Necessity or Contingency: The Master Argument (Center for the Study of Language and Information - Lecture Notes)

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 5 4 3 H 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

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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 Index of Proper Names 285

279

Introduction The Master Argument, recorded by Epictetus, indicates that Diodorus had deduced a contradiction from the conjoint assertion of three propositions. Epictetus adds that three solutions of the aporia had been obtained by denying one or another of the propositions advanced while maintaining the other two. The argument, which has to do with necessity and contingency and therefore with freedom, has attracted the attention of logicians above all. In any case there have been many attempts at reconstructing it in logical terms, without excessive worry about historical plausibility and with the foregone conclusion that it was sophistic since it directly imperiled our common sense notion of freedom. On both of these counts I have taken exception to recent tradition. The success of the argument with the Ancients, and with Ancients who were no mean logicians, seemed reason for presuming that the Master Argument is not sophistic and that the contradiction it produces is a real one. On the other side, I looked for a classical text containing the propositions stated by Epictetus and which could have furnished Diodorus with the material for his argument. I believe to have found such a text in Aristotle's De Caelo. In order to demonstrate the contradiction in the propositions thus restored, I had in my turn to translate them into logical terms. It is unlikely that Diodorus proceeded in such a way. Although the translation I have proposed tries to remain faithful to its models as they have been handed down to us, it inevitably gives them a precision they did not have in themselves. This indulgence in precision amounts to historical inexactitude but seemed necessary nevertheless as it had to do with restoring a reduction to the absurd. There is one distinctive feature of the translation that must be noticed. The propositions figuring in the Master Argument are in-

xii / NECESSITY OR CONTINGENCY: THE MASTER ARGUMENT terpreted in terms of temporal modal logic where both the modalities and the statements they govern have chronological indices. This means that the force of the argument comes not from purely logical or modal considerations, but from our experience of time. To bring to its complete end the research undertaken here, I would have had to assign to the Master Argument and to each of the solutions it is susceptible of, an explicit axiomatic system formalized according to a set of rules. For want of competence, of stamina, of time, I have been content to formulate only what was needed to elucidate the argumentation. Justification for the first four chapters is to be found in the Epictetus passage. The remaining chapters extend the debate about the Master Argument to Greek philosophy at large. In this way it is seen that principles are challenged-even logical ones at that-which are not mentioned in the Epictetus passage but which must have played their role in the argument. The reader will judge whether that extension is legitimate or not. As one well imagines, the debate on the issue was continued by the philosophers of the Middle Ages and the Moderns. This was quite generally done in ignorance of the Master Argument itself; but I have had no hesitation in appealing to them where they might be apt to help explain or specify the position of the Ancients.

INTRODUCTION / xiii

Acknowledgements This book builds on earlier studies (Vuillemin, 1979, 1983) and especially on Necessite ou contingence, I'aporie de Diodore et les systemes philosophiques (Les Editions de Minuit-La Fondation Singer Polignac, Paris, 1984). I considerably shortened this last work and eliminated the systematic considerations not directly pertinent to the Master Argument. I corrected it on the occasion of an objection raised by M.H. Angstl (his letter and my reply to it were published in the Allgemeine Zeitschrift fur Philosophic, XI 3, 1986, pp. 79-87). Finally I added the present, unpublished Epilogue. M. Thomas F. Morran has translated into English this new French version. My thanks go to Professor J. Moravcsik for his criticism, Bill Graham, who revised the text, Mrs. L. von Kampen, who transformed a manuscript into a book, and to Patrick Suppes, my good friend.

Part I

The Master Argument

The Master Argument. On the Shortcomings of Some Past Interpretations. Conditions to be Fulfilled by any Acceptable Interpretation. 1.1

The text of Epictetus.

Epictetus gives the following account of the argument. Here, it seems to me, are the points upon which the Master Argument was posed: there is, for these three propositions, a conflict between any two of them taken together and the third: 'Every true proposition about the past is necessary. The impossible does not logically follow from the possible. What neither is presently true nor will be so is possible'. Having noticed this conflict, Diodorus used the plausibility of the first two to prove the following: 'Nothing is possible which is not presently true and is not to be so in the future'. Another, for the two propositions to keep, will maintain these two: 'There is a possible which neither is presently true nor will be so; the impossible does not logically follow from the possible'; but then it is not exact to say that every true proposition about the past is necessary; that is what the school of Cleanthes seems to maintain (SVF I 489) with whom Antipater is generally in agreement (SVF III Ant. 30). Others (namely Chrysippus, SVF II 283) admit the two other propositions: There is a possible which neither is presently true nor will be so; every true proposition about the past is necessary'; but then the impossible follows logically from the possible. But there is no way to maintain the three propositions

4 / NECESSITY OR CONTINGENCY: THE MASTER ARGUMENT at once, since in every case there is a conflict between one and the other two.1 To this account Epictetus adds an ironic commentary on the virtues of erudition. To one who boasted of having read Antipater's treatise on the Master Argument he exclaims: "What more do you have, you, for having read it? What opinion have you formed on the question? You might just as well speak to us of Helen, of Priam and of that isle of Calypso that hasn't existed in the least and never will".2 The irony of Epictetus is aimed neither at the doctrine nor at the moral consequences that could be drawn from the argument, but only at the vanity of logical quibbles. We cannot speculate then on any opposition of principle that Epictetus might have had to the supposedly morally disastrous consequences of the argument. Such is the only explicit text on the Master Argument. Most interpretations and reconstructions of the argument that have been given can be put into one of three categories. They all agree, implicitly at least, on denouncing its disastrous moral consequences and on flushing out some ambiguity or other in the premises, which they in turn hold responsible for these consequences. In order to save human freedom called into question by the Master Argument it has been postulated that Diodorus was guilty of making one of the following confusions. He took the word 'follow' in two different senses in the first two premises. He played, in the first premise, either on two possible senses of the way in which a proposition can be concerned with the past or on two senses of the word 'necessary'. Or finally, he played on a more general ambiguity hidden in the usage of indeterminate grammatical tenses.

