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Published online by Cambridge University Press:  05 August 2014

Kamran Karimullah*
Institute of Islamic Studies, McGill University, 3485 rue McTavish Montreal, QC H3A 01E, Canada Department of Classics and Ancient History, University of Manchester, Oxford Road Manchester, M13 9PL, United Kingdom


I examine the theory of conditional propositions (qaḍāyā šarṭiyya muttaṣila) and conditional syllogisms (qiyāsāt šarṭiyya) in the logical works of Alfarabi (d. 950). I contextualize Alfarabi's logical doctrines related to conditional reasoning against the backdrop of the context-theory of logic, which was developed by Aristotle's ancient commentators. I show that Alfarabi thought that conditional propositions have truth-conditions. I provide conjectural truth-conditions for conditional propositions, and conjectural validity-conditions for connective conditional syllogisms. These truth-conditions and validity-conditions are shown to be sensitive to the pragmatic conditions in which conditional propositions and arguments are deployed. I end by suggesting that Alfarabi's logical pragmatism is a consequence of his adoption of the late antique context-theory of logic rather than a result of his developing Aristotle's formal syllogistic theory adumbrated in the Prior Analytics.


Dans cette étude j'examine la théorie des propositions conditionnelles (qaḍāyā šarṭiyya muttaṣila) d'Alfarabi (m. 950) et son système des syllogismes conditionnels (qiyāsāt šarṭiyya). J'établis qu'Alfarabi a formulé sa théorie des propositions conditionnelles et syllogismes conditionnels comme une extension d'une théorie de langue dans laquelle le contexte dialectique demeure au centre de l'analyse des propositions et des syllogismes (appelée ‘context-theory’). Je démontre que selon l'avis d'Alfarabi les propositions conditionnelles ont conditions de vérité. Je fournis des conditions de vérité conjecturales et des conditions de validité conjecturales. Je suggère que ces conditions de vérité et ces conditions de validité sont sensibles aux conditions pragmatiques dans lesquelles les prémisses conditionnelles et les arguments conditionnels sont utilisés. Je conclus que le pragmatisme logique d'Alfarabi est une conséquence de son adoption d'une théorie logique sensible au contexte dialectique d'antiquité tardive plutôt qu'une conséquence de développement de la théorie syllogistique formelle d'Aristote dans les Premiers Analytiques.

Research Article
Copyright © Cambridge University Press 2014 

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1 On Avicenna's theory of conditional propositions and conditional syllogisms, see Avicenna, The Propositional Logic of Avicenna, trans. Shehaby, N. (Dordrecht/Boston, 1973)Google Scholar; Maróth, M., Ibn Sīnā und die peripatetische “Aussagenlogik”, trans. Till, J. (Leiden/New York, 1989)Google Scholar; Gätje, H., ‘Zur Lehre von den Voraussetzungsschlüssen bei Avicenna’, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften, 2 (1985): 140204Google Scholar. In this article I will refer to ‘if … then’ sentences as ‘conditional sentences’ or simply as ‘conditionals’.

2 Alfarabi, Al-Manṭiq ʿinda al-Fārābī, vol. 2, ed. Ağam, R. (Beirut, 1985), pp. 1164Google Scholar. Hereafter, I refer to this work as follows: Alfarabi, Madḫal; id., in Al-Manṭiq ʿinda al-Fārābī, vol. 2, pp. 65–93. Hereafter, I refer to this work as follows: Alfarabi, Qiyās.

3 Street, T., ‘‘The eminent later scholar’ in Avicenna's Book of the Syllogism’, Arabic Sciences and Philosophy, 11 (2001): 205–18CrossRefGoogle Scholar.

4 In Joep Lameer's superb work on Alfarabi's syllogistic, there are chapter length treatments of Alfarabi's categorical syllogisms, induction, example (tamṯīl), which Lameer translates as ‘paradigm’, analogy from the present to the absent (istidlāl bi-al-šāhid ʿalā al-ġāʾib), and legal deduction (qiyās fiqhī). Not four pages are given conditional syllogisms; cf. Lameer, J., Al-Fārābī and Aristotelian Syllogistics: Greek Theory and Islamic Practice (Leiden/New York, 1994), pp. 44–7Google Scholar.

