Lore and Science in Ancient Pythagoreanism

542 Pages·1972·17.482 MB·English

by  Walter Burkert

Walter Burkert
Translated by Edwin L. Minar, Jr.
Harvard University Press
Cambridge, Massachusetts
1972
© Copyright 1972 by the President and Fellows of Harvard College
All rights reserved
English edition, translated with revisions from Weisheit und Wissenschafi:
Studien zu Pythagoras, Philolaos und Platon, Copyright 1962 by
Verlag Hans Carl, Nurnberg
Library of Congress Catalog Card Number 70-162856
SBN 674-53918-4
Printed in the United States of America
Preface to the German Edition
If Pythagoras does not present himself to our rninds as a sharply
outlined figure, standing in the bright light of history, this is not merely
the result of accidents in the course of historical transmission. From the
very beginning, his influence was mainly felt in an atmosphere of
miracle, secrecy, and revelation. In that twilight period between old
and new, when Greeks, in a historically unique achievement, were
discovering the rational interpretation of the world and quantitative
natural science, Pythagoras represents not the origin of the new, but the
survival or revival of ancient, pre-scientific lore, based on
superhuman authority and expressed in ritual obligation* The lore of
number is multifarious and changeable. That which was later regarded
as the philosophy of Pythagoras had its roots in the school of Plato.
Outlines of an earlier reformulation of Pythagorean doctrine in the
manner of the φυσιολογία of the fifth century can be detected in the
fragments of Philolaus. As the old and the new interpenetrated and
influenced each other, the picture of Pythagoras became distorted until,
with the victory of rational science, he came to seem its true founder.
To investigate these interrelationships is still a somewhat risky
undertaking; but an attempt has been made to take more account than
has previously been done of the variety in the kinds of evidence
available and, above all, to clarify the ramifications and the divagations
of the tradition.
I am indebted for much advice and encouragement to my teachers
Otto Seel, Reinhold Merkelbach, and Helmut Berve, as well as to
Dr. Ludwig Koenen and to Dr. Burkhart Cardauns, who also helped
me with the proofs. To all of these I offer hearty thanks.
Erlangen Walter Burkert
April 1962
In revising this book for translation, it has been impossible to add
references to all the literature on the subject which has appeared since
1962.1 have tried to concentrate on the ancient evidence, to cut down
polemics, and to incorporate whatever I have learned in these years,
notably from some reviews of the German edition, and from
continuous discussions with B. L. van der Waerden. In the question of the
" discovery of the irrational," I have taken a stand which is less critical
of the tradition; and more thorough acquaintance with ancient religion
has pushed the concept of "shamanism'* further into the background.
But though a good number of passages have been revised, and though
there are some small rearrangements in the order of treatment, still the
book has remained, in all the main lines, the same.
New and comprehensive accounts of Pythagoreanism have been
given by Kurt von Fritz, H. Dorrie, and B. L. van der Waerden in
Pauly-Wissowa (XXIV 171-300; Supp. X 843-864), and by W. K. C.
Guthrie in his History of Greek Philosophy, vol. I; and the same year
(1966) saw the appearance of two books with the title Pythagoras and
Early Pythagoreanism, by C.J. de Vogel and J. A. Philip. Discussion is
certain to continue. I cannot claim to have provided a definitive
history of Pythagoreanism, or a complete account of Pythagoras, the
man and the genius. Still I trust that this book gives a full and
perspicuous presentation of the evidence and thus will be useful even to those
who are not inclined to draw the same conclusions from it.
My special thanks are due to Edwin L. Minar, Jr., who not only
completed the laborious task of translation in a spirit of most pleasant
collaboration, but to whom is due the original initiative which brought
about the English edition. The responsibility for the content, and for
all that may be wrong in it, remains mine.
