93-110

Empson William Seven Types of Ambiguity 2nd ed London Chatto and Windus 1949

Fairbanks Arthur ldquoHerodotus and the Oracle at Delphirdquo Classical Journal 1 (1906) 37-48

mdashmdashmdash ldquoOn Plutarchs Quotations from the Early Greek Philosophersrdquo TAPA 28 (1897)

75-87

Ficino Marsilio All Things Natural Ficino on Platos Timaeus trans Arthur Farndell

London Shepheard-Walwyn 2010

136

Flaceliegravere R ldquoPlutarque et la Pythierdquo Revue Des Eacutetudes Grecques 56 264265 (1943)

72-111

Fontenrose J The Delphic Oracle its responses and operations Berkeley University of

California Press 1978

Forshaw Peter J ldquoOratorium - Auditorium - Laboratorium Early Modern Improvisations on

Cabala Music and Alchemyrdquo Aries 10 (2010) 169-195

Fraumlnkel Hermann ldquoA Thought Pattern in Heraclitusrdquo AJP 59 (1938) 309-337

Franklin J C ldquoHarmony in Greek and Indo-Iranian Cosmologyrdquo Journal of Indo-European

Studies 30 (2002) 1-25

Frede Dorothea and Andreacute Laks eds Traditions of Theology Studies in Hellenistic theology

its Background and Aftermath Leiden Boston Koumlln Brill 2002

Freeman Kathleen Ancilla to the Pre-Socratic Philosophers Oxford Harvard University

Press 1957

Gee Emma Aratus and the Astronomical Tradition Oxford Oxford University Press 2013

Gerber Douglas E A Companion to the Greek Lyric Poets Leiden New York Koumlln Brill

1997

mdashmdashmdash Greek Iambic Poetry from the seventh to the fifth centuries BC Cambridge Mass

Harvard University Press 1999

Goldin Owen ldquoHeraclitean Satiety and Aristotelian Actualityrdquo The Monist 74 (1991) 568-

578

Goldschmidt Victor Le paradigme dans la dialectique platonicienne Paris Presses

Universitaires de France 1947

Grant Hardy ldquoMathematics and the Liberal Artsrdquo The College Mathematics Journal 30

(1999) 96-105

Gregory T E ldquoJulian and the last oracle at Delphirdquo GRBS 24 (1983) 355

Griffiths J Gwyn ldquoThe Delphic E A New Approachrdquo Hermes 83 (1955) 237-245

Guillon Pierre La Beacuteotie antique Paris Les Belles Lettres 1948

137

Gummere Richard M trans Seneca Ad Lucilium Epistulae Morales 3 vols Cambridge

Mass Harvard University Press London William Heinemann Ltd 1917-1925

Hadzsits George Depue Prolegomena to a Study of the Ethical Ideal of Plutarch and of the

Greeks of the First Century A D Cincinnati Ohio University of Cincinnati Press

1906

Hardie Alex ldquoPindarrsquos lsquoTheban Cosmogonyrsquo (The First Hymn)rdquo Bulletin of the Institute of

Classical Studies 44 (2000) 19-41

Heath Thomas History of Greek Mathematics 2 vols Oxford Clarendon 1921

mdashmdashmdash A Manual of Greek Mathematics Oxford Oxford University Press 1931 (Reprinted

by Dover New York 1968)

Heidegger Martin and Eugen Fink Heraclitus Seminar trans Charles H Seibert Evanston

Illinois Northwestern University Press 1993

Hershbell Jackson P ldquoPlutarch and Heraclitusrdquo Hermes 2 (1977) 179-201

Hodge A T ldquoThe mystery of Apollorsquos E at Delphirdquo AJA 8 (1981) 83-84

Holden H A ldquoPlutarchs Moraliardquo Classical Review 4 (1890) 306-07

Holland Philemon Trans Plutarchs ldquoMoraliardquo Twenty Essays London J M Dent amp

Sons 1911

Hunt A S and C C Edgar trans Private Documents Vol 1 of Select Papyri ed

Jeffrey Henderson Cambridge MA Harvard University Press 1932

Huxley George ldquoPetronian Numbersrdquo Greek Roman and Byzantine Studies 91 (Spring

1968) 55

Ilievski Petar ldquoThe Origin and Semantic Development of the Term Harmonyrdquo Illinois

Classical Studies18 (1993) 19-29

Imhoof-Blumer Friedrich and Percy Gardner lsquolsquoNumismatic Commentary on Pausaniasrdquo

Journal of Hellenic Studies 6 (1885) 50ndash 101 7 (1886) 57ndash 113 8 (1887) 6ndash 63)

Isenberg Meyer William ldquoThe Unity of Platos Philebusrdquo Classical Philology 35 (1940)

154-179

138

Jones C P ldquoPlutarchs Moraliardquo GampB 15 (1968) 130-146

mdashmdashmdash ldquoPausanias and His Guidesrdquo in Pausanias travel and memory in Roman Greece 33-

39 Edited by Susan E Alcock John F Cherry and Jas Elsner New York Oxford


Jones Roger Miller The Platonism of Plutarch with an introduction by Leonardo Taraacuten

New York Garland Publications 1980

Kahane Jean-Pierre ldquoBernoulli convolutions and self-similar measures after Erdős A

personal hors doeuvrerdquo Notices of the American Mathematical Society 62 (2015)

136ndash140

Kahn Charles H ldquoA New Look at Heraclitusrdquo American Philosophical Quarterly 1 (1964)

189-203

mdashmdashmdash ldquoThe Greek verb lsquoto bersquo and the concept of beingrdquo Foundations of Language 2

