Kennedy MSPD FrontMat

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e Musical Structure

of Platos DialoguesJ. B. Kennedy

ACUMEN


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J. B. Kennedy 2011

is book is copyright under the Berne Convention.

No reproduction without permission.All rights reserved.

First published in 2011 by Acumen

Acumen Publishing Limited4 Saddler Street

DurhamDH1 3NP

www.acumenpublishing.co.uk

: 978-1-84465-266-2 (hardcover)

: 978-1-84465-267-9 (paperback)

British Library Cataloguing-in-Publication DataA catalogue record for this book is available

from the British Library.

Printed and bound in the UK by Berforts Group Limited


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For Louise Crascall


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But, friend, when you grasp the number and nature of the intervals ofsound, from high to low, and the boundaries of those intervals, and howmany scales arise from them, which those who came before handed downto us, their followers, to call harmonies, and when you grasp the variousqualities inhering in the motions of the body, which they said must bemeasured with numbers and named rhythm and metre, and when you

apprehend that every One and Many should be so investigated, when youhave grasped all of that, then you are wise Plato (Phlb., 17c11e1)

Nothing is so characteristic of the Pythagorean philosophy as symbolism(to symbolikon), a kind of teaching which mixes speech and silence asin mystery rites what they signify is immediately lucid and clear forthose who are accustomed to it, but dark and meaningless to the inexpe-rienced with the Pythagorean symbols what seems to be armed isreally being concealed, and what seems to be concealed is discerned bythe mind. Plutarch (in Stobaeus iii.i.199 [Wachsmuth & Hense])

Our discussion will be adequate if it has as much clearness as the subject-

matter admits of, for precision is not to be sought for in equal degree inall arguments it is the mark of an educated mind to look for precisionin each kind just so far as the nature of the subject admits; it is evidentlyequally foolish to accept probable reasoning from a mathematician andto demand demonstrative proofs from a rhetorician

Aristotle (Eth. Nic. 1094b11. [aer Ross])

Les anciens philosophes avoient une double doctrine; lune externe, pub-lique ou exotrique; lautre interne, secrete ou sotrique. La premieresenseignoit ouvertement tout le monde, la seconde toit reserve pourun petit nombre de disciples choisis Ce qui a fait prendre le changeaux anciens & aux modernes sur le but de la double doctrine, & leura fait imaginer quelle ntoit quun artice pour conserver la gloire dessciences & de ceux qui en faisoient profession, a t lopinion gnraleque les fables des dieux & des hros avoient t inventes par les sagesde la premiere antiquit, pour dguiser & cacher des vrits naturelles &morales Diderot and DAlembert (Encyclopdie ou Dictionnaire

raisonn des sciences, des arts et des mtiers)


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Contents

Preface xii

Abbreviations xvii

1. e nature and history of philosophical allegory 1

1.1 Rehabilitating ancient ways of reading 2

1.2 Allegory, Socrates and Plato 5

1.3 Symbols, reserve and Pythagoreanism 91.4 Persecution and the politics of allegory in classical Athens 12

1.5 Plato and Pythagoreanism: two puzzles 14

1.6 e allegorical Plato in history 18

1.7 Methodological precedent: early Christianity 23

1.8 Methodological precedent: Renaissance Platonism 25

2. Introducing the dialogues musical structure 29

2.1 Structuring a dialogue 31

2.2 Ancient Greek music: three key ideas 32

2.3 Platos symbolic scheme 36

2.4 Harmony and consonance, disharmony and dissonance 37

2.5 Sevenths and mixture 382.6 Guide to the strongest evidence 40

2.7 Methodology for line-counting 45

2.8 Canons of criticism 46

2.9 Responses to possible objections 48


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3. Independent lines of evidence 52

3.1 Simple, objective measurements 52

3.2 Parallel passages at the same relative location 54

3.3 Ranges of positive and negative concepts 56

3.4 Preview of the musical structure in the Republic 57

3.5 A control: falsiability and the pseudo-Platonica 59

4. An emphatic pattern in the Symposiums frame 61

4.1 A theory of music 62

4.2 Recurring clusters of features in the frame 63

4.3 A new kind of commentary 64

5. Making the Symposiums musical structure explicit 78

5.1 Phaedrus 78

5.2 Pausanias 84

5.3 Eryximachus 96

5.4 Aristophanes 104

5.5 Agathon 116

5.6 Socrates and Diotima 126

5.7 Alcibiades 154

6. Parallel structure in the Euthyphro 178

6.1 e same scale and the same symbolic scheme 1786.2 Guide to the strongest evidence 179

