Research on Plato and Pythagoras
Kennedy, University of Manchester
Introduction for Non-Experts
Introduction for Scholars
to Papers and Files
Research: an invitation to philosophers, musicologists, historians of
science, textual critics, and papyrologists
Version for release on 28 June, 2010.
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
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.
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,
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
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
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
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
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,
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
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
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
through today's culture wars.
Introduction for Scholars
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
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.
The Breadth and Depth of
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.
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.
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
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.
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.
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
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).
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.
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.
with the History of Stichometry. Line-counting was
routinely used from the classical period onwards, and is mentioned in
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
ordinary objects had some similar kind of substructure.
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
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.
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.
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:
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
3. A brief presentation with pictures and graphics
'A Visual Introduction
to the Musical Structure of Plato's Symposium'
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
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
1. Plato's Symposium
2. Plato's Euthyphro
Research: an Invitation
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
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
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
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
This page is fairly static. I have set up a
to track developments, upcoming lectures, forthcoming
university web page.
My Facebook page: search for Jay Kennedy Manchester.
My university email is firstname.lastname@example.org
My mailing address is:
Centre for the History of Science, Technology,
Simon Building, Oxford Rd., M13 9PL, United Kingdom
It is common in some disciplines to put drafts and pre-prints online:
Philosophy: Chalmer's list of online papers.
Philosophy of science: University of Pittsburgh, HPS
My textbook on the Philosophy of Space and
Time, from Aristotle to Einstein:
Space, Time and Einstein
(Any of my students who buys a copy gets a free cup of coffee or tea.)
'A very clear and enjoyable book. A real strength is the way it relates
issues about space and time that physicists have grappled with, over
the history of science, to deep and longstanding philosophical issues.
Introductory books sometimes make passing reference to the deep
philosophical questions, but I've never read one that introduces them
so clearly, and then uses them so effectively, to enliven and
illuminate the issues.' -- Carl Hoefer
'This work covers the philosophical heart of the issues of space and
time. It introduces the revolutionary ideas of Einstein, along with the
concepts and arguments of philosophers, both ancient and modern, which
have proved of lasting value. The text serves to introduce the subject
as well as provide a clear statement of the
"state of the debate". Topics include
Einstein's special and general relativity, how to build an atom bomb,
the four-dimensional universe, the possibility of time travel, the
impossibility of motion, whether space curves, the big bang, black
holes, as well as an inflationary and accelerating universe.'
Biography (From University
studied mathematics and computers at Princeton. My doctorate is in
philosophy from Stanford University, with a specialty in the history
and philosophy of mathematical physics. My advisors were Nancy
Cartwright, Peter Galison, and John Dupre. I also studied Greek
philosophy with Julius Moravcsik, Jean Hampton, and Wilbur Knorr. I was
a student for a year at the Wissenschaftskolleg zu Berlin. I was an
assistant professor at Notre Dame University for three years and spent
a year doing research at Cambridge University, where I was the
principal investigator with an NSF grant, before moving to Manchester
At Manchester, I have taught courses on the history
of mathematics, on the philosophy of science, on introductory
philosophy, on Plato's Republic,
on Aristotle's Ethics,
on the history
of computers, and on science and literature. My partner Louise has a
requires frequent travel, and so I am the primary caregiver for Lily
and John and now teach part-time.
Before becoming a teacher, I worked for a year on
the oil rigs in the Gulf of Mexico. I put myself through university by
repairing computers. For some five years, I worked with NEC Inc. in
Tokyo, and was a professional translator (from Japanese to English).
NEC sent me to the National Computer Centre in Baghdad, where I
lectured for a term.
My legal name is 'John Bernard Kennedy, Jr.' but I go by the nickname