(1966) 245-65

mdashmdashmdash The art and thought of Heraclitus an edition of the fragments with translation and

commentary Cambridge Cambridge University Press 1979

Kerenyi Karol Dionysos archetypal image of indestructible life Translated by Ralph

Manheim Princeton Princeton University Press 1976

Kingsley Peter In the Dark Places of Wisdom Inverness California The Golden Sufi

Centre 1999

Kirk G S ldquoNatural Change in Heraclitusrdquo Mind 60 237 (1951) 35-42

mdashmdashmdash Heraclitus The Cosmic Fragments Cambridge Cambridge University Press 1962

Korab-Karpowicz W Julian The Presocratics in the Thought of Martin Heidegger

New York Peter Lang 2017

Kouremenos Theokritos ldquoThe tradition of the Delian problem and its origins in the Platonic

corpusrdquo Trends in Classics 3 (2011) 341ndash364

Krappe Alexander H ldquoAΠOΛΛΩN KΥKNOΣrdquo Classical Philology 37 (1942) 353-370

139

Kurke Leslie ldquoAncient Greek Board Games and How to Play Themrdquo Classical Philology 94

(1999) 247-67

Laird Person Persona

Lamberton Robert Plutarch New Haven and London Yale University Press 2001

Lanzillotta L R ldquoPlutarch at the Crossroads of Religion and Philosophyrdquo in Plutarch in the

Religious and Philosophical Discourse of Late Antiquity edited by Lautaro Roig

Lanzillotta and Israel Muntildeoz Gallarte 1-21 Leiden Boston Brill 2012

Lawlor Robert and Deborah Lawlor Theon of Smyrna Mathematics useful for understanding

Plato translated from the 1892 GreekFrench edition of J Dupuis San Diego

Wizards Bookshelf 1979

Lernould Alain ldquoPlutarque sur lrsquoE de Delphes 390 B 6-8 et lrsquoexplication de la vision de

lsquoTimeacuteersquo 45 B-Drdquo Methodos 5 (2005) 1-19

mdashmdashmdash ldquoPlutarque E de Delphes 387 d 2-9 Une interpreacutetation philosophique de leacutepisode de

lenlegravevement du treacutepied par Heacuteraclegraves une erreur de jeunesserdquo Revue des Eacutetudes

Grecques 113 (2000) 147-171

Losada L A and K Morgan ldquoThe E at Delphi Again Reply to A T Hodgerdquo AJA 85

(1984) 115-117

Lowry S Todd ldquoThe Archaeology of the Circulation Concept in Economic Theoryrdquo Journal

of the History of Ideas 35 (1974) 429-444

Marcovich M Heraclitus Greek Text with a Short Commentary Merida Venezuela Los

Andes University Press 1967

mdashmdashmdash ldquoA New Poem of Archilochus lsquoP Colonrsquo inv 7511rdquo GRBS 16 (1975) 5ndash14

Martin Hubert Jr ldquolsquoAmatoriusrsquo 756 E-F Plutarchs Citation of Parmenides and Hesiodrdquo

AJP 90 (1969) 183-200

Mates Benson ldquoDiodorean Implicationrdquo The Philosophical Review 58 (1949) 234-242

Mates Benson ldquoStoic Logic and the Text of Sextus Empiricusrdquo AJP (1949) 290-298

140

Mathiesen Thomas J Apollos lyre Greek music and music theory in antiquity and the

Middle Ages Lincoln NE and London University of Nebraska Press 1999

Mathieu J M ldquoTrois notes sur le traiteacute De EI apud Delphos de Plutarque (384E 391F-393A

393D-Erdquo Kentron 7 (1991)

McClain Ernest G ldquoA new look at Platorsquos Timaeusrdquo Music and Man 1 (2000) 341-360

McNamee Kathleen and Michael L Jacovides ldquoAnnotations to the Speech of the Muses

(Plato Republic 546B-C)rdquo Z Papyrologie Epigraphik 144 (2003) 31-50

Meeusen Michiel Caroline ldquoPlutarch and the Wonder of Nature Preliminaries to Plutarchrsquos

Science of Physical Problemsrdquo Apeiron 47 (2014) 310-341

Merkelbach R and M L West ldquoEin Archilochos-Papyrusrdquo Z Papyrologie Epigraphik 14

(1974) 97-113

Merker Anne La vision chez Platon et Aristote Sankt Augustin Academia Verlag 2003

Michael D Bailey Fearful Spirits Reasoned Follies The Boundaries of Superstition in Late

Medieval Europe Ithaca Cornell University Press 2013

Middleton J Henry ldquoThe Temple of Apollo at Delphirdquo Journal of Hellenic Studies 9 (1888)

282-322

Miller Dana R ldquoPlatorsquos Argument for the Plurality of Worlds in De Defectu Oraculorumrdquo

424c10-425e7rdquo Ancient Philosophy 17 (1997) 375-394

Mueller Ian ldquoStoic and Peripatetic Philosophyrdquo Archiv fuumlr Geschichte der Philosophie 51

(1969) 173-186

Muumlller Alexander ldquoDialogic structures and forms of knowledge in Plutarchrsquos lsquoThe E at

Delphirsquordquo Studies in History and Philosophy of Science Part A 43 (2012) 245-249

Naber S A ldquoObservationes Miscellaneae ad Plutarchi Moraliardquo Mnemosyne 28 (1900) 85-