6.3 e sevenths 180

6.4 e connection to music 181

6.5 Another kind of evidence: parallels between dialogues 183

6.6 e Euthyphro is not aporetic 184

6.7 Marking the notes 185

7. Extracting doctrine from structure 236

7.1 Aristotle on virtues and means 236

7.2 Stichometry and the divided line 238

7.3 Reading the dialogues in parallel 240

7.4 e logic of the argument and its consequences 241

8. Some implications 244

8.1 Summary of the case 244

8.2 Interpreting the dialogues 245

8.3 Problems with anonymity and intentionality 246


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8.4 Interpreting Plato, Pythagoras and Socrates 247

8.5 History of music and mathematics 249

8.6 History of literature and literary theory 251

8.7 Ancient book production, papyrology, textual studies 251

8.8 e forward path 252

1: More musicological background 253

2: Neo-Pythagoreans, the twelve-note scale and themonochord 260

3: Markers between the major notes 265

4: e central notes 271

5: Systematic theory of the marking passages 274

6: Structure in Agathon and Socrates speeches 287

7: Euripides and line-counting 288

8: Data from the Republic 291

9: OCT line numbers for the musical notes 294

Notes 297

Bibliography 309

Index 315


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Preface

e following arguments and evidence for the musical structure of Platos dia-logues were rened and strengthened in lectures for classicists at the University ofManchester, University College London, the University of Leeds and the Classi-cal Association Conference at Durham University. ey amplify many times overthe grounds for the conclusions rst reported in my Platos Forms, PythagoreanMathematics, and Stichometry (2010), and I am grateful to Acumen for bringingthis book out promptly in response to the debate they occasioned.

At a time when the study of the humanities in universities is endangered, thisdebate has brought an extraordinary degree of attention to classics and ancientphilosophy. e scholars and journalists who discussed this research in newspa-pers, broadcasts and online forums throughout the world have reminded many ofthe living importance of ancient Greek philosophy and literature.

ese ndings open up new lines of research, many more than can be pursuedby any one scholar, and it may take time to assess their implications. As my titleindicates, this book has a limited aim. It is a study of the musical structure in twodialogues, prefaced by some general and historical evidence.

However tantalizing, there are two reasons for proceeding in this way. First,Platos musical symbols are repeated at regular intervals through the text of eachdialogue and so can be studied rigorously and objectively. Claims can be veriedrst by making comparisons within a dialogue and then by showing that the samestructure recurs in dierent dialogues. Second, the study of the symbols with doc-trinal content depends on rst establishing that the dialogues have a stichometricand musical structure. us the musical symbols are prior both methodologicallyand logically.

Nonetheless, a glimpse of doctrine is aorded by Chapter 7, Extracting Doc-trine from Structure, which focuses on a single, ethical doctrine but shows gener-ally that stichometry will yield up revisionist insights into Platos philosophy.


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PREFACE

is research has already stimulated new work and led to a number of collabo-rative projects. Given the nature and the magnitude of these ndings, however,scholars coming to these claims for the rst time will naturally and properly reactwith scepticism. Although it was common for some een hundred years to regardPlato as a symbolic writer and although Platos familiarity with Pythagorean numer-ology is well attested in his writings, modern scholars have uniformly denied thatPlatos dialogues are in any general way symbolical, allegorical or numerological.

Researchers in the history of science have, for a generation or so now, becomeaccustomed to the idea that the study of primitive pseudo-sciences is essential tounderstanding the growth of modern science. e births of astronomy, chemistryand mathematics are to be found in astrology, alchemy and numerology. Histori-ans of science have also become accustomed to stories of the neglect or marginali-

zation of the histories of these pseudo-sciences in earlier work. e discovery ofNewtons alchemical experiments and Pythagoreanism by Keynes and others is themost prominent case. Similar cases of neglect and rediscovery, more closely relatedto Platonism, are discussed below to establish certain methodological precedents.

is research grew out of a project on Greek mathematics, particularly on theconnections between Platos Republic and Euclids Elements. e University ofManchester encouraged me to shi my teaching into related areas. In the phi-losophy department, therefore, I was teaching an advanced course on the Republicand found myself lecturing on the literature about its rather puzzling narrativestructure by Lear, Annas and Rutherford. In the history of science centre, I wasteaching another course on the history of mathematics, which dealt in part withPythagorean mathematics and music theory. A series of unexpected insights led to

the gradual realization that Pythagorean musical theory was key to the Republicsnarrative structure. Discussion of Platos doctrines, that is, the consequences forinterpreting Platos philosophy, must be postponed. ey will be the subject offuture research.