5 Black, D., Logic and Aristotle's Rhetoric and Poetics in Medieval Arabic Philosophy (Leiden, 1990), pp. 1751Google Scholar.

6 Black, Logic and Aristotle's Rhetoric and Poetics, p. 52.

7 Ibid., p. 79: ‘The development by the Islamic philosophers of an alternative solution to the problem of how to divide and classify the logical disciplines seems to be closely linked to their resolution of another key issue in the Alexandrian versions of the context theory, that of the degree to which all the logical arts, including rhetoric and poetics, are syllogistic in their structures. In this regard, there is general agreement among the Islamic philosophers that both rhetoric and poetics are syllogistic in some way, although there remains considerable diversity in the syllogistic interpretation provided for them’.

8 Speca, A., Hypothetical Syllogistic and Stoic Logic (Leiden, 2001)Google Scholar. Citing Boethius, Miklós Maróth reports that a hypothetical syllogistic of some sort was developed by Aristotle's students Theophrastus and Eudemus; Maróth, Aussagenlogik, pp. 33ff. Cf. Barnes, J., Terms and Sentences: Theophrastus and Hypothetical Syllogisms (London, 1984)Google Scholar. Maróth must be referring to Theophrastus' theory of “prosleptic syllogisms”, in which one premise appears in the form of a conditional sentence; see Lejewski, C., “On prosleptic syllogisms”, Notre Dame Journal of Formal Logic, 2–3 (1961): 158–76CrossRefGoogle Scholar.

9 Lameer, Al-Fārābī and Aristotelian Syllogistics, p. 45.

10 Black, Logic and Aristotle's Rhetoric and Poetics, p. 103.

11 Alfarabi, Al-Manṭiq ʿinda al-Fārābī, vol. 3, ed. ʿAğam, R. (Beirut, 1985), pp. 1396Google Scholar. Hereafter, I refer to this book as follows: Alfarabi, Ğadal. There are two dissertation-format translations of Alfarabi's Kitāb al-Ğadal. The first is by Dominique Mallet, “La dialectique dans la philosophie d'Abū Naṣr al-Fārābī”, PhD diss., Université de Lille III, 1992. The second is by Michael DiPasquale, “Alfarabi and the starting point of Islamic philosophy: a study of the Kitāb al-Jadal (Book of Dialectic)”, PhD diss., Harvard University, Harvard University, 2002.

12 Black, Logic and Aristotle's Rhetoric and Poetics, pp. 181–92.

13 Black, Logic and Aristotle's Rhetoric and Poetics, p. 76. For a thematically related treatment of taṣdīq (and iḏʿān), see also Smith, W. C., ‘Faith as taṣdīq’, in Morewedge, P. (ed.), Islamic Philosophical Theology (Albany, 1979), pp. 96119Google Scholar.

14 Black, Logic and Aristotle's Rhetoric and Poetics, pp. 75f.

15 Ibid., pp. 36–51.

16 Alfarabi, Kitāb al-Alfāẓ al-mustaʿmala fī al-manṭiq, ed. Mahdi, M. (Beirut, 1968), p. 96.2–3Google Scholar. It is important to note that it is not until §55 that Alfarabi finally explicitly identifies as ‘syllogisms’ those things he refers to prior to §55 as ‘the ways and things’ that lead the mind to give its assent to something. Alfarabi's words suggest that, in his view, logic and syllogism are coextensive.

