Necessity or Contingency: The Master Argument

303 Pages·1996·14.96 MB·English

by  Jules Vuillemin

NECESSITY
or
CONTINGENCY

CSLI
Lecture Notes
No. 56
NECESSITY
or
CONTINGENCY
THE MASTER ARGUMENT
Jules Vuillemin
Publications
CENTER FOR THE STUDY OF
LANGUAGE AND INFORMATION
STANFORD, CALIFORNIA
Copyright © 1996
Center for the Study of Language and Information
Leland Stanford Junior University
Printed in the United States
99 98 97 96 96 543H
Library of Congress Cataloging-in-Publication Data
Vuillemin, Jules.
[Ne'cessite' ou contingence. English]
Necessity or contingency : the master argument / Jules Vuillemin.
p. cm. — (CSLI lecture notes ; no. 56)
Includes bibliographical references and index.
ISBN 1-881526-85-2 (pbk. : alk. paper)
ISBN 1-881526-86-0 (hardback : alk. paper)
i. Necessity (Philosophy) — History. 2. Contingency (Philosophy) — History.
3. Diodorus Cronus, 4th cent. B.C. 4. Philosophy, Ancient. I. Title. II. Series.
1996
— dc2O 95-50100
CIP
Cover design by Tony Gee
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International, and Xerox PARC to further research and development of integrated
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Contents
Introduction xi
Acknowledgements xiii
Part I The Master Argument 1
1 The Master Argument. On the Shortcomings of Some
Past Interpretations. Conditions to be Fulfilled by
any Acceptable Interpretation. 3
1.1 The text of Epictetus. 3
1.2 Zeller's interpretation. Confusion of the logical and the
chronological. 4
1.3 Ambiguity in the first premise: Necessity and
irrevocability. Signification of the first premise. 7
1.4 Prior's interpretation: It supposes two supplementary
premises, one of which is explicitly rejected by Aristotle;
it supposes the first premise ambiguous. 8
2 Reconstruction of the Master Argument. 15
2.1 An Aristotelian paradigm: De Caelo, I, 28366-17; its
context. 15
2.2 The principle of the conservation of modal status. 16
2.3 The principle of the possible realization of the possible
interpreted as a principle of pure modal logic. 18
2.4 The principle of possible realization of the possible as
principle of synchronic contraction of the possible and
diachronic expansion of the necessary. 21
2.5 The principle of conditional necessity. 24
2.6 The irrevocability of the past or the principle of the
impossibility of realizing the possible in the past. 26
vi / CONTENTS
2.7 The principle of the subsistence of a possible that is not
to be realized. 31
2.8 Reconstruction of the De Caelo demonstration. 33
2.9 Reconstruction of the Master Argument. 35
2.10 Sketch of a formal reconstruction of the Aristotelian
reasoning at De Caelo, I, 283*6-17. 36
2.11 Sketch of a formal reconstruction of the Master
argument. 38
Part II Systems of Necessity: The Megarians
and the Stoics 41
3 A System of Logical Fatalism: Diodorus
Cronus. 43
3.1 Diodorus' Solution. 43
3.2 Two possible interpretations as regards the object of the
Diodorean modalities: nominalism and realism. 46
3.3 The meaning of Diodorean implication. 52
3.4 Diodorean nominalism. 56
3.5 Diodorus' necessitarianism. 62
4 Eternal Return and Cyclical Time: Cleanthes'
Solution. 69
4.1 First conjecture. Necessity of the past secundum vocem
and secundum rem: Ockham's conception on Prior's
hypothetical reconstruction. Modality de dicto and
modality de re. 70
4.2 Inadequacy of Ockham's solution. Incrimination of the
principle of conditional necessity: John Duns
Scotus. 79
4.3 Cleanthes again and the second conjecture: the
conditional character of the necessity of the past
according to Cleanthes; the interpretation of
Leibniz. 92
4.4 Third conjecture: cyclical time and the numerical
conception of the identity of beings in eternal
return. 97
5 Freedom as an Element of Fate: Chrysippus. 105
