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(D. 1037), Logical Theory, and the Aristotelian Tradition

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AVICENNA (D. 1037), LOGICAL THEORY, AND THE ARISTOTELIAN TRADITION The Institute of Islamic Studies at McGill University, Montreal January 2014 A Thesis submitted to McGill University in partial fulfillment of the requirements for the degree of Doctor of Philosophy ©Kamran I. Karimullah 2014 1 ABSTRACT In this study I examine Avicenna’s (d. 1037) theory of conditional propositions, (or “if, then” sentences, qaḍāyā šarṭiyya muttaṣila), and his system of repetitive and conjunctive syllogisms (qiyāsāt istiṯnāʾiyya, qiyāsāt iqtirāniyya). I show that Avicenna’s theory of conditional propositions is conceived as a rejection of Alfarabi’s “context theory”–based system of conditional propositions and conditional syllogisms (qaḍāyā šarṭiyya). I also show that Avicenna’s “if, then” connectors operate as propositional connectives in the modern, technical sense of that term. However, the theoretical bases of Avicenna’s conjunctive syllogistic belong to the Prior Analytics. The system of conjunctive syllogisms and quantified conditionals, which is one of Avicenna’s most important contributions to the history of formal logic, is explicable in terms of Aristotle’s syllogistic theory. Stoic logic, on the other hand, plays a minor role. 2 RÉSUMÉ Dans cette étude, j’examine la théorie des propositions conditionnelles (qaḍāyā šarṭiyya muttaṣila) d’Avicenne (m. 1037) ainsi que son système des syllogismes répétitifs et conjonctifs (qiyāsāt istiṯnāʾiyya et qiyāsāt iqtirāniyya). J’établie que Avicenne a formulé sa théorie des propositions conditionnelles afin de rejeter le système des propositions conditionnelles et syllogismes hypothétiques (qiyāsāt šarṭiyya) d’Alfarabi (m. 950), qui s’est fondé sur une théorie de langue dans laquelle le contexte dialectique demeure au centre de l’analyse des propositions et des syllogismes (appelée “context theory”). Ainsi je démontre que le connecteur conditionnel “si, alors” dans la logique hypothétique d’Avicenne fonctionne comme l’opérateur logique au sens technique du terme. Pourtant, les bases théorétiques du syllogisme conjonctif sont tirées des Premiers Analytiques d’Aristote. Le système du syllogisme conjonctif et la théorie des conditionnelles quantifiées, que je considère ici parmi les apports les plus importants á l’histoire de la logique formelle, sont explicables à la lumière de la théorie syllogistique d’Aristote. Cependant, la logique stoïcienne ne joue pas un rôle essentiel. 3 ACKNOWLEDGMENTS My debt to my thesis supervisor Robert Wisnovsky cannot be expressed adequately in words. His kindness, generosity, wisdom, attention to detail, and encouragement at every instance has been more than could be expected. He will serve as a model for me in the future. This thesis could not have been written without the support of my beloved wife Sirad. It has been a long road, though with much joy: Mustafa and Nusayba were born during this journey. I thank her for help, support, good-humor, and, above all, patience. And to my parents, for—everything. 