117+129-156+329-364

Nordgren Lars Greek Interjections Syntax Semantics and Pragmatics Berlin Boston


141

ldquoNote on the Symposiacs and Some Other Dialogues of Plutarchrdquo Classical Review 32

(1918) 150-53

OBrien D ldquoDerived Light and Eclipses in the Fifth Centuryrdquo Journal of Hellenic Studies 88

(1968) 114-127

Oikonomides A N ldquoRecords of lsquoThe Commandments of the Seven Wise Menrsquo in the 3rd

century BCrdquo The Classical Bulletin 63 (1987) 67-76

Opsomer Jan Geert Roskam and Frances B Titchener eds A Versatile Gentleman

Consistency in Plutarchs Writing Leuven Leuven University Press 2016

mdashmdashmdash ldquoM Annius Ammonius A Philosophical Profilerdquo in The origins of the Platonic

system edited by M Bonazzi and J Opsomer 123-186 Louvain 2009

Palmer Richard E ldquoThe Postmodernity of Heideggerrdquo Boundary 2 4 ldquoMartin Heidegger and

Literaturerdquo (Winter 1976) 411-432

Parke H W and D E W Wormell The Delphic oracle 2 vols Oxford Blackwell 1956

Parker Robert ldquoThe Problem of the Greek Cult Epithetrdquo Opuscular Atheniensia 28 (2003)

174-183

Patrick G T W ed and trans The Fragments of the Work of Heraclitus of Ephesus on

Nature translated from the Greek text of Bywater Baltimore N Murray 1889

Pickard-Cambridge Arthur Wallace Sir Dithyramb Tragedy and Comedy Oxford

Clarendon Press 1927

Podlecki Anthony ldquoPlutarch and Athensrdquo Illinois Classical Studies 13 (1988) 231-43

Ramanujan S ldquoHighly Composite Numbersrdquo Proc London Math Soc 14 (1915) 347-409

mdashmdashmdash Collected Papers edited by G H Hardy P V S Aiyar and B M Wilson


Riginos Alice Swift Platonica The Anecdotes Concerning the Life and Writings of Plato

Leiden Brill 1976

Robbins F E ldquoThe Lot Oracle at Delphirdquo Classical Philology 11 (1916) 278-292

142

mdashmdashmdash ldquoPosidonius and the Sources of Pythagorean Arithmologyrdquo Classical Philology 15

(1920) 309-22

mdashmdashmdash ldquoThe Tradition of Greek Arithmologyrdquo Classical Philology 16 no 2 (1921) 97-123

Robert Louis ldquoDe Delphes a lOxus Inscriptions grecques nouvelles de la Bactrianerdquo CRAI

(1968) 442-454

Robin Leacuteon La Penseacutee Grecque Paris Editions Albin Michel 1963

mdashmdashmdash Platon Paris Presses Universitaires de France 1968

Robins R H ldquoDionysius Thrax and the Western Grammatical Traditionrdquo Transactions of the

Philological Society 56 (1957) 67-106

Rodier Georges Eacutetudes de philosophie grecque Paris Librarie philosophique J Vrin 1969

Roskam Geert Review of Plutarch De E apud Delphos Uumlber das Epsilon am Apolltempel

in Delphi by Henrik Obsieger Antiquiteacute Classique 84 (2015) 314-320

Roux Georges Delphes son oracle et ses dieux Paris Les Belles Lettres 1976

Russell D A ldquoOn Reading Plutarchs Livesrdquo Greece and Rome 13 (1966) 139-154

mdashmdashmdash ldquoOn Reading Plutarchs Moraliardquo Greece and Rome 15 (1968) 130-146

mdashmdashmdash Plutarch London Duckworth 1973

Sandbach F H ldquoRhythm and Authenticity in Plutarchs Moraliardquo Classical Quarterly 33

(1939) 194-203

mdashmdashmdash ldquoPlutarch and Aristotlerdquo ICS 7 (1982) 207-232

Sansone David ldquoOn Hendiadys in Greekrdquo Glotta 62 (1984)16-25

Sedley D N ldquoThe Etymologies in Platorsquos lsquoCratylusrsquordquo Journal of Hellenic Studies 118

(1998) 140-154

mdashmdashmdash Platorsquos Cratylus Cambridge Cambridge University Press 2003

Shilleto A R Plutarchs Morals ethical essays London George Bell and sons 1888

Sirinelli Jean Plutarque de Cheacuteroneacutee Un philosophe dans le siegravecle Paris Fayard 2000

143

Soissons Jean-Pierre Jacques Amyot (1513-1593) Chaintreux Eacuteditions France-Empire

Monde 2013

Sosiades ldquoCommandments of the Seven Wise Men (Stobaeus Anthologium 31173)rdquo in

Stobei Anthologium edited by Curt Wachsmuth and Otto Hense Vol 3 Berlin 1894

125ff

Soury D La deacutemonologie de Plutarque essai sur les ideacutees religieuses et les mythes dun

platonicien eacuteclectique Paris Belles Lettres 1942

Spitzer Leo ldquoClassical and Christian ideas of World Harmony Prolegomena to an

Interpretation of the Word lsquoStimmungrsquo Part Irdquo Traditio 2 (1944) 409-464



Stanley Richard P ldquoHipparchus Plutarch Schroumlder and Houghrdquo American Mathematical

Monthly 104 (1997) 344-350

Taraacuten Leonardo ldquoThe River-Fragments and their Implicationsrdquo Elenchos Rivista di Studi

Sul Pensiero Antico 20 (1999) 9-52

Tarrant D ldquoColloquialisms Semi-Proverbs and Word-Play in Platordquo Classical Quarterly 40

