O'Meara,
Dominic J. Professor
of Philosophy, University of Fribourg
P
ythagoras
Revived
Mathematics
and Philosophy in Late Antiquity
Print
ISBN 0198239130, 1990
Table of
Contents
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|
Part I
|
The Revival
Of Pythagoreanism In the Neoplatonic School
1.
|
Varieties
of Pythagoreanism in the Second and Third Centuries ad
9
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1.
Numenius of Apamea 10
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2.
Nicomachus of Gerasa 14
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3.
Anatolius 23
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4.
Porphyry 25
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2.
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Iamblichus'
Work On
Pythagoreanism:
Title, Plan, the First Four Books 30
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|
1. The
Title and Overall Plan 32
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2.
Pythagoras (Book I: On
the Pythagorean Life)
35
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3.
Pythagorean Philosophy (Book II: the Protreptic)
40
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4.
Pythagorean Mathematical Science (Book III: On
General Mathematical Science)
44
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5.
Arithmetic (Book IV: On
Nicomachus' Arithmetical Introduction)
51
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3.
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On
Pythagoreanism
V - VII: The Excerpts in Michael Psellus 53
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1.
Michael Psellus, Philosophical Excerptor 53
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2.
Psellus' Excerpts from On
Pythagoreanism
V - VII 57
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3. On
Pythagoreanism
V 60
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(i)
General Plan 60
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(ii)
Physical Number 62
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(iii)
Formal and Material Causation 62
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(iv)
Efficient Causation 64
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(v)
Change 64
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(vi)
Place 66
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(vii) The
Void 67
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(viii)
Conclusion 68
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end p.ix
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4. On
Pythagoreanism
VI 70
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(i)
General Plan 70
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(ii) The
First Principles of Ethics 71
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(iii) The
Powers of the Soul 72
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(iv)
Virtue 73
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(v)
Particular Virtues 74
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(vi)
Conclusion 75
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5. On
Pythagoreanism
VII 76
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(i)
General Plan 76
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(ii)
Divine Number 79
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(iii) The
Approach by Analogy 81
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(iv)
Conclusion 84
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4.
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Iamblichus'
Work On
Pythagoreanism:
General Conclusions 86
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1. On
Pythagoreanism:
A Brief Review 87
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2. The
Relation of On
Pythagoreanism
to Iamblichus' Other Works and Interests 91
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3.
Iamblichean Pythagoreanism and its Predecessors 101
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Part II
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Iamblichean
Pythagoreanism In the Athenian School
5.
|
Hierocles
109
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|
1. The
Introduction of Iamblichean Philosophy at Athens in the Fourth
Century 110
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2.
Hierocles on the History of Philosophy 111
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3.
Pythagoreanism in Hierocles' Commentary
on the Golden Verses
114
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4.
Conclusion 118
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6.
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Syrianus
119
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1. The
History of Philosophy in Syrianus 119
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2.
Philosophy as Revelation in Hermias' Commentary
on the Phaedrus
124
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3.
Mathematics and Philosophy in Syrianus' Commentary
on the Metaphysics
128
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|
(i)
Syrianus' Commentary
and Iamblichus' On
Pythagoreanism
128
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(ii) The
Tripartite Structure of Reality in Syrianus 131
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end p.x
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(iii)
Number and the Soul 132
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(iv)
'Physical Number' 134
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(v)
Number in Metaphysics 135
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(vi)
Syrianus and Iamblichus 138
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7.
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Proclus:
Some Preliminary Issues 142
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1. The
Rivalry with the Mathematician Domninus of Larissa 143
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2. Plato
and Pythagoras 145
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3. The
Theory of Superior Souls 149
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4.
Learning, Discovery, and Revelation 152
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8.
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Proclus
on Mathematics 156
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1.
General Mathematics 157
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(i)
Iamblichus' On
Pythagoreanism
III and Proclus' On
Euclid
Prol. I 157
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(ii)
Proclus' Revisions of Iamblichus 164
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|
2.
Arithmetic and (or?) Geometry 166
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3.