Schwerzenbach-Ziirich Walter Burkert
August 1970
Introduction ι
I. Platonic and Pythagorean Number Theory 15
1. The Platonic Theory of Ideal Numbers 15
2. The Philosophy of the Pythagoreans according to Aristotle 28
3. The Later Non-Aristotelian Tradition and Its Sources, 53
Speusippus, Xenocrates, and Heraclides Ponticus
4. Pythagoreanism in Plato and the Origin in Platonism of the 83
Pythagorean Tradition
I1I. .P ySthoaguorrasc ine t hPe Eraorlbieslte Tmradisti o9n 977
2. Historical Background 109
4. Acusmata 166
3. Metempsychosis and "Shamanism" 120
5. Acusmatici and Mathematici 192
6. Early Evidence for Pythagoras as a Scientist? 208
III. Philolaus 218
1. The Special Position of Philolaus* Book in the Pythagorean 218
Tradition
2. The Spurious and the Genuine in the Philolaus Fragments 238
3. Reflections of Pythagorean Philosophy in the Fifth 277
Century B.C.?
IV. Astronomy and Pythagoreanism 299
1. The Structure of the World and the Planetary System 299
2. The Theory of Planetary Movements 322
3. The Cosmos of Philolaus 337
4. Harmony of the Spheres and Astral Immortality 350
Contents
V. Pythagorean Musical Theory 369
1. Speculation, Experimentation, and Fiction 369
2. Number Symbolism and Calculation of Proportions in 386
Philolaus
VI. Pythagorean Number Theory and Greek Mathematics 401
1. Did the Pythagoreans Lay the Foundations of Greek Mathe- 401
2.m aPticsy? thagorean Arithmetic 427
43. .P yNthaguormean bGeeomr eatryn andd MCathoemsamticaol Ssec r4ets6 4547
Abbreviations 485
Bibliography 493
Greek Words Discussed 509
Index of Passages 510
General Index 528
/
Introduction
The "Pythagorean question" has sometimes been compared with
the Homeric question. Not that the details of the problem would
especially suggest this; what does remind one of that most famous of
philological controversies is the difficulty of the argument and the lack
of agreement on methodology, as well as the multiplicity and
contradictory character of the solutions advanced. Another similarity, and
not the least striking, lies in the tremendous importance of the questions
about the life, activity, and influence of Pythagoras of Samos. Over
the origins of Greek philosophy and science, as over the beginning of
Greek literature, lies the shadow of a great traditional name. The
attempts of scholarship to grasp the underlying historical reality keep
getting entangled in contradictions; where some think they discern the
figure of a world-historical genius, others find little more than empty
nothingness.
Pythagoras' influence was a lasting one. The ancient tradition of the
history of philosophy made him the ancestor of the "Italian School"
and therefore, after Thales, the second, and more important, originator
of philosophia—in fact, the inventor of the word. The doctrine
transmitted under his name, that numbers are the principles of what exists,
that the "One" is its primal ground, became part of the amalgam of
Neoplatonism. In the trend set by Iamblichus, Pythagoras was the
high priest, par excellence, of the divine wisdom^ He then became, in
the trivializing school tradition of the Middle Ages, the master of the
quadrivium, and in particular the inventor of arithmetic. The early
modern period discovered Pythagoras as the creator of natural science,
which was just then being reborn; what Copernicus and Galileo
taught was regarded by their contemporaries as a revival of
Pythagorean science.1
Subsequently, as research based on historical perspective increasingly
1E.g., Campanella in a letter to Galileo of Jan. 13, 1611 (T. Cainpanella, Lettere, ed.
V. Spampanato [Bari, 1927] 165). Further literature in Capparelli, I 2QfF; see below,
ch. IV 3, nn. 1-2.
INTRODUCTION
replaced the uncritical appropriation of ancient culture, the traditional
picture of Pythagoras, imposing though also vague in outline,
inevitably gave way more and more before criticism. In the scholarly
controversy that followed scarcely a single fact remained undisputed,
save that in Plato's day and then later, in the first century B.C., there
were Pythagoreioi. The "wisdom of Pythagoras," however, has also
had passionate defenders, who opposed to criticism a countercritique:
one-sided, self-sufficient methodology, they protested, had substituted
hypothesis for tradition.