(1946) 109-117

mdashmdashmdash ldquoMore Colloquialisms Semi-Proverbs and Word-Play in Platordquo Classical Quarterly

ns 8 (1958) 158-160

mdashmdashmdash ldquoGreek Metaphors of Lightrdquo Classical Quarterly 10 (1960) 181-187

Tarrant Harold Platorsquos First Interpreters Ithaca New York Cornell University Press 2000

Taylor Thomas trans Iamblichus Life of Pythagoras or Pythagoric Life London

J M Watkins 1818

Thompson E A The Last Delphic Oracle Classical Quarterly 40 (1946) 35-36

Trivigno Franco V ldquoEtymology and the Power of Names in Platorsquos lsquoCratylusrsquorsquorsquo Ancient

Philosophy 32 (2012) 35-75

144

Van Den Hoek Annewies ldquoTechniques of Quotation in Clement of Alexandria A View of

Ancient Literary Working Methodsrdquo Vigiliae Christianae 50 (1996) 223-243

Van Sickle John ldquoThe Doctored Text Translating a New Fragment of Archilochusrdquo MLN

90 (1975) 872-85

Vlastos Gregory ldquoOn Heraclitusrdquo AJP 76 (1955) 337-368

Waterfield A H ldquoPlato Philebus 52 c1 ndash d1 Text and Meaningrdquo Rheinisches Museum fuumlr

Philologie Neue Folge 129 (1986) 358-360

Waterfield Robin trans The Theology of Arithmetic On the Mystical Mathematical and

Cosmological Symbolism of the First Ten Numbers Attributed to Iamblichus

Foreword by Keith Critchlow Grand Rapids MI Phanes Press 1988

Waterfield Robin ldquoEmendations of Iamblichus Theologoumena Arithmeticae (De Falco)rdquo

Classical Quarterly 38 (1988) 215-227

Webster T B L ldquoPersonification as a Mode of Greek Thoughtrdquo Journal of the Warburg and

Courtauld Institutes 17 (1954) 10-21

West M L ldquoArchilochus Ludens Epilogue of the Other Editorrdquo Z Papyrologie Epigraphik

16 (1975) 217-19

mdashmdashmdash Ancient Greek music Oxford Clarendon Press 1994

mdashmdashmdash ldquoThe Eternal Triangle Reflections on the Curious Cosmology of Petron of Himerardquo

in Apodosis Essays Presented to Dr W W Cruickshank to Mark His Eightieth

Birthday (London St Paulrsquos School) 1992 105-110

Wiggins D ldquoHeraclitusrsquo Conceptions of Flux Fire and Material Persistencerdquo in Language

and Logos Studies in Ancient Greek philosophy Presented to G E L Owen eds M

Schofield and M Nussbaum 1-32 Cambridge Cambridge University Press 1982

Whittaker John ldquoAmmonius on the Delphic Erdquo Classical Quarterly 19 (1969) 185-192

mdashmdashmdash ldquoPlutarch Plato and Christianityrdquo in Neoplatonism and Early Christian Thought

Essays in Honour of AH Armstrong ed A H Armstrong H J Blumenthal and

R A Markus 50-63 Ann Arbor Variorum Publications 1981

145

mdashmdashmdash ldquoThe lsquoEternityrsquo of the Platonic Formsrdquo Phronesis 13 (1968) 131-144

Wilberding James ldquoEternity in Ancient Philosophyrdquo in Eternity ed Y Melamed 14-55

Oxford Oxford University Press 2016

Wright George T ldquoHendiadys and Hamletrdquo PMLA 96 (1981) 168-193

Yates Frances The Occult Philosophy in the Elizabethan Age London Routledge 1979

Zuntz G ldquoNotes on Plutarchrsquos Moraliardquo Rheinisches Museum fuumlr Philologie Neue Folge 96

Bd 3 (1953) 232-235

UNIVERSITY OF CALGARY

Plutarchrsquos De E apud Delphos Translation and Commentary

by


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

copy Judith Anne Alexander 2018

ii

ABSTRACT




the Delphian god







iii

PREFACE









iv

ACKNOWLEDGMENTS

















v

DEDICATION



vi

TABLE OF CONTENTS

ABSTRACTii

PREFACEiii

ACKNOWLEDGMENTSiv

DEDICATIONhellipv

TABLE OF CONTENTSvi

LIST OF FIGURESvii


EPIGRAPH1

INTRODUCTION2









vii

LIST OF FIGURES







viii




















Teubner 1889







1903-5


1945

ix









De exil = De exilio




De mus = De musica














1

EPIGRAPH









2

INTRODUCTION
















on religious themes




3
























4

























5






close to Chaeronea

















6








English and French





















7



Giroux 2000 xxii)






















8























verse

9


discussion to come





















10













is in German










11

























12







with the same model
















13
























14


















than the letter






15





meaning of the E












16

TRANSLATION





















17

























(sections 13-16)

18







others8













one of theserdquo



19













powerful men










20













sanctuaryrdquo21













21







questions




















22









of all propositions











truth




23

















charming







24


























25










overpowered














26


























27



























28






















29















SECTION 12 (390 B)










30



fiverdquo78




















31
























pedigreerdquo


32












ownrdquo87











as in the other



33










speaker
















34
























(Timaeus 27 D)

35








really exists
















36


common mould103























37








Beingrdquo





Hence he is











38


genesis










uncorruptedrdquo














39












towards destruction











rightly spoke of

40


















41








5 396 F and 18 402 F






















42
































43

































mystegravere

44































45































46































47





























ἔργον 7397 E)