Geometry 170
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(i) The
Composition of On
Euclid
Prol. II 170
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(ii)
Euclid as Platonist 170
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(iii) The
Method of Geometry 171
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(iv) The
Transposition of Geometry 173
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4.
Conclusions 175
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9.
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Mathematics
and Physics in Proclus 177
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1.
Aristotle's Physics Geometricized 177
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2.
Plato's Timaeus
as 'Pythagorean' Physics 179
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3. The
Geometrical Method of Plato's Physics 181
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4. Is
Physics a Science? 182
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5. The
Application of Mathematical Truths in Physics 185
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|
6.
Concluding Comment 192
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10.
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Mathematics
and Metaphysics in Proclus 195
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1. The
Elements
of Theology:
A Geometrical Metaphysics? 196
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|
2. The
Science of Dialectic 198
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3.
Mathematical Theology and Dialectic 204
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4.
Concluding Comment 208
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Conclusion
210
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end p.xi
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Appendices
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|
I. The
Excerpts from Iamblichus' On
Pythagoreanism
V - VII in Psellus: Text, Translation, and Notes 217
|
|
II. The
Arabic Commentaries on the Golden
Verses
attributed to Iamblichus and Proclus 230
|
|
Bibliography
233
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1.
Ancient Authors 233
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|
2. Modern
Authors 236
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|
Index 247
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end
p.xii
Preface
Research begun
many years ago with the support of a Junior and Visiting Fellowship
at the Dumbarton Oaks Center for Byzantine Studies brought me to the
texts and theses explored in this book. A sabbatical grant and
generous leave of absence from The Catholic University of America and
a grant provided in ideal circumstances by the Alexander von
Humboldt-Stiftung allowed me to develop these theses. Completion of
the book was made possible by the support made available by the
Université de Fribourg. I am also much indebted to friends and
colleagues for their assistance. Henri-Dominique Saffrey made many
helpful suggestions and corrections for which I am grateful, as I am
to Oxford University Press's reader for constructive and detailed
comments. Ilsetraut Hadot also proposed improvements to the book,
which is indebted to her research as it is to the work of Pierre
Hadot, a longstanding source of inspiration for me. Leendert
Westerink and John Duffy were unfailing in their expert assistance. I
am particularly grateful to Werner Beierwaltes: he put me on the
track of Iamblichus and gave me invaluable advice and help during my
stay in Freiburg-im-Breisgau and Munich. The deficiencies that remain
in the book are of course mine. My wife Carra gave my work her full
encouragement and support throughout many years. Amy Eiholzer-Silver
prepared the typescripts of the final revisions of the book with
intelligent care.
In an effort to
simplify footnotes as far as possible, I have adopted the practice of
referring to modern works by the name of the author and the year of
publication: further details may be found in the second part of the
Bibliography. The texts of ancient authors are cited by page and line
in the editions listed in the first part of the Bibliography (for
fragments, by fragment number and line). In cases where this seemed
appropriate, I have added a chapter number before the page reference
(e.g. I ch. 2,
3=vol.
I, chapter 2,
page 3). Translations are mine, unless otherwise noted. The following
standard abbreviations are used:
CAG
|
Commentaria
in Aristotelem Graeca,
Berlin, 1870 ff.
|
DK
|
H. Diels, W.
Kranz, Die
Fragmente der Vorsokratiker,
Berlin, 1952.
|
end p.vii
LSJ
|
Liddell,
Scott, Jones, Greek—English
Lexicon.
|
RE
|
Pauly,
Wissowa, Kroll, Realencyclopädie
der classischen Altertumswissenschaft.
|
SVF
|
Stoicorum
veterum fragmenta,
ed. H. von Arnim, Leipzig, 1905-24.
|
This book was
completed early in 1986. I have tried to include mention of what has
been published since, but have only been able to take account to a
limited extent in particular of the important Paris colloquium on
Proclus: Proclus,
lecteur et interprète des anciens,
ed. J. Pépin, H.-D. Saffrey, Paris 1987.
D.J.O'M.
Fribourg,
Switzerland
Christmas
1987
end
p.viii