When we set out to survey the most important attitudes and trends
in modern Pythagorean scholarship, the point of departure must be
the work of Eduard Zeller.2 In it the material is not only collected, with
a completeness scarcely to be surpassed, but sifted with uncommon
methodological rigor. The criterion for the value of a tradition is its
age, and Zeller arrives at the verdict, often cited since in agreement and
disagreement: "The tradition about Pythagoreanism and its founder
thus has more and more to tell, the further it lies, chronologically,
from the events..." (I 364). This "expansion of the tradition" (ibid.)
arose basically from "dogmatic preconceptions, partisan interests,
dubious legends, and spurious writings'' (365). The most important
source, nearly the only one which is left, is in the reports of Aristotle,
in his surviving treatises. A second primary source is found in the
fragments of Philolaus, in which August Boeckh, in his day, claimed
to have found a firm foothold amidst the bog of Pythagorean pseud­
epigrapha.3 But Aristotle speaks of "Pythagoreans," not of
"Pythagoras"; so the figure of the master fades off in a mist of nonhistorical
legend. Pythagoras is still recognized as the "founder of a religious
society" and teacher of transmigration (411), but all philosophical
significance is denied his ethical and religious doctrines (557*0·
Alongside this stands, without connection, the number philosophy of the
Pythagoreans. This can be reconstructed from Aristotle and is confirmed
by Philolaus, though aside from him the Pythagoreans remain
anonymous and scarcely datable. Sharply separated from all this ancient
material is the neo-Pythagorean school, which (Zeller thinks) arose,
compounded of Platonic and Aristotelian elements, not before the
first century B.C. (Ill 2.02fF).
21 361-617, III 2.92-254. The text is essentially that of the second edition (1856).
Zeller summarized his position under the title "Pythagoras und die Pythagoraslegende,"
Vortr. u. Abh. I (Leipzig, 1865) 30-50.
3 But contrary to Boeckh, Zeller pronounced the fragment on the world soul (21)
spurious (I 476.1); cf. below, ch. Ill 2, n. 21.
2
Introduction
Zeller's work had a decisive influence, especially in Germany; it
dominates Diels's arrangement of testimonia in the Fragmente der
Vorsokratiker. In the chapter on Pythagoras (DK 14), the biographical
reports $re assembled, along with the reports as to whether or not
Pythagoras wrote anything.4 In the separate chapter on "The
Pythagorean School" (DK 58), the most important section is the
collection pf "ancient Peripatetic'' material (s8B),5 following Iambli­
chus' catalogue of Pythagoreans (58A), and itself followed by the
acusmata (58C), the Pythagorikai apophaseis of Aristoxenus (58D), and
the allusions to "Pythagorists" in the Middle Comedy (58E). Between
these two chapters are found, in chronological order as far as possible,
the testimonies on individual Pythagoreans, notably Hippasus (DK 18),
Philolaus (DK 44), and Archytas (DK 47). Hermann Diels follows
Zeller also in the question of the genuineness of the Philolaus fragments.
Zeller's solution, however, left a number of problems unsolved, and
later research entered in with supplement, modification, and criticism.
Above all, a gap had opened between Pythagoras the religious founder
and the number philosophy of anonymous Pythagoreans; to connect
these disparate elements and to show their original unity was bound
to be an extremely enticing challenge. For at this time the tide of system
building in philosophy, which had borne the work of Zeller, was
ebbing, and this very change made possible a deeper understanding of
cultural history. As the boundaries of philosophy became fluid, the
connections with pre-scientific, religious-mythical thought became
clearer. So the task appeared to be to comprehend how religion and
philosophy could be united in Pythagoras: mysticism and science (or
at least the germ from which science sprang). Then came the high
tide of the evolutionary idea, and it began to seem possible, with its
help, to explain the contradictions of the tradition and to give
everything its place in an extended and detailed history of Pythagoreanism.
The direction was set by August Doring (1892); his thesis became
most influential because he was followed by John Burnet in the later
editions of his Early Greek Philosophy* The unity of science and religion
is found in the ideal of catharsis; scientific activity is the highest form
4 Two doxographical reports are arbitrarily added (14.20, 21; cf. below, ch. IV 1,
nn. 39-41; I 3, n. 151-153).
8 From the fifth edition on, the excerpt from the Hypomnemata has been added, as a
result of the discussion of Max Wellmann (58Bia; cf. below, ch. I 3, n. 1).
6 Burnet refers to Doring (EGP 98 n. 3); as a result, the extent of what Burnet traced
back to Pythagoras himself increased considerably after the first edition (London, 1892,
I05ff).
3