48































49

































50































examples



51































52











1976 145 Kouremenous 2011 349)




















53




















by Krappe 1942 354)














54
































55









finger)





irony

















56

















tens













57





mother of the sun

























58
































59

































60

































61








1994 218)


















harmonic theory







62















20-31)


















(Barker 2007 55)

63

































64













describes this as





















65



in De anima (27-11)


















Lattimore)












66































67






















even and odd











68


Philebus






























69




are by this episode














Fowler










templerdquo







70































71


















Simonides 193)














72
































73




































74







existencerdquo
























circumstances


75
































76































77
































78
































79





158-9)


























80

















(De def 31 426 F)


















81






















82






(Diels 104)




















83












sense in Heraclitus













84


























85
























86

























in Nature 94 (1914) 455

87



























88






















89


seem to have been16

















fragments










90

























91























92


exchange21












reflect the idea










93







law and order

















speak




94


























95


























96
























97










physics
















98







Phaethon

99
























100
























101


























102






















revealed



103























caused

104


















connotations




499)


105



in De def

















details4




106














narration of De E








(2007) 650-67



107
























here


108
























the discussion



109
























110

























111


























112

























113























114


























115












and learning










116


























117













Pythagorean lore












118





1 +2+3 +4 = 10




numbers are 3 6 10 15 21 28 36










119
























know of him


198a sq

120





















Champion 1915) 249-268



121



pursued here)



1

2 3

4 9

8 27















122



cube








1

2 3

4 6 9

8 12 18 27








123






















124

6

12 18

24 36 54

48 72 108 162






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







125








unmistakable














126





















1979)

127






















Natali 1811)



128





432 x 25 = 432 x 5 x 5 = 10800

108 x 100 = 108 x 4 x 25 = 10800



Figure 5 5040 = 7 x 5 x 144



numberrdquo14













129





Erdős







130

BIBLIOGRAPHY










Press 1927-2004






1684-94


1509


Geneva 1572

131


1941


Belles Lettres 1974






Ludgate-Hill 1657


















132







Mnemosyne 30 1 (1977) 28-39












Librairie Droz 1965



Anciennes 82 (1980) 5-29





133




Press 2007





Brill 1992










235







Gruyter 2008



134


2002




Brill 1997










Press 1977





348


355





135










357-364















75-87



136


72-111







Studies 30 (2002) 1-25




Press 1957



1997




578




(1999) 96-105




137





1906












Sons 1911




1968) 55






154-179

138









136ndash140


189-203


(1966) 245-65






Centre 1999








139


(1999) 247-67













Grecques 113 (2000) 147-171


(1984) 115-117







AJP 90 (1969) 183-200



140











(1974) 97-113





282-322




(1969) 173-186




117+129-156+329-364



141


(1918) 150-53


(1968) 114-127











174-183










Leiden Brill 1976


142


(1920) 309-22



(1968) 442-454













(1939) 194-203




(1998) 140-154




143


Monde 2013



125ff








Monthly 104 (1997) 344-350




(1946) 109-117


ns 8 (1958) 158-160




J M Watkins 1818



Philosophy 32 (2012) 35-75

144




90 (1975) 872-85












16 (1975) 217-19












145







Bd 3 (1953) 232-235

ii

ABSTRACT




the Delphian god







iii

PREFACE









iv

ACKNOWLEDGMENTS

















v

DEDICATION



vi

TABLE OF CONTENTS

ABSTRACTii

PREFACEiii

ACKNOWLEDGMENTSiv

DEDICATIONhellipv

TABLE OF CONTENTSvi

LIST OF FIGURESvii


EPIGRAPH1

INTRODUCTION2









vii

LIST OF FIGURES







viii




















Teubner 1889







1903-5


1945

ix









De exil = De exilio




De mus = De musica














1

EPIGRAPH









2

INTRODUCTION
















on religious themes




3
























4

























5






close to Chaeronea

















6








English and French





















7



Giroux 2000 xxii)






















8























verse

9


discussion to come





















10













is in German










11

























12







with the same model
















13
























14


















than the letter






15





meaning of the E












16

TRANSLATION





















17

























(sections 13-16)

18







others8













one of theserdquo



19













powerful men










20













sanctuaryrdquo21













21







questions




















22









of all propositions











truth




23

















charming







24


























25










overpowered














26


























27



























28






















29















SECTION 12 (390 B)










30



fiverdquo78




















31
























pedigreerdquo


32












ownrdquo87











as in the other



33










speaker
















34
























(Timaeus 27 D)

35








really exists
















36


common mould103























37








Beingrdquo





Hence he is











38


genesis










uncorruptedrdquo














39












towards destruction











rightly spoke of

40


















41








5 396 F and 18 402 F






















42
































43

































mystegravere

44































45































46































47





























ἔργον 7397 E)



48































49

































50































examples



51































52











1976 145 Kouremenous 2011 349)




















53




















by Krappe 1942 354)














54
































55









finger)





irony

















56

















tens













57





mother of the sun

























58
































59

































60

































61








1994 218)


















harmonic theory







62















20-31)


















(Barker 2007 55)

63

































64













describes this as





















65



in De anima (27-11)


















Lattimore)












66































67






















even and odd











68


Philebus






























69




are by this episode














Fowler










templerdquo







70































71


















Simonides 193)














72
































73




































74







existencerdquo
























circumstances


75
































76































77
































78
































79





158-9)


























80

















(De def 31 426 F)


















81






















82






(Diels 104)




