4 CONTENTS ABSTRACT RÉSUMÉ ACKNOWLEDGMENTS INTRODUCTION CHAPTER 1: THE STUDY OF AVICENNA’S THEORY OF CONDITIONAL PROPOSITIONS AND REPETITIVE AND CONJUNCTIVE SYLLOGISMS §1.0: CHAPTER OVERVIEW §1.1: VIRTUES OF RESCHER’S INTERPRETATION OF AVICENNA’S THEORY OF HYPOTHETICAL (“IF…THEN…” AND “EITHER…OR…”) PROPOSITIONS §1.2.0: INADEQUACIES OF RESCHER’S INTERPRETATION OF AVICENNA’S THEORY OF HYPOTHETICAL (“IF…THEN…” AND “EITHER…OR…”) SYLLOGISMS §1.2.1: HISTORIOLOGICAL CRITICISMS OF RESCHER’S INTERPRETATION §1.2.2: CONCEPTUAL CRITICISMS OF RESCHER’S INTERPRETATION §1.3: AFTER RESCHER 1: SHEHABY, GÄTJE AND MARÓTH ON ALFARABI AND AVICENNA’S THEORY OF HYPOTHETICAL (“IF…THEN…” AND “EITHER…OR…”) SYLLOGISMS §1.4: AFTER RESCHER 2: SHEHABY AND MARÓTH ON AVICENNA’S “PROPOSITIONAL LOGIC” §1.5: AFTER RESCHER 3: AVICENNA AND ARISTOTLE’S LOGICAL THEORY CHAPTER 2: ALFARABI ON CONDITIONALS §1 INTRODUCTION §2 THE ‘CONTEXT THEORY’ OF LOGIC: TRUTH, ASSENT, AND CONDITIONALS §3 CONDITIONALS IN ARGUMENTATIVE CONTEXTS §4 CLASSIFICATION OF IMPLICATION (LUZŪM) IN APCA: CONDITIONS OF ASSENT, CONTRADICTION §5 CONDITIONAL PROPOSITIONS AND INFERENTIAL VALIDITY §6 CONCLUSION CHAPTER 3: AVICENNA AND ALFARABI ON THE SUBJECT MATTER OF LOGIC, AND AVICENNA’S REJECTION OF COMPLETE (TĀMM) AND INCOMPLETE (ĠAYR TĀMM) CONNECTION §3.0 INTRODUCTION §3.1.1 ALFARABI ON THE SUBJECT MATTER OF LOGIC §3.1.2 AVICENNA ON THE AIMS, UTILITY AND SUBJECT MATTER OF LOGIC §3.2.0 COMPLETE/INCOMPLETE VS. COINCIDENTAL/RESTRICTED FOLLOWING: INTRODUCTION 5 §3.2.1 THE NATURE OF CONNECTIVE CONDITIONAL PROPOSITIONS AND THE COMPLETE/INCOMPLETE DIVISION OF CONNECTION (ITTIṢĀL) §3.3.0 AVICENNA ON REPETITIVE SYLLOGISMS IN ŠQ VIII: INTRODUCTION §3.3.1 AVICENNA’S SIMPLICITER AND RESTRICTED CONDITIONALS IN REPETITIVE SYLLOGISMS IN ŠQ VIII CHAPTER 4: INTERPRETING AVICENNA’S CONDITIONAL SYLLOGISTIC AS A PROPOSITIONAL LOGIC §4.0 INTRODUCTION §4.1 PROPOSITIONAL LOGIC IN ISLAMIC LATE ANTIQUITY? ENGAGING IN ANACHRONISM §4.2 CONDITION FP: AVICENNA ON DOUBT AND CONDITIONALITY §4.3 CONDITION WFF: AVICENNA ON NESTED CONDITIONALS AND REPETITIVE SYLLOGISMS (QIYĀSĀT ISTIṮNĀʾIYYA) CHAPTER 5: AVICENNA ON PRIOR ANALYTICS A23: CONJUNCTIVE SYLLOGISMS, REPETITIVE SYLLOGISMS, AND REDUCTION §5.1 INTRODUCTION §5.2.1 INTRODUCTORY REMARKS ON AVICENNA’S CONJUNCTIVE SYLLOGISMS (QIYĀSĀT IQTIRĀNIYYA): §5.2.2 AVICENNA’S CONJUNCTIVE SYLLOGISMS: ON THE “MIDDLE PART”, SYLLOGISTIC FIGURES, AND “STRONG RELEVANCE” §5.2.3 AVICENNA’S CONJUNCTIVE SYLLOGISMS: A-, I, E, O-CONDITIONALS §5.2.4 AVICENNA’S CONJUNCTIVE SYLLOGISMS: DIRECT AND INDIRECT REDUCTION IN AVICENNA AND ARISTOTLE §5.3.1 INTRODUCTORY REMARKS ON THE PROBLEM OF REPETITIVE SYLLOGISMS, AND THEIR REDUCTION TO CONJUNCTIVE SYLLOGISMS §5.3.2 ARISTOTLE ON DIRECT AND INDIRECT REDUCTION, AND THE REDUCTION OF PER IMPOSSIBILE SYLLOGISMS AND “SYLLOGISMS FROM A HYPOTHESIS” §5.3.3 AVICENNA ON THE REDUCTION OF CONDITIONAL SYLLOGISMS CONCLUSION BIBLIOGRAPHY 6 INTRODUCTION This study has two main objectives. The first is to examine Avicenna’s theory of conditionals. According to the convention Avicenna inherited from earlier logicians— especially Alfarabi—what I call conditionals, or “if, then” sentences, Avicenna calls “connective conditional propositions (qaḍāyā šarṭiyya muttaṣila)”.1 The second objective is to examine how Avicenna deploys