1.2

Zeller's interpretation. Confusion of the logical and the chronological.

Zeller3 has given the following syllogistic interpretation of the argument. "If something was possible which neither is nor will be, an impossible would result from a possible. But an impossible cannot result from a possible. Thus nothing is possible which neither is nor will be". The minor premise illustrates Diodorus' second proposition. The conditional major premise has Diodorus' third proposition as antecedent Epictetus, 1916, II, 19 1-4; Doring, 1972, p. 131; the parentheses refer to the von Arnim collection, 1905; I follow the Brehier translation, revised by Goldschmidt in Brehier, 1962, pp. 932-933. Brehier translates axoXoutfetv correctly by 'logically follows'. 2 Ibid., p. 933. 3 Zeller, 1910, p. 254.

ZELLER'S INTERPRETATION / 5 and the negation of his second as consequent. The correlation of the two must evidently express the argument's first proposition. "The hypothetical major premise was in need of some basis; and it found it by way of the proposition saying that every past fact is necessary. Indeed, when of two mutually exclusive cases one has turned out to be realized, the possibility of the other finds itself cancelled out, since that which has happened can no longer be changed... This second case, then, is now impossible; had it been possible beforehand, then, in the opinion of Diodorus, an impossible would have resulted from a possible". This reconstruction supposes a quaternio terminorum in the argument of Diodorus: one based on the ambiguity of the words OLnoXovdelv and d&warof. In the major premise, the first of these words does indeed have the temporal sense of 'follow in succession', whereas, in the minor premise, on the contrary, it has the logical sense of 'follow logically'. In the major premise, from the realization of a possible can and must result the de facto impossibility of another possible, since the event realized excludes the contrary of what it produces. But the minor premise signifies that nothing is possible of which the realization would result in something impossible in itself. According to P.M. Schuhl, it is possible to restore a purely logical meaning to the conditional major premise, thereby validating the argument in rendering its elements homogeneous. It is not that the impossibility of an event simply succeeds its possibility: it is rather a strict consequence of it, given the realization of its contrary.4 To illustrate with an example from Kurt von Fritz,5 the conditional major premise would mean "If the Carthaginians win today at Cannes, it follows that the Romans don't win today at Cannes, which, beforehand, had seemed possible". But as von Fritz points out, Zeller would have answered that the impossibility referred to by Schuhl is not an impossibility in itself, in the logical sense, but on the contrary a de facto impossibility, which is not actually far removed from the impossibility due to temporal succession, as understood by Zeller. Mr. G.H. von Wright has given an elegant and logically impeccable, formally modified version of the intuition contained in this type of interpretation. 6 He begins by supposing p to be possible. As a consequence of that supposition, for some future moment, t, it is possible that p at t. But, in virtue of Diodorus' third premise, it is true that not-p at t. As a consequence of his first premise, for every moment, i', 4

Schuhl, I960, pp. 74-75. Von Fritz, review of Schuhl, 1962, pp. 138-152. 6 von Wright, 1979a. Compare, however, von Wright's interpretation of the second premise with the interpretation that will be given in 2.3 and 2.4. 5

6 / NECESSITY OR CONTINGENCY: THE MASTER ARGUMENT later than t, it will be impossible that p at t'. Thus the supposition of the non-realization of the possible leads to an impossibility, if one interprets the second Diodorean premise as follows: if the proposition p at t is prospectively possible, that same proposition cannot become impossible at some later moment of time. In interpreting the second Diodorean premise as a prohibition of the proposition p's changing modality over time, Mr. von Wright brings to light the metaphysical, as opposed to the logical, sense that this first type of interpretation is obliged to suppose. The difficulty is that the retrospective impossibility of p, which, according to the first premise, follows upon the non-realization of p at t begins at a moment, t', later than t, no matter what hypothesis might be made as to the continuity of time. The Master Argument would be incontestable only if t' coincided with t, and the second premise is then supposed to be meant to assure the validity of the synthetic judgment by which the conservation of the modality of p from t to t' is guaranteed. In all these cases, the commentators reject the validity of the Master Argument in accusing Diodorus of confusing a de facto necessity with a necessity of principle; and in so doing they are immediately in conflict with all of the ancient commentators. The translation of Epictetus accepted here, and against these modern commentators, disqualifies these interpretations from the start, in taking v.K.oXovdelv as 'follow logically'. In this way the tradition of the Ancients is respected, though without, of course, an a priori refusal to examine whether the notions of possible and of impossible here have a univocal meaning or not.7 As Mr. Boudot points out, "the term rendered by 'follow [logically]' (aKoXovtieli1) is that which the Megaro-Stoics use for designating what we call implication. Certainly the definition varies from author to author, but no one identifies implication and temporal succession.8 For Diodorus, '