83












sense in Heraclitus













84


























85
























86

























in Nature 94 (1914) 455

87



























88






















89


seem to have been16

















fragments










90

























91























92


exchange21












reflect the idea










93







law and order

















speak




94


























95


























96
























97










physics
















98







Phaethon

99
























100
























101


























102






















revealed



103























caused

104


















connotations




499)


105



in De def

















details4




106














narration of De E








(2007) 650-67



107
























here


108
























the discussion



109
























110

























111


























112

























113























114


























115












and learning










116


























117













Pythagorean lore












118





1 +2+3 +4 = 10




numbers are 3 6 10 15 21 28 36










119
























know of him


198a sq

120





















Champion 1915) 249-268



121



pursued here)



1

2 3

4 9

8 27















122



cube








1

2 3

4 6 9

8 12 18 27








123






















124

6

12 18

24 36 54

48 72 108 162






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







125








unmistakable














126





















1979)

127






















Natali 1811)



128





432 x 25 = 432 x 5 x 5 = 10800

108 x 100 = 108 x 4 x 25 = 10800



Figure 5 5040 = 7 x 5 x 144



numberrdquo14













129





Erdős







130

BIBLIOGRAPHY










Press 1927-2004






1684-94


1509


Geneva 1572

131


1941


Belles Lettres 1974






Ludgate-Hill 1657


















132







Mnemosyne 30 1 (1977) 28-39












Librairie Droz 1965



Anciennes 82 (1980) 5-29





133




Press 2007





Brill 1992










235







Gruyter 2008



134


2002




Brill 1997










Press 1977





348


355





135










357-364















75-87



136


72-111







Studies 30 (2002) 1-25




Press 1957



1997




578




(1999) 96-105




137





1906












Sons 1911




1968) 55






154-179

138









136ndash140


189-203


(1966) 245-65






Centre 1999








139


(1999) 247-67













Grecques 113 (2000) 147-171


(1984) 115-117







AJP 90 (1969) 183-200



140











(1974) 97-113





282-322




(1969) 173-186




117+129-156+329-364



141


(1918) 150-53


(1968) 114-127











174-183










Leiden Brill 1976


142


(1920) 309-22



(1968) 442-454













(1939) 194-203




(1998) 140-154




143


Monde 2013



125ff








Monthly 104 (1997) 344-350




(1946) 109-117


ns 8 (1958) 158-160




J M Watkins 1818



Philosophy 32 (2012) 35-75

144




90 (1975) 872-85












16 (1975) 217-19












145







Bd 3 (1953) 232-235

iii

PREFACE









iv

ACKNOWLEDGMENTS

















v

DEDICATION



vi

TABLE OF CONTENTS

ABSTRACTii

PREFACEiii

ACKNOWLEDGMENTSiv

DEDICATIONhellipv

TABLE OF CONTENTSvi

LIST OF FIGURESvii


EPIGRAPH1

INTRODUCTION2









vii

LIST OF FIGURES







viii




















Teubner 1889







1903-5


1945

ix









De exil = De exilio




De mus = De musica














1

EPIGRAPH









2

INTRODUCTION
















on religious themes




3
























4

























5






close to Chaeronea

















6








English and French





















7



Giroux 2000 xxii)






















8























verse

9


discussion to come





















10













is in German










11

























12







with the same model
















13
























14


















than the letter






15





meaning of the E












16

TRANSLATION





















17

























(sections 13-16)

18







others8













one of theserdquo



19













powerful men










20













sanctuaryrdquo21













21







questions




















22









of all propositions











truth




23

















charming







24


























25










overpowered














26


























27



























28






















29















SECTION 12 (390 B)










30



fiverdquo78




















31
























pedigreerdquo


32












ownrdquo87











as in the other



33










speaker
















34
























(Timaeus 27 D)

35








really exists
















36


common mould103























37








Beingrdquo





Hence he is











38


genesis










uncorruptedrdquo














39












towards destruction











rightly spoke of

40


















41








5 396 F and 18 402 F






















42
































43

































mystegravere

44































45































46































47





























ἔργον 7397 E)



48































49

































50































examples



51































52











1976 145 Kouremenous 2011 349)




















53




















by Krappe 1942 354)














54
































55









finger)





irony

















56

















tens













57





mother of the sun

























58
































59

































60

































61








1994 218)


















harmonic theory







62















20-31)


















(Barker 2007 55)

63

































64













describes this as





















65



in De anima (27-11)


















Lattimore)












66































67






















even and odd











68


Philebus






























69




are by this episode














Fowler










templerdquo







70































71


















Simonides 193)














72
































73




































74







existencerdquo
























circumstances


75
































76































77
































78
































79





158-9)


























80

















(De def 31 426 F)


















81






















82






(Diels 104)




















83












sense in Heraclitus













84


























85
























86

























in Nature 94 (1914) 455

87



























88






















89


seem to have been16

















fragments










90

























91























92


exchange21












reflect the idea










93







law and order

















speak




94


























95


























96
























97










physics
















98







Phaethon

99
























100
























101


























102






















revealed



103























caused

104


















connotations




499)


105



in De def

















details4




106














narration of De E








(2007) 650-67



107
























here


108
























the discussion



109
























110

























111


























112

























113























114


























115












and learning










116


























117













Pythagorean lore












118





1 +2+3 +4 = 10




numbers are 3 6 10 15 21 28 36










119
























know of him


198a sq

120





















Champion 1915) 249-268



121



pursued here)



1

2 3

4 9

8 27















122



cube








1

2 3

4 6 9

8 12 18 27








123






















124

6

12 18

24 36 54

48 72 108 162






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







125








unmistakable














126





















1979)

