Aspects of Aristotle’s Logic of Modalities

247 Pages·1989·10.715 MB·English

by  Jeroen van Rijen (auth.)

ASPECTS OF ARISTOTLE'S LOGIC OF MODALITIES
SYNTHESE HISTORICAL LIBRARY
TEXTS AND STUDIES IN THE IllSTORY OF
LOGIC AND PIffi.,OSOPHY
Editors:
N. KRETZMANN, Cornell University
G. NUCHELMANS, University ofL eyden
Editorial Board:
J. BERG,Munichlnstitute of Technology
L. M. DE RDK. University ofL eyden
D. P. HENRY, University of Manchester
J. HlNTIKKA, Florida State University. Tallahassee
B. MATES, University of California. Berkeley
J. E. MURDOCH, Harvard University
G. PA1ZIG, University of Gottingen
VOLUME 35
JEROEN VAN RIJEN
Philosophy Department, Erasmus University,
Rotterdam, The Netherlands
ASPECTS OF
ARISTOTLE'S LOGIC
OF MODALITIES
KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON
Library of Congress Cataloging in Publication Data
Rijen, Jeroen van, 1950-
Aspects of Aristotle's logic of modalities / Jeroen van Rljen.
p. cm.
Based on the author's dissertatl0n--University of Leiden, 1986.
Bibliography: p.
Includes index.
1. Arlstotle--Contributions in logic of modalities. 2. Modality
(Logic) I. Title.
B491.L8R55 1989
166--dc19 88-31904
CIP
ISBN-13: 978-94-010-7696-8 e-ISBN-13: 978-94-009-2651-6
DOl: 10.1007/ 978-94-009-2651-6
Published by Kluwer Academic Publishers,
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© 1989 by Kluwer Academic Publishers
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CONTENTS
PREFACE AND ACKNOWLEDGEMENTS ix
CHAPTER ONE/ SUBJECT AND PROGRAMME
1. Introduction 1
2. Quandaries in recent Aristotle research 4
3. The programme of this study 10
Notes to Chapter One 13
CHAPTER TWO/ THE GENERAL DOCTRINE I
SOME THEOREMS AND RULES
1. Multifariousness and common core 15
2. A provisional assumption 16
3. Cornmon properties 16
4. Comparisons 25
Notes to Chapter ~wo 28
CHAPTER THREE/ THE GENERAL DOCTRINE II
ABSOLUTE AND QUALIFIED MODALITIES
1. Introduction 30
2. Qualified vs. absolute modalities 31
3. Qualified necessity, syllogisms and the proof per impossibile 36
4. Absolute impossibility and the commensurability of the diagonal 45
5. Real and assumed background knowledge 51
6. Relations between temporal and modal concepts 53
Notes to Chapter Three 56
CHAPTER FOUR/ MODALITY AND TIME (I)
THE PRINCIPLE OF PLENITUDE
1. Introduction 59
2. The Principle of Plenitude and its role in Aristotle's modal
thinking 60
3. The evidence 65
Notes to Chapter Four 72
vi CONTENTS
CHAPTER FIVE! MODALITY AND TIME (II)
DE CAEW 1.12 AND THE NECESSITY OF WHAT IS ETERNAL
1. The problem 73
2. Williams and the supposed logical errors 74
3. Hintikka and the confusion in Aristotle's "Master Argument" 79
4. Judson and the "grossness of Aristotle's fallacy" 81
5. The metaphysics in De Caelo 1.12 as exposed by Waterlow 82
6. De Caelo 1.12 and the necessity of what is eternal 87
7. Some extrapolations and the role of hyle phtharte 95
Notes to Chapter Five 101
CHAPTER SIX! MODALITY AND TIME (III)
DE INTERPRETATIONE 9
1. Introduction 103
2. The traditional views 103
3. De Interpretatione 9 on the statistical reading 106
4. Deliberation and chance events in De Interpretatione 9 110
5. The interpretation 117
Notes to Chapter Six 130
CHAPTER SEVEN! POSTERIOR ANALYTICS 1.4-6
THE DE OMNI-PER SE DISTINCTION
1. Introduction 132
2. Zabare11a on Aristotelian necessity 133
3. Inseparable accidents 136
4. A first look at Posterior Analytics 1.4-6 137
5. Some commentaries on Posterior Analytics 1.4 and 6 140
6. Real or conceptual modalities? 145
7. Aristotle, matter, and definition 149
Notes to Chapter Seven 154
CHAPTER EIGHT! POSTERIOR ANALYTICS 1.4-6
NAMES AND NAMING
1. Abstraction in Metaphysics XIII.3 157
2. Abstraction and naming 160
3. The issue of names and naming 162
4. A new look at Posterior Analytics 1.4-6, part one 165
5. Some major differences 170
CONTENTS
6. A new look at Posterior Analytics 1.4-6, part two 172
7. Belonging kath' hauto and homogeneity 177
8. Homogeneity, the necessity of what is always and the concept of
possibility 179
Notes to Chapter Eight 183
CHAPTER NINEj APODEICTIC SYLLOGISTIC
1. Introduction 185
2. External criticism 186
3. The nature of Aristotle's syllogistic theory 189
4. Apodeictic syllogistic 192
5. Incoherence 194
6. McCall's reconstruction 199
7. The four apodeictic categorical sentences and apodeictic ecthesis 200
8. The apodeictic conversion rules 205
9. The apodeictic Barbaras and domains of discourse 205
10. The status of ALuU 209
11. The soundness of the inference base 210
12. Conversion rules and shifts of type of predication 212
13. Conclusions 214
Notes to Chapter Nine 216
BIBLIOGRAPHY 219
INDEX OF NAMES 229
INDEX OF SUBJECTS 233
~REFACE AND ACKNOWLEDGEMENTS
This book is an elaboration of the study which I submitted as a disserta
tion at the University of Leiden in the autumn of 1986. It was conceived on
the basis of the conviction that for all the work done on this subject,
there is still not a satisfactory explanation of Aristotle's modal logic.
To the present day all efforts to detect in Aristotle's works a coherent
and consistent theory of modalities have utterly failed. Many studies of