17 Alfarabi, Alfāẓ, pp. 98.11–100.2.

18 Black, Logic and Aristotle's Rhetoric and Poetics, pp. 76f.

19 Ibid., p. 34.

20 Ibid., p. 181.

21 Ibid., p. 76.

22 I will return to this important point with respect to the truth of conditionals in particular in Section 4.

23 Lear, J., Aristotle and Logical Theory (Cambridge, 1980), p. 36Google Scholar.

24 Ibid., p. 34.

25 Ibid.

26 Sc. al-qiyās al-šarṭī al-muttaṣil.

27 Reading ‘tatabayyanu’ for ‘yatabayyanu’.

28 Some authors (Afnan, S., Avicenna: His Life and Works [London, 1958], p. 93Google Scholar; Avicenna, Remarks and Admonitions, Part One: Logic, trans. Inati, S. [Toronto, 1984], p. 13Google Scholar) have translated ‘taḍammun’ as ‘implication’, which, if adopted, would be a source of great confusion. ‘Taḍammun’ is used to talk about the way in which terms signify meanings; in the way that, for example, the term ‘human’ signifies animal. It is for this reason that Ahmed (Avicenna, Avicenna's Deliverance: Logic, trans. Ahmed, A. [Karachi, 2011], pp. 10f, 174Google Scholar) translates ‘taḍammun’ as ‘inclusion’, viz. a concept such as human includes the concept of animal in it because of the genus-species relation between them. Similarly, Goichon (Avicenna, Livre des directives et remarques, trans. Goichon, A.-M. [Paris, 1951], pp. 82fGoogle Scholar) takes ‘taḍammun’ to mean the way in which a term (nom, lafẓ) such as ‘triangle’ refers (se refère, yadullu ʿalā) indirectly to a concept such as ‘figure’, which is a constitutive part of the concept to which the term properly belongs, viz. ‘three-sided figure’. Obviously, none of these is quite the sense that Alfarabi intends to convey here.

29 Reading ‘lam yubṭal bi-himā’ for ‘lam tubṭal bi-himā’.

30 Alfarabi, Ğadal, p. 103.

31 Grice's view (Grice, P., ‘Indicative conditionals’, in Studies in the Way of Words [Cambridge, Massachusetts, 1989], pp. 5887Google Scholar) that material conditionals as the logical interpretation of how conditionals are used in natural language has been shown to be indefensible; see Adams, E., The Logic of Conditionals: An Application of Probability to Deductive Logic (Dordrecht/Boston, 1975)CrossRefGoogle Scholar; for psychological studies showing empirically that indicative conditionals are not normally understood as material conditionals, see J. Evans, D. Over, If (New York, 2004), p. 38. See also Bennett, J., A Philosophical Guide to Conditionals (Oxford/New York, 2003), pp. 2033CrossRefGoogle Scholar. For possible worlds semantics of counterfactual conditionals, see Stalnaker, R., ‘A theory of conditionals’, in Stalnaker, R., Harper, W., Pearce, G. (eds.), Ifs: Conditionals, Belief, Decision, Chance, and Time (Dordrecht/Boston, 1981), pp. 4156Google Scholar; Lewis, D., Counterfactuals (Malden, Massachusetts, 2001)Google Scholar. For conditionals as conditional assertions, see Von Wright, G., Logical Studies (London, 1957), pp. 127–65Google Scholar; Gauker, C., Conditionals in Context (Cambridge, Massachusetts, 2005)Google Scholar.

32 Cf. Evans and Over, If, pp. 38f.

33 Aristotle's notion of validity (i.e. what conditions must be fulfilled to be a syllogism) are formulated for categorical syllogisms only. However, George Boger's work on Aristotle (Boger, G., ‘Aristotle's underlying logic’, in Woods, J., Gabbay, D. (eds.), The Handbook of the History of Logic, vol. 1 [Amsterdam/Boston, 2004], pp. 101246, p. 234Google Scholar) can be taken to show that, loosely speaking, Aristotle's notion of validity is close enough to contemporary ones that it can be used here without too much violence being done to the text and context. John Woods and Andrew Irvine (Woods, J., Irvine, A., ‘Aristotle's early logic’, in The Handbook of the History of Logic, vol. 1, pp. 2999, p. 38Google Scholar) make what I think is a helpful distinction between Aristotle's notion of categorical syllogistic validity and syllogistic simpliciter. While the former is very different from contemporary ideas about deductive validity, the latter is rather closer. For accounts of Aristotle's notion of syllogistic validity, viz. what it means to be a syllogism, see Smiley, T., ‘What is a syllogism?’, Journal of Philosophical Logic, 2/1 (1973): 136–54CrossRefGoogle Scholar; Corcoran, J., ‘A mathematical model of Aristotle's syllogistic’, Archiv für Geschichte der Philosophie, 55/2 (1973): 191219CrossRefGoogle Scholar.

