New Research on Plato and Pythagoras

Jay Kennedy, University of Manchester

Quick Introduction for Non-Experts

Introduction for Scholars

Links to Papers and Files

Future Research: an invitation to philosophers, musicologists, historians of science, textual critics, and papyrologists

Other Useful Links

Brief Biography

Version for release on 28 June, 2010.

Thanks for visiting my personal web pages at the Centre for the History of Science, Technology, and Medicine at the University of Manchester. I use these web pages to introduce my recent research to students and other scholars. Thanks too to all those who have responded to my writings and lectures.

My research builds upon recent advances in several areas of scholarship. Burkert, Huffman, and Kahn have brought rigour and clarity to the early history of Pythagoreanism. Sedley, Struck, Ford and others have revised the history of symbolism, allegory, and etymology in Plato and the circles around Socrates. Barker, West, and others have advanced the study of Greek music and harmonics. Sayre, Tarrant, Dillon and others have opened up new ways of thinking about Platonism and its history. I gratefully acknowledge this work and cite it fully in the papers accessible in the links section below.

LATEST DEVELOPMENTS: In a paper in the journal Apeiron and the draft of the related book currently being circulated (see below), I argued there were musical structures embedded in Plato's dialogues. Correspondence with an expert in ancient Greek music has now clarified the nature of these structures. The paper argued that Plato divided each dialogue into twelve parts, each of which corresponded to a musical note in a twelve-note scale. This scale was, I claimed, similar (1) to the equally-divided scales of a school of Greek theorists called the Harmonists and also (2) to the scales produced with a monochord, an instrument important in the later Pythagorean tradition. I have now been convinced that the scale embedded in the dialogues is not like the Harmonists' scale, but would in fact appear naturally with a monochord (whether theoretically or practically with an actual instrument). This moves the debate ahead, and strongly reinforces the main claim of the Apeiron paper that the symbolic structures in the dialogues are evidence of Plato's Pythagoreanism.

Quick Introduction for Non-Experts

Plato was the most important philosopher and scientist of the Greek Englightenment, playing a key role in the birth of Western culture. As Whitehead said, 'All of Western philosophy is a series of footnotes to Plato.' Some thirty or so of his books survive from the fourth-century before Christ, but they are mysterious and even today are studied by thousands of scholars around the world. In particular, his books -- though brilliant, seductive, and inexhaustively rich -- often end frustratingly without definite conclusions. Some have thought he was a destructive sceptic who, like his teacher Socrates, claimed to know only that he knew nothing, and that Plato therefore had no positive philosophy. Others have painstakingly tried to piece together the pieces of his philosophy from the hints in his writings.

In antiquity, many of Plato's followers said, in various ways, that Plato wrote symbolically or allegorically, and that his true philosophy would be found in the layers of meaning underneath the surface stories he tells. In ancient religions, sects, guilds, and fraternities, it was normal to 'reserve' knowledge to initiates and Plato, they contended, had used symbols to hide his philosophy within his writings.

The view that Plato's writings contained symbols was a mainstream and sometimes dominant view for more than a thousand years: from about the time of Christ until the Renaissance. Beginning in the 1700's, theologians in Germany who emphasised rigourous and literal methods of interpretation fiercely opposed this view. They argued that there was no consistent system of symbolism in Plato's writings, and that claiming such was a sign of credulity and mystery-mongering. The ancient defenders of the symbolic approach to Plato were dubbed 'neo-Platonists' in an effort to segregate them from Plato and Platonism. The view that Plato's writings were not symbolic became the standard view among modern scholars and has remained so ever since.

I was teaching a course for philosophers on Plato's most famous book, the Republic, and another course on the history of mathematics for mathematicians, which dealt with Pythagorean mathematics and music. This was a combustible mixture. A series of insights led to the surprising conclusion that the Republic did use symbols, but that recognising and unravelling these symbols required knowledge of Pythagorean music theory.

I am a philosopher who specialises in an area called the History and Philosophy of Science. This field was transformed a generation or so ago when it was widely recognised that the study of primitive pseudo-sciences was necessary to understand the birth of our modern sciences. To understand chemistry, it was necessary to study alchemy; to understand astronomy, it was necessary to study astrology. Unusually among Plato scholars, I was therefore familiar with the numerology and music theory which was at the heart of early Pythagoreanism. This interdisciplinary preparation enabled me to see and decipher Plato's musical symbolism.

These claims will need to be thoroughly debated and verified by other scholars (see below), but they promise to revolutionise the history of the birth of Western thought. We now better understand the literary strategies of Plato's writings. All thirty books contain unexcavated layers of meanings. These not only explain the structure of Plato's narrative but contain new doctrine and his positive philosophy. Moreover, since the symbolic structures are organised musically and mathematically, they transform our view of Plato's science. For the first time we see Plato doing elaborate calculations. We can show that he was at the forefront of the advanced mathematics of his day, as some of his followers said. We learn more about the Pythagoreans, who are sometimes credited with pushing Western culture toward mathematics and science. The often puzzling history of philosophy after Plato, and especially the repeated claims that he was a Pythagorean, now make sense.