127






















Natali 1811)



128





432 x 25 = 432 x 5 x 5 = 10800

108 x 100 = 108 x 4 x 25 = 10800



Figure 5 5040 = 7 x 5 x 144



numberrdquo14













129





Erdős







130

BIBLIOGRAPHY










Press 1927-2004






1684-94


1509


Geneva 1572

131


1941


Belles Lettres 1974






Ludgate-Hill 1657


















132







Mnemosyne 30 1 (1977) 28-39












Librairie Droz 1965



Anciennes 82 (1980) 5-29





133




Press 2007





Brill 1992










235







Gruyter 2008



134


2002




Brill 1997










Press 1977





348


355





135










357-364















75-87



136


72-111







Studies 30 (2002) 1-25




Press 1957



1997




578




(1999) 96-105




137





1906












Sons 1911




1968) 55






154-179

138









136ndash140


189-203


(1966) 245-65






Centre 1999








139


(1999) 247-67













Grecques 113 (2000) 147-171


(1984) 115-117







AJP 90 (1969) 183-200



140











(1974) 97-113





282-322




(1969) 173-186




117+129-156+329-364



141


(1918) 150-53


(1968) 114-127











174-183










Leiden Brill 1976


142


(1920) 309-22



(1968) 442-454













(1939) 194-203




(1998) 140-154




143


Monde 2013



125ff








Monthly 104 (1997) 344-350




(1946) 109-117


ns 8 (1958) 158-160




J M Watkins 1818



Philosophy 32 (2012) 35-75

144




90 (1975) 872-85












16 (1975) 217-19












145







Bd 3 (1953) 232-235

iv

ACKNOWLEDGMENTS

















v

DEDICATION



vi

TABLE OF CONTENTS

ABSTRACTii

PREFACEiii

ACKNOWLEDGMENTSiv

DEDICATIONhellipv

TABLE OF CONTENTSvi

LIST OF FIGURESvii


EPIGRAPH1

INTRODUCTION2









vii

LIST OF FIGURES







viii




















Teubner 1889







1903-5


1945

ix









De exil = De exilio




De mus = De musica














1

EPIGRAPH









2

INTRODUCTION
















on religious themes




3
























4

























5






close to Chaeronea

















6








English and French





















7



Giroux 2000 xxii)






















8























verse

9


discussion to come





















10













is in German










11

























12







with the same model
















13
























14


















than the letter






15





meaning of the E












16

TRANSLATION





















17

























(sections 13-16)

18







others8













one of theserdquo



19













powerful men










20













sanctuaryrdquo21













21







questions




















22









of all propositions











truth




23

















charming







24


























25










overpowered














26


























27



























28






















29















SECTION 12 (390 B)










30



fiverdquo78




















31
























pedigreerdquo


32












ownrdquo87











as in the other



33










speaker
















34
























(Timaeus 27 D)

35








really exists
















36


common mould103























37








Beingrdquo





Hence he is











38


genesis










uncorruptedrdquo














39












towards destruction











rightly spoke of

40


















41








5 396 F and 18 402 F






















42
































43

































mystegravere

44































45































46































47





























ἔργον 7397 E)



48































49

































50































examples



51































52











1976 145 Kouremenous 2011 349)




















53




















by Krappe 1942 354)














54
































55









finger)





irony

















56

















tens













57





mother of the sun

























58
































59

































60

































61








1994 218)


















harmonic theory







62















20-31)


















(Barker 2007 55)

63

































64













describes this as





















65



in De anima (27-11)


















Lattimore)












66































67






















even and odd











68


Philebus






























69




are by this episode














Fowler










templerdquo







70































71


















Simonides 193)














72
































73




































74







existencerdquo
























circumstances


75
































76































77
































78
































79





158-9)


























80

















(De def 31 426 F)


















81






















82






(Diels 104)




















83












sense in Heraclitus













84


























85
























86

























in Nature 94 (1914) 455

87



























88






















89


seem to have been16

















fragments










90

























91























92


exchange21












reflect the idea










93







law and order

















speak




94


























95


























96
























97










physics
















98







Phaethon

99
























100
























101


























102






















revealed



103























caused

104


















connotations




499)


105



in De def

















details4




106














narration of De E








(2007) 650-67



107
























here


108
























the discussion



109
























110

























111


























112

























113























114


























115












and learning










116


























117













Pythagorean lore












118





1 +2+3 +4 = 10




numbers are 3 6 10 15 21 28 36










119
























know of him


198a sq

120





















Champion 1915) 249-268



121



pursued here)



1

2 3

4 9

8 27















122



cube








1

2 3

4 6 9

8 12 18 27








123






















124

6

12 18

24 36 54

48 72 108 162






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







125








unmistakable














126





















1979)

127






















Natali 1811)