34 Alfarabi, Ğadal, p. 20.

35 Alfarabi, Al-Manṭiq ʿinda al-Fārābī, ed. ʿAğam, vol. 2, pp. 95–129. Hereafter, I cite this work as follows: Alfarabi, Taḥlīl. Roughly speaking, Ğadal seems to be a summary of books I and VIII of the Topics, whereas Taḥlīl seems to be related to Topics II to VII but also to Prior Analytics 27–32; see Mallet, D., “Le kitāb al-Taḥlīl d'Alfarabi”, Arabic Sciences and Philosophy, 4/2 (1994): 317–35CrossRefGoogle Scholar.

36 Black, Logic and Aristotle's Rhetoric and Poetics, pp. 103f.

37 Alfarabi, Ğadal, p. 14.

38 Alfarabi, Ğadal, p. 14.2–9: wa-al-ǧadalu huwa muḫāṭabatun bi-aqāwīla mašhūratin yaltamisu bihā al-insānu iḏā kāna sāʾilan ibṭāla ayyi ǧuzʾin min ǧuzʾayi al-naqīḍi ittafaqa an yatasallamahu bi-al-suʾāli ʿan muǧībin taḍammana ḥifẓahū, wa-iḏā kāna muǧīban iltamasa bihā ḥifẓa ayyi ǧuzʾin min ǧuzʾayi al-naqīḍi ittafaqa an ʿaraḍahu li-sāʾlin taḍammana ibṭālahu. fa-ibṭālu al-sāʾili ʿalā al-muǧībi mā taḍammana ḥifẓahu huwa ġaraḍu al-sāʾili wa-ḏālika huwa ġalabatuhu li-al-muǧībi, wa-ḥifẓu al-muǧībi mā taḍammana al-sāʾilu ibṭālahu huwa ġaraḍu al-muǧībi wa-ḏālika huwa ġalabatuhu li-al-sāʾili. wa-Arisṭūṭālīsu yarā anna šaʾna al-ǧadalī awwalan ibṭālu al-aqāwīli ʿalā anna al-ibṭāla innamā huwa bi-intāǧi muqābili mā yaltamisu ibṭālahu wa-lākinna šaʾnahu ʿalā al-qaṣdi al-awwali huwa al-ibṭāli wa-ammā al-iṯbātu fa-huwa min šaʾnihi ʿalā al-qaṣdi al-ṯānī.

39 See Alfarabi, Ğadal, p. 13.6.

40 For this form of the quaesitum (maṭlūb), see Alfarabi, Taḥlīl, p. 96.

41 The argument format is simplified here in order to focus on the formal logical aspects of the debate. In reality, Q does not know the thesis R is trying to defend. As a consequence, Q uses devices to try to get R to reveal the thesis to be overthrown. On the other hand, R tries to prevent Q's discovering the thesis he has been tasked with defending by dissimulation, ambiguity, and misdirection. In fact, perhaps the majority of the debate is given to this sort of jockeying for position. In the post-classical period, the analysis and formalization of these methods became a scientific discipline in its own right called adab al-baḥṯ wa-al-munāẓara. For now and in the rest of the article, I systematically suppress these combative prolegomena. See also Section 2, Text 1 above.

42 There is not a great deal of secondary literature on dialectic and the topoi in the Arabic philosophical tradition. Nevertheless, see: Maróth, M., ‘Die Rolle der Topik Avicennas in den arabischen Wissenschaften’, Acta Antiqua Academiae Scientiarum Hungariae, 29 (1981): 3341Google Scholar; id., Aussagenlogik, pp. 88–99. See also Rescher, N., The Development of Arabic Logic (Pittsburgh, 1964), 1532Google Scholar; id. Al-Kindī's sketch of Aristotle's Organon’, in Studies in the History of Arabic Logic (Pittsburgh, 1963), 32–7Google Scholar; id. ‘The logic chapter of Muḥammad ibn Aḥmad al-Khwārizmī's Encyclopaedia, Keys to the sciences (c. A.D. 980)’, Studies, pp. 74f; Black, Logic and Aristotle's Rhetoric and Poetics, pp. 156–7; Lameer, Al-Fārābī and Aristotelian Syllogistics, p. 149; Hugonnard-Roche, H., Elamrani-Jamal, A., ‘Les topiques’, in Goulet, R. (ed.), Dictionnaire des philosophes antiques, vol. 1 (Paris, 1989–2003), pp. 524–6Google Scholar.