Even for those who are not specialists, these results should be thrilling. Western culture is sometimes said to rest on the twin pillars of Socrates and Jesus, two poor men who wrote nothing. Plato's teacher Socrates launched philosophical and scientific research in Athens, but we know of him primarily through Plato's writings. The philosophy and science of Socrates and Plato combined with the religions of the East in the Roman period to create central strands of what became modern European culture. Now our understanding of the birth of that culture will need to be reworked. Plato is sometimes thought of as a cold fish who banished poets and pushed the West toward logic, mathematics, and science. Now we know he was a hidden romantic. The philosophy contained beneath his stories mixes science and mysticism, mathematics and God. By understanding our roots better, we understand ourselves better.

The two most surprising ideas in Plato's hidden philosophy may be explained simply. First, the musical and mathematical structures he hid in his writings show that he was committed to the radical idea that the universe is controlled not by the gods on Olympus but by mathematical and scientific law. Today we take it for granted that the book of nature is written in the language of mathematics, but it was a dangerous and heretical idea when it struggled for acceptance in the Scientific Revolution of the 1600s. Giordano Bruno was burnt at the stake and Galileo was condemned and imprisoned. After Socrates was executed for sowing doubts about Greek religion, Plato had every reason to hide his commitment to a scientific view of the cosmos. But we now know that Plato anticipated the key idea of the Scientific Revolution by some 2000 years.

Perhaps even more surprisingly, Plato's positive philosophy shows us how to combine science and religion. Today we hear much of the culture wars between believers and atheists, between those who insist our world is imbued with meaning and value and those who argue for materialism and evolution. For Plato, music was mathematical and mathematics was musical. In particular, we hear musical notes harmonising with each other when their pitches form simple ratios. For him, the perception of this beauty in music was at once the perception of a beauty inherent in mathematics. Thus mathematics and the laws governing our universe were imbued with beauty and value: they were divine. Modern scientists don't ask where their fundamental laws come from; for Plato, the beauty and order inherent in mathematical law meant its source was divine (a Pythagorean version of modern deism). Plato may light a middle way through today's culture wars.

Introduction for Scholars

The Central Claim. The Apeiron article and the sample chapters below concentrate on showing that Plato used a consistent scheme of symbols to embed a musical structure in each genuine dialogue.

In short, each dialogue was divided into twelve parts. At each twelfth, i.e., at 1/12, 2/12, etc., Plato inserted passages to mark the notes of a musical scale. This regular structure resembles a known Greek scale. According to Greek musical theory, some notes in such a scale are harmonious (if they form a small whole number ratio with the twelfth note) and the others are dissonant or neutral. Plato's symbolic passages are correlated with the relative values of the musical notes. At more harmonious notes, Plato has passages about virtue, the forms, beauty, etc.; at the more dissonant notes, there are passages about vice, negation, shame, etc. This correlation is one kind of strong evidence that the structure is a musical scale.

This musical structure can be studied rigorously because it is so regular. Subsequent work will show that other symbols are used to embed Pythagorean doctrines in the surface narratives. It is surprising that Plato could deploy an elaborate symbolic scheme without disturbing the surface narratives of the dialogues, but in this respect he does not differ from other allegorical writers like Dante or Spenser.

Plato's Musical Code

The Breadth and Depth of the Evidence. Scepticism is a natural first reaction to these claims. The Apeiron article assembles a number of lines of evidence; they are independent but mutually reinforcing.

Objective Measurements of the Lengths of Speeches. Although this line of evidence may appear trivial, it is easily and objectively measurable. Set speeches in the Symposium and other dialogues show clear evidence that Plato was counting the number of (hexameter) lines in his compositions.
Objective Measurements of the Lengths of the Dialogues. The Apology is twelve times 100 lines. The Republic is twelve times 1000 lines. The lengths of the other dialogues form a regular but complicated pattern.
Correlation of Features of the Narrative with the Musical Structure. Once locations in the text are marked to show the musical structure, it is patent that Plato used the musical scale as a kind of outline for his dialogues. Episodes fill out musical intervals. Major turns in the argument and major concepts are introduced at musical notes.
Correlation of the Symbolic Passages with the Relative Harmony of the Notes. As explained above, the symbols used to mark the notes reflect whether they are harmonious or dissonant.
The Divided Line Argument. A complicated argument in the Apeiron paper shows that Plato used symbols that directly referred to their mathematical location. These allows us to gauge the difference between the location of passages within the modern OCT texts and Plato's autograph (despite the alterations and corruptions that have crept into the texts, this discrepancy is generally a small fraction of a percent).
Consonance with Musical History. The scale embedded in the text corresponds to what is known of Pythagorean musical theory (in Archytas, Aristoxenus, and later writers like Theon of Smyrna).
Consonance with Reports of Plato's Pythagoreanism and Late Ontology. From Aristotle onward, Plato's students and followers associated him with Pythagoreanism. Modern scholars like Burkert and Huffman tend to reject this because Pythagoras is rarely mentioned in the dialogues. Unravelling Plato's symbols shows a number of Pythagorean structures and doctrines, thus confirming the early reports.
Consonance with Reports that Plato's Dialogues are Symbolic. From Neo-Pythagoreans like Numenius through Renaissance Neo-Platonists like Ficino, it was common to insist that Plato concealed his philosophy in symbols embedded in the dialogues. Although much of their literary interpretations were not rigorously demonstrable and sometimes appear even frivolous, we can now show that their general thesis was correct. My work is conservative in the sense that it restores the status quo ante.
Consonance with the History of Stichometry. Line-counting was routinely used from the classical period onwards, and is mentioned in the Laws. Vitruvius briefly says that Pythagoreans used line counts to organise their works. Plato used line-counting to give his works a musico-mathematical substructure, just as the Pythagoreans said that the cosmos and ordinary objects had some similar kind of substructure.
Consonance with the History of Literary Symbolism. A new wave of research stimulated in part by debates over the Derveni papyrus, has shown that symbolism and allegory were much debated in the circles around Socrates. Plato's dialogues explicitly attest his interest in this area, but we now know he assiduously applied these literary theories.

