The Theology of Arithmetic: On the Mystical, Mathematical and Cosmological Symbolism of the First Ten Numbers

136 Pages·1988·1.77 MB·English

by  ps-Iamblichus

THE THEOLOGY
OF
ARITHMETIC
TRANSLATED BY
Robin Waterfield
WITH A FOREWORD BY
Keith Critchlow
THE THEOLOGY OF ARITHMETIC
Other translations
by Robin Waterfield:
Plato: Philebus
Penguin Books, 1982
Plato: Theaetetus
Penguin Books, 1987
Plato: Early Socratic Dialogues
Penguin Books, 1987
with T.J. Saunders, et al.
Xenophon: Conversations of Socrates
Penguin Books, 1990
with H. Tredennick
Plutarch: Essays
Penguin Books, 1990
Epicurus: Letter on Happiness
Rider, 1993
Plato: Republic
Oxford University Press, 1993
Plato: Symposium
Oxford University Press, 1994
Plato: Gorgias
Oxford University Press, 1994
Plato: Statesman
Cambridge University Press, 1995
Aristotle: Physics
Oxford University Press, 1996
T he T heology
of
A rithmetic
On the Mystical, Mathematical
and Cosmological Symbolism
of the First Ten Numbers
Attributed to Iamblichus
T ranslated from the G reek by
ROBIN WATERFIELD
W ith a Foreword by
KEITH CRITCHLOW
A Kairos Book
Phanes Press
© 1988 by Kairos
All rights reserved. No part of this publication may be reproduced or transmitted in
any form, with the exception of short excerpts used in reviews, without permission
in writing from publisher.
96 2
Published by Phanes Press, PO Box 6114, Grand Rapids, Michigan 49516, usa.
Designed by David R. Fideler
Printed and bound in the United States
Find us online at: http://wvrw-piiaiies.com
This book is printed on alkaline paper which conforms to the permanent paper
standard developed by the National Information Standards Organization.
Library of Congress Cataloging-in-Publication Data
Iamblichus, ca. 250-ca. 330
[Theological principles of arithmetic. English]
The theology of arithmetic: on the mystical, mathematical and cosmological
symbolism of the first ten numbers / attributed to Iamblichus; translated from the
Greek by Robin Waterfield; with a foreword by Keith Critchlow.
p. cm.
Translation of: Theological principles of arithmetic.
Bibliography: p.
ISBN 0-933999-71-2 (alk. paper). ISBN 0-933999-72-0 (pbk.: alk paper).
1. Symbolism of numbers—Early works to 1800.2. Pythagoras and Pythagorean
school—Early works to 1800.1. Waterfield, Robin A. H. n. Title.
B669.Z7I1713 1988
119—dcl9 88-23012
CIP
To Pythagoras
who taught that for health, art and science are inseparable
"By him that gave to our generation the Tetraktys, which
contains the fount and root of eternal nature"
(Pythagorean oath)
and to Steve Lee, reluctant arithmologist

Contents
Foreword by Keith Critchlow............................................................9
Introduction by Robin Waterfield...................................................23
The Theology of Arithmetic............................................................33
On the Monad.............................................................................35
On the Dyad................................................................................41
On the Triad...............................................................................49
On the Tetrad.............................................................................55
On the Pentad.............................................................................65
On the Hexad..............................................................................75
On the Heptad............................................................................87
On the Octad.............................................................................101
On the Ennead..........................................................................105
On the Decad............................................................................109
Glossary.............................................................................................117
Biography..........................................................................................123
Bibliography......................................................................................127
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Foreword
Kairos is privileged to present this timely translation of The
Theology of Arithmetic, and is most grateful to Robin Waterfield
for his dedicated and scholarly translation. We offer the following
observations to emphasize the inner nature of a document like this,
which invites interpretation.
Aetius (first or second century A.D.) is one of the most important
sources for the opinions of the earliest Greek philosophers, whose
actual works have for the most part perished. He says of Pythagoras
(1.3.8) that he was the first to call the search for wisdom "philo­
sophy," and that he "assumed as first principles the numbers and
the symmetries existing among them, which he calls harmonies,
and the elements compounded of both, that are called geometrical.
And," Aetius continues, "he says that the nature of Number is the
Decad." However 'unreliable' we choose to treat this transmission,
even this brief extract does contain some remarkably significant
possibilities which call for interpretation.
That numbers were assumed as first principles is not unex­
pected, but the idea of "symmetries existing among them" is
particularly evocative. Their harmonies are likewise said to be
among them. Further, the geometricals are elements compounded
of the numbers with their inherent symmetrical harmonies. The
progression given by Aetius is from first principles to numbers,
symmetries, harmonies and geometricals, and it seems to reflect
the progression arithmetic, harmonic and geometric, which are the
three primary means that Plato proposed that the Divine Artificer
(demiurgos) used to proportion the 'world soul' (Timaeus 36).
Finally, that "the nature of Number is the Decad" could place
quite a different perspective on the issues that took up so much of
Aristotle's time, as he chewed over the paradox of the linear
generation of the 'incomparable' ideal numbers. The indication is
that the Decad is both complete and is the essential nature of all
number—a monad of minimum ten. That ten is 'complete at four'
is a well-known Pythagorean paradox based on the simple cumu­
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