43 Alfarabi, Taḥlīl, p. 95. See Alfarabi's characterization of the topoi in Alfarabi, Ğadal, p. 68.

44 Cf. Abed, S., Aristotelian Logic and the Arabic Language in Alfārābī (Albany, NY, 1991), pp. 2fGoogle Scholar.

45 Alfarabi, Al-Manṭiq ʿinda al-Fārābī, vol. 1, ed. ʿAğam, R. (Beirut, 1985), pp. 5562, p. 60Google Scholar.

46 Ibid., p. 61.

47 Alfarabi, Taḥlīl, p. 101.

48 I am grateful to Stephen Menn for encouraging me to rethink my analysis of how Alfarabi uses the topoi. I had originally claimed that the variables used to state the topoi are simply “linguistic entities” such as “terms” that we can attach universal quantifiers to. I now realize that what makes the topoi work, so to speak, are the relations of inclusion and exclusion (partial and complete) that the topical rules assume to hold between the terms that the topical rules take as objects. These relations of inclusion and exclusion are the basis for the theory of the five predicables as Alfarabi seems to have understood it.

49 in kāna al-šayʾu mawğūdan fī amrin mā fa-ḍiddu ḏālika al-šayʾ mawğūdun fī ḍiddi ḏālika al-amri; literally, ‘if the thing is in something else, then the contrary of that thing is in the contrary of that something else’; Alfarabi, Ğadal, p. 68.2–3. The examples listed above are not Alfarabi's.

50 Alfarabi, Taḥlīl, pp. 95–6.

51 Black, Logic and Aristotle's Rhetoric and Poetics, p. 105.

52 The adjective ‘negative (salbī, sālib)’ describes the quality of the sentence, indicating that the sentence is such that it possesses a negative particle in its logical structure. Contradiction (tanāquḍ) and contrariness (taḍādd), and opposition (taqābul) generally, are best understood as characterizing the quality of the logical relation between two sentences and in relation to each other. Thus, a single sentence might be described as ‘negative’, but only a pair of sentences can be contradictory or contrary, each with respect to the other. On the other hand, irtifāʿ, literally ‘elimination’ and similar in its import to the phrase ‘negated of (maslūban ʿan)’, is a cognitive or linguistic act carried out by the reasoner on a sentence of a given quality that converts the quality of the sentence to its opposite. To this extent, ‘negation’ would be an appropriate translation of irtifāʿ, which conveys Alfarabi's intended meaning, if we keep the following point in mind. Though irtifāʿ behaves in some ways like propositional negation, it should not be understood a purely linguistic unary function that takes a sentence as an operator and generates a sentence as a value. It often has, though not necessarily in this particular passage, a metaphysical counterpart. Sometimes, when we say about something that it has been eliminated or negated (e.g. ‘elimination of the thing [irtifāʿ al-šayʾ]’), we do not mean exclusively that a sentence has been negated, but sometimes, the absence of a condition outside the soul that is in line with what the sentence expresses about it. In a complementary way, the presence of the thesis (wuğūd al-waḍʿ), say, means the presence of a condition outside the soul that is in line with what the thesis expresses about it.

53 Alfarabi, Taḥlīl, p. 102.

54 Alfarabi, Taḥlīl, pp. 104ff.

55 Stalnaker, ‘A theory of conditionals’, p. 44.

56 Ibid., p. 43 says: ‘According to this line of thought, a conditional is to be understood as a statement which affirms that some sort of logical or causal connection holds between the antecedent and consequent. [In order to determine whether a conditional understood in this way is true], you should look, not at the truth values of the two clauses, but at the relation between the propositions expressed by them’. As we will see, the connective scheme to conditional evaluation is what informs Alfarabi's thoughts about conditionals.

57 Alfarabi, ‘Al-Fārābī's paraphrase of the Categories of Aristotle’, trans. Dunlop, D., The Islamic Quarterly, 5 (1959): 2154, p. 34Google Scholar. Hereafter, I will cite this work as follows: Alfarabi, APCA.

58 Alfarabi, Ğadal, p. 82.

59 Martin, C., ‘The logic of negation in Boethius’, Phronesis 36/3 (1991): 277304, p. 279CrossRefGoogle Scholar; id., Denying conditionals: Abaelard and the failure of Boethius' account of the hypothetical syllogism’, Vivarium, 45 (2007): 153–68CrossRefGoogle Scholar; cf. R. Stalnaker, ‘A defense of conditional excluded middle’, in Harper, Stalnaker, Pearce (eds.), Ifs, pp. 87–104.