Aristotelian modalities have appeared which deal with various isolated as
pects or with particular text fragments without any attempt to fit the
findings into a more comprehensive framework which could be named 'Aris
totle's modal theory'. Most of the studies with a wider scope have even
ended up with the conclusion that there is no general Aristotelian theory
of modalities. The few reconstructions which seek to show this theory to be
coherent and consistent can, on the other hand, all be proved to be defect
ive. These facts show that many of the ideas underlying Aristotle's hand
ling of modalities are still obscure. Some of these ideas pertain to the
meaning of the logical operators 'necessary' and 'possible'. To this day,
not even the outlines of Aristotle's logic of these modal qualifiers are
known. Nevertheless, knowledge of his modal logic seems clearly to be a
necessary precondition for a complete understanding of the many doctrines
and discussions of Aristotle in which modalities are involved. As a conse
quence it seems worth exploring Aristotle's modal logic not only for its
own sake, but also for more general reasons.
The present book is an exposition of several basic aspects of Aris
totle's views on the logic of modalities. In the course of my exposition it
will appear that the body of his theory as expounded in Chapters Two and
Three of this study is simply and transparent. In fact, it is so simple
that it will hardly be able to excite the formal logician. Yet, some as
pects of Aristotle's extension of this basic theory, especially the seman
tical presuppositions of his logic of modally qualified categorical senten
ces as set out in Chapters Eight and Nine, may strike those who are working
on theories of reference. As a consequence of this simplicity, readers who
have no knowledge of modern formal logic should have no trouble with the
main line of this study. Most of the argument will be completely accessible
to them. Some basic knowledge of modern logic, however, will certainly fa
cilitate the reading of Chapter Nine.
x PREFACE AND ACKNOWLEDGEMENTS
The book opens with an exposition of the subject and programme of the
study. Next, in Chapters Two and Three, Aristotle's general ideas about the
logic of modalities are set out. Chapter Four introduces the main competing
reconstruction of Aristotle's modal logic, i.e., Hintikka's interpretation
in terms of the statistical model. In this model, what is always the case
is necessary, and what is possible is at least once actualized. In the
course of the next chapters, I develop my rejection of Hintikka's view
while elaborating my own interpretation. In Chapter Five I show how the so
called proof of the necessity of what is always in De Caelo 1.12 can be in
corporated in the general framework set out in Chapters Two and Three. Sev
eral other explanations of De Caelo 1.12, including that of Hintikka, are
rejected. Chapter Six shows how an interpretation of De Interpretatione 9
can be provided on the basis of Aristotle's general theory of modalities.
In Chapters Seven and Eight, the relation between omnitemporality or per
manency and necessity in Posterior Analytics 1.4-6 is explored. It appears
that there is no discrepancy between what Aristotle is saying here and the
contents of De Caelo 1.12. Finally, in Chapter Nine, Aristotle's apodeictic
syllogistic is examined. It is shown that its base consisting of the per
fect apodeictic moods, the apodeictic conversion rules and apodeictic ec
thesis is sound with respect to the interpretation Aristotle has in mind.
Moreover, a striking variance between what is said about apodeictic syllo
gisms in Prior Analytics and in Posterior Analytics is dissolved. Hence,
the outcome of this study is that Aristotle's modal logic exhibits a coher
ence and consistency which is much greater than it has usually been credit
ed with.
The debts I have incurred while I was writing this book are numerous. One
of my principal debts is to Professor L.M. de Rijk of the University of
Leiden, who has been a source of intellectual stimulation during the entire
period of conceiving and preparing this work. Other persons have contribut
ed to its completion as well. Professor G. Nuchelmans meticulously read an
earlier version of this study and helped me with several valuable remarks.
I have also profited from the criticism and advice of Professor H.M.
Bracken, who draw my attention to various flaws in the penultimate version.
Dr. J.A. van Eck criticized an earlier draft of Chapter Six. Professor S.
Knuuttila commented on an older version of Chapter Seven, while Dr. E.C.W.
Krabbe saved me from some infelicities in Chapter Nine. I owe thanks as
well to Mr. J. Kearey, who corrected my English. Much of Chapter Seven ap-
PREFACE AND ACKNOWLEDGEMENTS xi
peared in Van Rijen (1984), in Archiv fur Geschichte der Philosophie. I
thank the editors of this Journal for permitting me to use this material
again. Finally, I would like to express my gratitude to Ms. C. de Ruiter
and Ms. M. Schoor1emmer, who produced the typescripts of several drafts of
this text with great patience and care.