5.1 Were Chrysippus' doubts about the thesis of pure modal
logic according to which from the possible the impossible
does not follow, they would be about its negative form,
not about its positive form. 106
CONTENTS / vii
5.2 Chrysippus' doubt about the interdefinability of the
modalities. From the non-possibility of an event's
occurrence it cannot be concluded that its opposite is
necessary. 110
5.3 The non-standard modal system according to
Chrysippus. 115
5.4 A system related to Prior's system Q; the double logical
square of Chrysippean modalities and the double
temporal index in the Master Argument's second
premise. 120
5.5 A Philonian doubt about the second premise? 126
Part III Systems of Contingency: The Lyceum,
The Garden, The Academy 131
6 Towards Rehabilitating Opinion as Probable
Knowledge of Contingent Things. Aristotle. 133
6.1 De Interpretatione, Chapter IX. 133
6.2 Outline of the passage: Introduction (18a28-34): The
problem raised. 137
6.3 Validity of the principle of non-contradiction and the law
of excluded middle (18a38 and 18fc17-25). 139
6.4 Critical examination of the Megarian theory (18a34-18617
and 18ft25-19a22). 141
6.5 Aristotle's solution (19a22-1964); conditional necessity
and exceptions to the principle of bivalence. 144
6.6 Aristotle's general conception confirms the De
Interpretatione solution; the difference between Aristotle
and Diodorus. 149
6.7 First interpretative hypothesis: More than two
truth-values. 154
6.8 Second interpretative hypothesis: propositions without a
determinate truth-value. 157
6.9 Third interpretative hypothesis: probability. 161
7 Epicurus and Intuitionism. 169
7.1 First logical interpretation of the Epicurean denial of the
excluded middle: the three-valued logic of Lukasiewicz;
reasons for rejecting this solution. 171
7.2 Second logical interpretation of the Epicurean negation of
the excluded middle: The Intuitionist System. 173
viii / CONTENTS
7.3 Are the Epicurean 'criteria' compatible with
intuitionism? 174
7.4 Consequences of the Epicurean criteria: Plurality of
hypotheses and rejection of the excluded middle. 182
7.5 Epicureanism and the Master Argument. 185
7.6 Other intuitionist conceptions of reality: Descartes and
Kant. 187
8 Carneades and the Skeptical Nominalism of the
Modalities. 207
8.1 What is the relation between the principle of the
excluded middle and the principle of causality (De Fato,
X-XII)? 207
8.2 Aristotle's dogmatic definition of truth called into
question (De Fato, XIV). 210
8.3 Carneades and the Master Argument (De Fato, IX). 212
8.4 From Carneades to the logics of "fictive" names:
Buridan's ampliation. 215
8.5 Carneades does not abandon the principle of conditional
necessity; he simply deprives it of the ontological
involvement conferred upon it by the dogmatic
interpretation of truth. 219
9 Platonism and Conditional Necessity. 225
9.1 Platonism and the principle of conditional necessity. 225
9.2 Consequences of the connection between conditional
necessity and the substantiality of the sensible for
modality, causality and freedom. 230
9.3 The consequences of abandoning the principle of
conditional necessity and the substantiality of the
sensible world for the Platonic and Platonistic theories of
modality, causality and freedom. The same abandonment
entails similar consequences for Duns Scotus. 233
10 Epilogue 243
10.1 The impasse of natural language. 244
10.2 A probabilistic reconstruction of the Master Argument:
Diodorus' solution. 246
10.3 The special status of premise (C): Chrysippus' solution
and the 'Unique Law of Chance'. 251
10.4 Contingency and ignorance: The statistical mix. 257
10.5 Contingency and nature: The state of
superposition. 261
CONTENTS / ix
Bibliography 267
Index of quotations of ancient and mediaeval texts 279
Index of Proper Names 285