Methodological Precedents. Given the nature of these claims, a great deal of attention has been paid to methodology. Although this work required combining research from several different fields, its methods are not unusual. Literary scholars compile great tomes which elucidate the dense network of symbols in Dante, Spenser, Mann, Joyce, and so on. Although features of these later works should not be read back into Plato, the scholarship about them can be mined for fruitful techniques of interpretation. In particular, it was discovered a generation ago, that well-known shorter poems of Spenser contained undetected mathematical schemes. This is now universally accepted and has shifted the direction of research on Renaissance poetry and Spenser's Platonism.

Plato's Motivations. Secrecy and reserving knowledge were normal among sects, guilds, and fraternities in antiquity. The Pythagoreans were especially known for using symbols to conceal their doctrines. But the core of Platonism, the notion of forms beneath appearances, is already sufficient motivation for given the dialogues a mathematical substructure.

Links to Papers and Files

The following is a brief guide to the drafts in pdf format below (where all references will be found).

1. A Rigourous, Self-Contained Introduction: Background and Independent Lines of Evidence:
'Plato's Forms, Pythagorean Mathematics, and Stichometry' (pdf, Apeiron essay)

2. Sample Chapters which Defend Methodology, Review Key Musical Concepts, and Present Close Readings
The Musical Structure of Plato's Dialogues: a quick guide to the strongest evidence (pdf)

3. A brief presentation with pictures and graphics
'A Visual Introduction to the Musical Structure of Plato's Symposium' (pdf)

The following files contain Plato's dialogues in Greek (open-domain OCT editions) with musically and mathematically significant locations marked. The software (a Python program) which produced these files can be had upon request, but these are not user-friendly packages and probably require some familiarity with compiling and running programs. These pdf files are easy to download and read but are not easily searchable. Searchable Unicode files (whose use requires some knowledge of handling this format) may also be had upon request.

1. Plato's Symposium (pdf)

2. Plato's Euthyphro (pdf)

Future Research: an Invitation

I am currently working on a book which surveys the dialogues, compares their structures, and attempts to lay out the positive philosophical programme contained by the elaborate network of symbols in the dialogues, i.e., Plato's positive philosophy.

The essays above open up many exciting, new lines of research -- many more than any single scholar can pursue. The following brief indications lay out some of the territory that needs to be explored.

1. New Commentaries. The sample chapters from the draft book above show that we need new commentaries on the dialogues which annotate the musical passages and other symbols embedded in the texts. Writing out such a commentary is extremely useful for understanding Plato's symbolic techniques and for assessing the strength of the evidence for the embedded structures in the texts. Although the symbolic scheme is the same in all the genuine dialogues, it is methodically varied and its elucidation requires a fair amount of work. I have carried this out carefully in the finished draft of the book for two dialogues, and this might serve as one model for this new kind of commentary. I have surveyed all of the dialogues, but we will need similar book-length treatises for all of the dialogues before we can exhaustively catalogue the range of Plato's symbolism with precision.

2. History of Music. The musical structures embedded in the text are a new source for musicology, and may substantially revise our understanding of Pythagorean views of music and of the early history of the monochord.

3. History of Mathematics. As mentioned above, the structures show Plato performing elaborate calculations and using advanced mathematics. How does this fit with what is known of fifth-century mathematics and Pythagoreanism?

4. History of Pythagoreanism. The Pythagoreans were long reputed to reserve their doctrines and use secret symbols, and now we have proof. Does this up-end Burkert's view that Plato was innovative and not a proper Pythagorean? Does it shift our views of Aristotle as a reliable reporter for the history of Pythagoreanism?

5. Textual Studies and Papyrology. The Apeiron paper argues that we have a new method for gauging the integrity of our manuscipts and the degree of corruption (compared to Plato's autograph). What are the implications of this?

6. History of Platonism. The distance between 'neo-Platonism' and Platonism has been steadily diminishing since the work of Dodds. This work implies that the reports among Plato students that he was a Pythagorean in some strong sense were correct. This reaffirms the views among some neo-Pythagoreans and neo-Platonists. How is the history of the reception of Plato now altered?