60 This is how the contradiction of indicative conditionals is sometimes interpreted for natural language, e.g. Adams, E., ‘The logic of conditionals’, Inquiry, 8 (1965): 166–97, p. 184CrossRefGoogle Scholar. In this article Adams is interested in giving an analysis of indicative conditionals as they are used in natural language. In Adams' view, a conditional expresses the probability that a reasoner will assert the consequent given a certain probability that the antecedent. One pragmatic assumption in this theory is that a speaker will never be justified in asserting a consequent when he knows that the antecedent is false. Adams says (ibid., p. 178) “a pair of conditional statements of the form ‘if p then q’ and ‘if p then not q’ are seldom if ever justifiably asserted on the same occasion. When such a pair of statements is made on the same occasion, it is usually the case that one is asserted in contradiction to the other, and this carries the implication that the contradicted statement is false or at least that it may be justifiably denied (and non-vacuously)”.

61 Alfarabi, APCA, §58, 35.10–14.

62 The important relation between the notion of causality as a basis for our use of conditionals in everyday speech is recognized in the philosophical literature. For example, speaking about counterfactual conditionals, Dorthy Edgington says: ‘it is worth adding that subjunctive conditionals are supposed to do a lot of work for us within philosophy, as well as in ordinary life. They have been used to ‘analyse’ causation, dispositions, laws, and play a large part in some accounts of perception and knowledge. On the first, causation, I think we need to appeal to causal notions to get subjunctive conditionals right, and the order of explanation goes that way round'; Edgington, D., ‘On conditionals’, in Gabbay, D., Guenthner, F. (eds.), Handbook of Philosophical Logic, vol. 14 (Dordrecht, 2007), pp. 127221, p. 216CrossRefGoogle Scholar. See also Collins, J., ‘Counterfactuals, causation, and preemption’, in Jacquette, D. (ed.), Philosophy of Logic (Dordrecht, 2007), pp. 1127–43CrossRefGoogle ScholarPubMed; J. Williamson, ‘Causality’, in Handbook of Philosophical Logic, vol. 14, pp. 95–126.

63 The motivation for his discussion of implication appears to arise out of questions surrounding the meaning of the Greek expression hē tou einai akalouthēsis, which is consistently translated in the Arabic Categories as ‘luzūm al-wuğūd’ (Georr, K., Les Catégories d'Aristote dans leurs versions syro-arabes [Beirut, 1948], p. 243Google Scholar) and in English as ‘implication of existence’ (e.g. Aristotle, Aristotle's Categories and De Interpretatione, trans. Ackrill, T. [Oxford, 1963]Google Scholar). This expression, which is found at Categories 14a30, 35, 14b15, 30, 15a9, is used in the chapters on priority, posteriority, and simultaneity. In this context, ‘implication of existence’ is often said to be ‘reciprocal (pros antistrephonta, bi-al-takāfuʾ)’ or not (Georr, Les Catégories d'Aristote, p. 241), and ‘of necessity (bi-al-ḍarūra, ex anagkēs)’ (ibid., p. 230) or not, i.e. ‘accidentally (bi-al-ʿaraḍ, kata sumbebēkos), (ibid., p. 233). Alfarabi's wording in his epitome of the Categories closely matches Sergius of Rašaina's (d. 536) Arabic translation of Aristotle, often word for word; on Sergius of Rašaina, see ibid., pp. 17–24. As we will see, Alfarabi moves substantially beyond Aristotle's text just when he explicitly connects the discussion about the being of something following from something else with the construction of conditional and disjunctive premises and syllogisms in a way that strongly recalls his discussion of the ‘topoi of implications’ in Taḥlīl. Though al-Ḥasan b. Suwār's (born in 942) marginal notes on the Categories make no mention of this constellation of issues, such an obvious concern with showing the intertextual consistency in between the Categories, Topics, and the late antique discussion of hypothetical syllogisms suggests that Alfarabi's ideas in APCA grew out of a late antique commentary tradition that seems to have existed no later than Proclus (d. 485). As noted by Fritz Zimmermann (Alfarabi, Long Commentary, p. 128, n. 3), in his long commentary on De Interpretation, Alfarabi's condemnation of Proclus' incomprehension of Aristotle's doctrine of metathetic sentences adopts Proclus' use of reciprocal and nonreciprocal implication (ibid., pp. 123–31) in order to clarify Aristotle's meaning (at De Interpretatione 20a20–3).