128





432 x 25 = 432 x 5 x 5 = 10800

108 x 100 = 108 x 4 x 25 = 10800



Figure 5 5040 = 7 x 5 x 144



numberrdquo14













129





Erdős







130

BIBLIOGRAPHY










Press 1927-2004






1684-94


1509


Geneva 1572

131


1941


Belles Lettres 1974






Ludgate-Hill 1657


















132







Mnemosyne 30 1 (1977) 28-39












Librairie Droz 1965



Anciennes 82 (1980) 5-29





133




Press 2007





Brill 1992










235







Gruyter 2008



134


2002




Brill 1997










Press 1977





348


355





135










357-364















75-87



136


72-111







Studies 30 (2002) 1-25




Press 1957



1997




578




(1999) 96-105




137





1906












Sons 1911




1968) 55






154-179

138









136ndash140


189-203


(1966) 245-65






Centre 1999








139


(1999) 247-67













Grecques 113 (2000) 147-171


(1984) 115-117







AJP 90 (1969) 183-200



140











(1974) 97-113





282-322




(1969) 173-186




117+129-156+329-364



141


(1918) 150-53


(1968) 114-127











174-183










Leiden Brill 1976


142


(1920) 309-22



(1968) 442-454













(1939) 194-203




(1998) 140-154




143


Monde 2013



125ff








Monthly 104 (1997) 344-350




(1946) 109-117


ns 8 (1958) 158-160




J M Watkins 1818



Philosophy 32 (2012) 35-75

144




90 (1975) 872-85












16 (1975) 217-19












145







Bd 3 (1953) 232-235

v

DEDICATION



vi

TABLE OF CONTENTS

ABSTRACTii

PREFACEiii

ACKNOWLEDGMENTSiv

DEDICATIONhellipv

TABLE OF CONTENTSvi

LIST OF FIGURESvii


EPIGRAPH1

INTRODUCTION2









vii

LIST OF FIGURES







viii




















Teubner 1889







1903-5


1945

ix









De exil = De exilio




De mus = De musica














1

EPIGRAPH









2

INTRODUCTION
















on religious themes




3
























4

























5






close to Chaeronea

















6








English and French





















7



Giroux 2000 xxii)






















8























verse

9


discussion to come





















10













is in German










11

























12







with the same model
















13
























14


















than the letter






15





meaning of the E












16

TRANSLATION





















17

























(sections 13-16)

18







others8













one of theserdquo



19













powerful men










20













sanctuaryrdquo21













21







questions




















22









of all propositions











truth




23

















charming







24


























25










overpowered














26


























27



























28






















29















SECTION 12 (390 B)










30



fiverdquo78




















31
























pedigreerdquo


32












ownrdquo87











as in the other



33










speaker
















34
























(Timaeus 27 D)

35








really exists
















36


common mould103























37








Beingrdquo





Hence he is











38


genesis










uncorruptedrdquo














39












towards destruction











rightly spoke of

40


















41








5 396 F and 18 402 F






















42
































43

































mystegravere

44































45































46































47





























ἔργον 7397 E)



48































49

































50































examples



51































52











1976 145 Kouremenous 2011 349)




















53




















by Krappe 1942 354)














54
































55









finger)





irony

















56

















tens













57





mother of the sun

























58
































59

































60

































61








1994 218)


















harmonic theory







62















20-31)


















(Barker 2007 55)

63

































64













describes this as





















65



in De anima (27-11)


















Lattimore)












66































67






















even and odd











68


Philebus






























69




are by this episode














Fowler










templerdquo







70































71


















Simonides 193)














72
































73




































74







existencerdquo
























circumstances


75
































76































77
































78
































79





158-9)


























80

















(De def 31 426 F)


















81






















82






(Diels 104)




















83












sense in Heraclitus













84


























85
























86

























in Nature 94 (1914) 455

87



























88






















89


seem to have been16

















fragments










90

























91























92


exchange21












reflect the idea










93







law and order

















speak




94


























95


























96
























97










physics
















98







Phaethon

99
























100
























101


























102






















revealed



103























caused

104


















connotations




499)


105



in De def

















details4




106














narration of De E








(2007) 650-67



107
























here


108
























the discussion



109
























110

























111


























112

























113























114


























115












and learning










116


























117













Pythagorean lore












118





1 +2+3 +4 = 10




numbers are 3 6 10 15 21 28 36










119
























know of him


198a sq

120





















Champion 1915) 249-268



121



pursued here)



1

2 3

4 9

8 27















122



cube








1

2 3

4 6 9

8 12 18 27








123






















124

6

12 18

24 36 54

48 72 108 162






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







125








unmistakable














126





















1979)

127






















Natali 1811)



128





432 x 25 = 432 x 5 x 5 = 10800

108 x 100 = 108 x 4 x 25 = 10800



Figure 5 5040 = 7 x 5 x 144



numberrdquo14













129





Erdős







130

BIBLIOGRAPHY










Press 1927-2004






1684-94


1509


Geneva 1572

131


1941


Belles Lettres 1974






Ludgate-Hill 1657


















132







Mnemosyne 30 1 (1977) 28-39












Librairie Droz 1965



Anciennes 82 (1980) 5-29





133




Press 2007





Brill 1992










235







Gruyter 2008



134


2002




Brill 1997










Press 1977





348


355





135










357-364















75-87



136


72-111







Studies 30 (2002) 1-25




Press 1957



1997




578




(1999) 96-105




137





1906












Sons 1911




1968) 55






154-179

138









136ndash140


189-203


(1966) 245-65






Centre 1999








139


(1999) 247-67













Grecques 113 (2000) 147-171


(1984) 115-117







AJP 90 (1969) 183-200



140











(1974) 97-113





282-322




(1969) 173-186




117+129-156+329-364



141


(1918) 150-53


(1968) 114-127











174-183










Leiden Brill 1976


142


(1920) 309-22



(1968) 442-454













(1939) 194-203




(1998) 140-154




143


Monde 2013



125ff








Monthly 104 (1997) 344-350




(1946) 109-117


ns 8 (1958) 158-160




J M Watkins 1818



Philosophy 32 (2012) 35-75

144




90 (1975) 872-85












16 (1975) 217-19












145







Bd 3 (1953) 232-235