For better or worse, making sense of these insights forced me to draw onresearch in manyelds: classics, the history of philosophy, the history of literarycriticism, musicology, papyrology and the history of mathematics. Like all multi-disciplinary research, therefore, this book will commit sins of omission and com-mission. I was trained in an analytic philosophy department with a speciality inthe history and philosophy of science. For help in other areas, I am grateful forconversations and correspondence with many friends and colleagues, but errorsno doubt remain.

Scholars should not underestimate the epistemological complexity of theclaims advanced here. ey require not only the revision of certain accepted viewsabout Plato and his philosophy, but employ novel argumentative strategies whosestrength may not be at rst apparent. I nd that philosophers see the care withwhich each major assertion has been buttressed with independent lines of evi-dence, but tend to be unfamiliar with scholarly methods for interpreting allegori-cal literature. Some make evidentiary demands that would wipe out the study ofallegory in great swathes of the literary tradition. Musicologists are experts in the


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traditional scales and modes of ancient Greek music, but oen have little apprecia-tion of Platos innovations and reformist agenda in the mathematical sciences. Tomy surprise, classicists have a living disciplinary memory of spurious numerolo-gists within their midst, and so may not recognize the degree to which numerologyof various kinds was mainstream and even normal within elite science in ancienttimes.

Most importantly, the use of allegory and symbols to reserve doctrines,although surprisingly common (Ch. 1), will challenge the canons of criticism reg-ularly employed by scholars in the history of philosophy. In modern times, inter-preters of philosophical texts have placed great emphasis on rigour and objectivity,and sought to achieve these by means of literal, textual evidence and carefullyanalysed arguments.

e study of allegory confronts these methods with several problems. Alle-gorists seek a peculiar combination of communication and concealment. Greatcunning and ingenuity are applied precisely to deny readers clear and distinct evi-dence for the secondary layers of meaning, and yet also to ensure that readerswilling to do the detective work and follow the surface clues through a series ofinferences will arrive at a denite doctrine. Allegorists are subtle.ey use red her-rings, disrupt patterns that threaten to become too clear, and invent a sui generisprivate language that must be unravelled by careful study of each individual work.

In some cases, allegorists have separately and explicitly unveiled their methodsin later, informal ways. e letter to Can Grande attributed to Dante details thefour layers of meanings built into the Divine Comedy. James Joyce laid out thesubterranean correspondences between his Ulysses and Homers Odyssey in a

handwritten schema for his friend Stuart Gilbert. In most cases, however, literaryscholars must infer the nature and content of allegories from clues within the com-positions themselves. Generally, this means the literal meaning of the texts is onlythe starting-point, and not the nal arbiter of interpretations. Figurative meaningsare found only by making a series of comparisons and inferences and following atrail of clues. Such methods may be unfamiliar to historians of philosophy but, asthe evidence in Chapter 1 makes clear, they were quite familiar in the late classicalperiod when Plato was writing.

is research is, at least, a methodological victory for the new digital humani-ties movement. is growing eld hopes to show, in various ways, that computers,new databases, online collections of literature and the internet can make decisivecontributions to research in the humanities. e ndings reported here could not,as Chapter 1 explains, have been made without computers.e musical patterns inPlatos dialogues were, it will be argued, more accessible when the dialogues werein their original format: papyri arrayed with neat and mathematically uniformcolumns of Greek letters. Modern critical editions of Plato, like the Oxford Classi-cal Texts (OCT) used here, are the product of many centuries of editorial interven-tions. Although clearer in many ways, they obscure the regular patterns in Platosdialogues, which explains in part why they were not discovered sooner. Aer therst, tentative insights, I obtained electronic versions of the texts and used new


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soware to restore the OCT texts to their classical format. At once, the patternsbecame more visible. Much of the rigour, generality and objectivity that was nallyachieved was made possible by these new digital technologies.

I have presented this research in a series of scholarly lectures and enjoyeddiscussions about it with what now may amount to hundreds of scholars. I havelearned much, both from their queries and suggestions, and have revised much ofthis book to reect their contributions and clarify my methods. I encourage anyfuture critics to correspond with me.