conditionals in syllogistic forms of reasoning. These objectives are closely related, but if there is any deeper philosophical conclusion to be drawn from this study, it is that for Avicenna the second project is prior to the first project. In Avicenna’s systematic development of his theory of conditionals and conditional syllogisms in ŠQ V-IX, Avicenna presents his theory of restricted (ʿalā t-taḥqīq) and simpliciter (muṭlaq) conditionals,2 and his theory of quantified conditionals, before his presentation of the conjunctive syllogistic (qiyāsāt iqtirāniyya) in ŠQ VI,3 and before his exposition of repetitive syllogisms (qiyāsāt istiṯnāʾiyya) in ŠQ VIII.4 Nevertheless, despite the appearance that Avicenna develops his theory of conditionals prior to his theory of the syllogism, in fact, the converse is closer to the mark. It is Avicenna’s intuitions about what makes an argument with conditionals good that dictate the final form of his theory of conditional propositions, not the reverse. 1 These stand in contrast with “disjunctive conditional propositions (qaḍāyā šarṭiyya munfaṣila)”, which will not be dealt with in this study. 2 See N. Rescher, “Avicenna on the Logic of the ‘Conditional’ Proposition,” in Studies in the History of Arabic Logic (Pittsburgh: Pittsburgh University Press, 1963), 76-86. 3 Other manuscripts of this portion of the Šifāʾ make what is called Book VII in the edition follow Book V in the edition. The order in the printed edition is: V (conditional propositions) VI (conjunctive syllogisms) VII (conditional proposition equipollence). Other manuscripts (e.g. Ayasofia 2442 and Nuruosmaniye 2710) have the following order: (conditional propositions) (conditional proposition equipollence) (conjunctive syllogisms). This latter must be the correct one, since Avicenna uses the equipollence relations from ŠQ VII in the reduction of imperfect conjunctive syllogisms to perfect ones in ŠQ VI. 4 On the translation of istiṯnāʾī as “repetitive”, see K. Gyekye, “The Term ‘istithnāʾ’ in Arabic Logic”, Journal of the American Oriental Society 92 (1972): 88-92). 7 The truth that intuitions about what makes an argument good dictate the account of what makes a conditional true is evidently on display in Avicenna. Without a doubt, the theoretical work in ŠQ V and VII is undertaken in order to make possible an account of valid inferences with conditional premises and conclusions that closely parallels Aristotle’s syllogistic theory set out in An. Pr. A1-7. In other words, it is because Avicenna feels that Aristotle’s account of logical validity is the correct account that he feels the need to develop a theory of quantified conditionals, and a doctrine of genuine versus absolute following (luzūm) and concomitance (muwāfaqa, maʿiyya). Yet, this belief also impels him to reject earlier theories of the conditional such as those found in Alfarabi (and likely originating in the work of Galen5) that are based on complete (tāmm) and incomplete (ġayr tāmm, nāqiṣ) connection (ittiṣāl, ittibāʿ) and incompatibility (ʿinād, taʿānud) because they are incompatible with Aristotle’s views of syllogistic validity. To varying degrees, secondary literature has not appreciated
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