Table Of ContentAlexander of Aphrodisias
On Aristotle Prior Analytics 1.8-13
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Alexander
of Aphrodisias
On Aristotle
Prior Analytics 1.8-13
(with 1.17,36b35-37a31)
Translated by Ian Mueller with
Josiah Gould
Introduction, Notes and
Appendices by
Ian Mueller
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Bloomsbury Academic
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First published in 1999 by Gerald Duckworth & Co. Ltd.
Paperback edition first published 2014
© Ian Mueller, 1999
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to be identified as Author of this work.
All rights reserved. No part of this publication may be reproduced or transmitted in any form or
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British Library Cataloguing-in-Publicataion Data
A catalogue record for this book is available from the British Library.
ISBN HB: 978-0-7156-2855-3
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Acknowledgements
The present translations have been made possible by generous and imaginative funding from the
following sources: the National Endowment for the Humanities, Division of
Research Programs, an independent federal agency of the USA; the Leverhulme
Trust; the British Academy; the Jowett Copyright Trustees; the Royal Society (UK);
Centro Internazionale A. Beltrame di Storia dello Spazio e del Tempo (Padua); Mario Mignucci;
Liverpool University; the Leventis Foundation; the Humanities Research Board of the
British Academy; the Esmée Fairbairn Charitable Trust; the Henry Brown Trust; Mr and
Mrs N. Egon; The Netherlands Organisation for Scientific Research (NWO/GW).
The editor wishes to thank Jonathan Barnes, Tad Brennan, Kevin Flannery, Pamela Huby,
Michael B. Papazian, Richard Patterson and Donald Russell for their
comments on the volume, and Han Baltussen for preparing the volume for press.
Typeset by Ray Davies
Printed and bound in Great Britain
Contents
Editor’s Note vii
Preface ix
Introduction
I. Assertoric syllogistic 4
II. Modal syllogistic without contingency 9
II.A. Conversion of necessary propositions 9
II.B. NN-combinations 11
II.C. N+U combinations 13
III. Modal syllogistic with contingent propositions 19
III.A. Strict contingency and its transformation rules 19
III.B. Alexander and the temporal interpretation of
modality 23
III.C. Conversion of necessary propositions 25
III.D. Conversion of contingent propositions 27
III.D.1 Conversion of affirmative contingent
propositions 27
III.D.2 Non-convertibility of negative contingent
propositions 31
Notes 34
Summary (overview of symbols and rules) 39
Translation: The commentary
Textual Emendations 52
1.8 Combinations with two necessary premisses 53
1.9-11 Combinations with one necessary and one unqualified
premiss 58
1.9 The first figure 58
1.10 The second figure 70
1.11 The third figure 81
1.12 Summary remarks on the necessary and the unqualified 89
1.13 Remarks on contingency 93
1.17, 36b35-37a31 Failure of EE-conversion for contingent
premisses 106
vi Contents
Notes 117
Appendix 1. The expression ‘by necessity’ (ex anankês) 145
Appendix 2. Affirmation and negation 147
Appendix 3. Conditional necessity 148
Appendix 4. On Interpretation, chapters 12 and 13 153
Appendix 5. Weak two-sided Theophrastean contingency 155
Appendix 6. Textual notes on Aristotle’s text 159
Bibliography 163
English-Greek Glossary 165
Greek-English Index 169
Subject Index 185
Index Locorum 187
Editor’s Note
This text, translated in two volumes, is a very important one because
Alexander’s is the main commentary on the chapters in which Aristotle
invented modal logic, i.e. the logic of necessary (possible) and contingent
propositions. Because it is more technical than the other texts in this
series, Ian Mueller explains the modal logic in his masterly introduc-
tion, which takes an exceptional form, being couched in logical symbols
partly of his own devising. All symbols are explained on first occurrence.
Symbols are entirely excluded from the translation itself, and this can
be consulted freely by those who do not wish to master the entire modal
system.
In this volume, Alexander reaches the chapter of Aristotle’s Prior
Analytics (1.13) where Aristotle discusses the notion of contingency,
and we have added Alexander’s commentary on that part of 1.17 where
the conversion of contingent propositions is handled, the contingent
being what may or may not happen.
Aristotle also invented the theory of the syllogism, and in the present
chapters he discusses syllogisms consisting of two necessary proposi-
tions, as well as the more controversial syllogisms containing one
necessary and one non-modal premiss. The discussion of syllogisms
containing contingent propositions is reserved for the companion
volume.
December 1998 R.R.K.S.
Preface
This translation has been literally decades (two) in the making. Josiah
Gould, acting on a suggestion of Ian Mueller, prepared a first draft of
the translation. Mueller produced a second draft and, then, in consult-
ation with Gould, a third and final version with introduction, notes,
appendices, and indices. We are certain that errors remain, but know
that there would have been many more without the advice of Tad
Brennan, Glenn Most, Richard Patterson, Robin Smith, and several
anonymous readers whose friendly but stern admonitions turned us
from some paths. We take full responsibility for remaining on other
paths despite their counsel.
December 1998 I.M.
J.G.
Introduction
We offer here a translation of Alexander of Aphrodisias’ commentary on
chapters 8-13 and most of 17 of book 1 of Aristotle’s Prior Analytics. In
chapters 8-12 Aristotle presents what we call his modal logic as applied
to necessary and to what we call unqualified propositions. In chapter 13
Aristotle discusses the notion of contingency, and in the part of 17
translated here he treats the so-called conversion of contingent propo-
sitions. In a separate volume we have translated Alexander’s
commentary on chapters 14-22, in which Aristotle treats arguments
involving contingent propositions. Chapters 1, 2, and 4-7 of the Prior
Analytics constitute a self-contained presentation of what we will call
non-modal or assertoric syllogistic. Alexander’s commentary on this
material (and on chapter 3) has been admirably translated and dis-
cussed by Barnes et al. We refer the reader to their introduction for
information about Alexander, ancient commentaries, and the general
character of Alexander’s commentary on the whole Prior Analytics.
In making choices for how to deal with our task, we have always
begun by consulting Barnes et al. for guidance, and in many cases have
followed their practices. But the greater difficulty of the material we
have to present here has led us to diverge from them in some significant
ways. First of all, in our notes and discussions we have relied on a
quasi-formal symbolism. We hope that the symbolism is enlightening;
we are confident that a full exposition of our text not using some
formalism would run to much greater length. To put this another way,
if one used a formal symbolism one could encapsulate the full content
of Alexander’s commentary in many fewer pages than Alexander has
used.
We have, however, not thought it a good idea to introduce formal
symbolism into the translation itself. Our major departure from Alex-
ander’s text is that we have used considerably more variables than
Alexander uses; we have sometimes done the same thing in our trans-
lations of Aristotle. To give one example, at 121,4-6, where Alexander
writes,
In both cases the conclusion proved is a particular negative necessary
proposition of which the opposite is ‘It is contingent of all’ (endekhetai
panti).