Earlier stichometric studies of Platos dialogues are reviewed in Chapter 2,but it is important to recognize several anticipations of the claims made aboutthe Republic in Chapters 3 and 7, which already implied that Platos works have astichometric structure. Aer my Platos Forms, Pythagorean Mathematics, and

Stichometry appeared, several scholars contacted me about their earlier work.Vittorio Hsle of the University of Notre Dame published an important article,Did the Greeks Deliberately Use the Golden Ratio in an Artwork? (2008) sug-gesting that the Phaedrus and Republic had a mathematical design. Maya Alapinof Oxford University, in a thesis that follows up the work of John Bremer, exploresthe mathematical structure of the Republic.

e direction my research took would not have been possible without my teach-ers. At Princeton, while specializing in mathematics and computers, my sometimeadvisor Carlos Baker made me take a course in literature nearly every term. Forfour years, I was at least exposed to the rigours of the art of close reading in thepreceptorials of the English and comparative literature departments, and becameacquainted with the various structures used to unify their compositions by writers

such as Dante, Spenser, Mann and Ashbery. Later, while working on a PhD inphilosophy at Stanford University with Nancy Cartwright, Peter Galison and JohnDupre, I also studied Greek philosophy with Julius Moravcsik, Wilbur Knorr andJean Hampton. Although more of my time was spent with Aristotles physical andcosmological treatises, Knorr was kind enough to debate his research on structurein Platos Laws with me.

I would like to thank two Plato scholars here in Manchester who encouragedthis work in its early stages. e late David Melling was the rst to say, in a scrawlacross a dra, e patterns that you see exist. Harry Lesser greeted me aerreading another drawith a mischievous smile and said, Its just the kind of thingPlato would do.

is work has been supported in the rst place by my friends and colleaguesat the University of Manchester, whose critical enthusiasm and encouragementsurvived a long series of dra papers, several formal and informal lectures andmany animated conversations. I would like to thank the Centre for the History ofScience, Technology and Medicine, especially the director Michael Worboys andthe former director John Pickstone, the administrator Gillian Mawson, Ian Burney,JeHughes, Vladimir Jankovic, James Sumner, Carsten Timmermann, ElizabethToon and Simone Turchetti, for providing a welcoming home for this research;the philosophers who read my dras, Harry Lesser, David Melling, John Shand,


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Michael Rush and omas Uebel; and the philosophy and classics departments fortheir hospitality over the years. My friends and former colleagues in the philoso-phy department at Notre Dame encouraged me to teach courses on Aristotle, andI would especially like to thank Patricia Blanchette, David Burrell, Marian David,Chris Hamlin, Don Howard, Lynn Joy, Ernan McMullin, David OConnor, BillRamsey, Ken Sayre, Leopold Stubenberg and Paul Weithman.

For conversations and correspondence, both great and small, about this bookas well as other help, I would like to thank Peter Adamson, Tara Ahamed, MayaAlapin, Andrew Barker, John Bremer, Tad Brennan, Miles Burnyeat, David Creese,Armand DAngour, John Dillon, Silvia Fazzo, Kirk Fitzpatrick, Peter Gainsford,Peter Goldie, Roberto Grasso, Christopher Green, Andrew Gregory, MichaelGrin, Penny Gouke, Jim Hankinson, Malcolm Heath, Angela Hobbs, Vitto-

rio G. Hsle, David Howlett, Carl Human, Laura Jones, George Kenney, DavidLangslow, Brian Leiter, Alex Long, Regine May, M. M. McCabe, David Meadows,Gabriele Meloni, Kenneth Royce Moore, Maria-Ruth Morello, Andrew Morrison,Marcus Mota, Ian Mueller, Debra Nails, Liz Pender, Gerald A. Press, Lorna Rob-inson, Ken Sayre, Bob Sharples, Frisbee Sheeld, Mikaela Sitford, Suzanne Stern-Gillet, Peter Tallack, Harold Tarrant, Lauren Ware, James Wilberding and ColinWilson.

e excellent John Rylands Library at the University of Manchester providedunstinting support, but thanks must also be given for essential online resourcessuch as JSTOR, the esaurus Linguae Graecae, the Internet Archive, and thePerseus Digital Library. Several open-source soware projects were key: theTeXShop Latex program from the University of Oregon, the Python programming

language from the Python Soware Foundation, and the Unicode Consortium.For their conversations, support, and encouragement during these busy years

I would also like to thank Melanie Horton, H. P. Tinker, Amanda Williamson,Andrew Read, Steve Gingell, Andrew Grose, Iyabo Fatimilehin, Justin Hayes,Joanne Goldfeld, Tammy Goldfeld, Sylvia Berryman, Mim Kennedy, ScottKennedy, Sheryl Coe, Dan Kennedy, Jennifer Bush, Andrew Kaufman, Nathan-iel Dahl, Michael Tippner, Chris Scarlata, Cornelius OBoyle, Evelyn Donegan,Lilian Crascall-Kennedy, John Crascall-Kennedy, Carole Crascall, John Crascalland Louise Crascall.

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