64 Black, Logic and Aristotle's Rhetoric and Poetics, p. 35.

65 Alfarabi, APCA, p. 34.

66 Alfarabi, APCA, §56, 34.9–11.

67 Alfarabi, APCA, §55, 34.11–16. Note Alfarabi's explicit identify of alethic and statistical necessity.

68 Alfarabi, APCA, §57, 34.17–19.

69 Alfarabi, APCA, §57, 34.20–35.4.

70 Alfarabi, APCA, §57, 34.23–35.4.

71 Menn, S., ‘Al-Fārābī's Kitāb al-Ḥurūf and his analysis of the senses of being’, Arabic Sciences and Philosophy, 18 (2008): 5997CrossRefGoogle Scholar.

72 Perhaps, strictly speaking, in two steps of this “proof” Alfarabi would have had to rely on conjunction elimination, viz. ‘P and Q’ entails ‘P’ and ‘P and Q’ entails ‘Q’. It seems likely, however, that took the elimination steps to be obvious.

73 See Text 9 and Text 10 for Alfarabi's statistical reading of the modalities. In his so-called Short Treatise on Aristotle's De Interpretatione, Alfarabi is more explicit about the interdefinability of the ‘primary modes’ of necessity and possibility and statistical/temporal modalities: ‘Necessary is what exists permanently, not having ceased nor going to cease, and cannot not exist at any time. Possible is what does not exist now but is apt to exist and apt not to exist at any time in the future. The absolute is of the nature of possibility, but has come to exist now after having had the possibility of existing and the possibility of not existing, though it has the possibility of not existing again in the future’; Alfarabi, Alfarabi's Commentary and Short Treatise on Aristotle's De Interpretatione, trans. Zimmermann, F. (London, 1981), p. 242Google Scholar. On the notion of primary or basic modalities, and its role in the development of Avicenna's division of existence into necessary and possible, see Wisnovsky, R., Avicenna's Metaphysics in Context (Ithica, NY, 2003), pp. 219–25Google Scholar.

74 Technically speaking, the locution ‘necessary conditional’ means that it is a conditional sentence with necessary implication, ‘for-the-most-part conditional’ means that it is a conditional sentence possessing for-the-most-part implication, and ‘per accidens conditional’ means that it is a conditional sentence possessing per accidens implication.

75 Alfarabi, Qiyās, pp. 82f; cf. Alfarabi, Al-Fārābī's Short Commentary on Aristotle's Prior Analytics, trans. Rescher, N. (Pittsburgh, 1963), pp. 74–7Google Scholar. Alfarabi, Madḫal, pp. 31ff.

76 Black, Logic and Aristotle's Rhetoric and Poetics, pp. 170f.

77 Ibid., p. 108.

78 Ibid., pp. 86ff.

79 Ibid., p. 87.

80 Ibid., p. 98.

81 Ibid., p. 170.

82 Alfarabi, Deux ouvrages inédits sur la Rhétorique, ed. Langhade, J., Grignaschi, M. (Beirut, 1986), p. 95.6–13Google Scholar: ‘Connective conditional syllogisms are only persuasive (muqniʿa) when the conditional proposition is stated explicitly, the asserted [minor] premise is withheld, and one simply sets forth the conclusion. In this art (i.e. in rhetoric) the conclusion of a connective conditional syllogism may be the opposite of the consequent, or the opposite of the antecedent. [Whatever conclusion the speaker decides to work with] will depend on what the speaker feels will be most beneficial to him. By withholding the asserted [minor] premise, the locus of the sophistry in each of these conclusions will be obscured, for at first glance (fī bādiʾ al-raʾī) most people (ğumhūr) can hardly tell what must be asserted, or which assertion will produce the conclusion. For all of this is obscure to the majority of people’. Hereafter, I will cite this work as follows: Alfarabi, Rhétorique. Cf. Alfarabi, Kitāb fī al-Manṭiq: al-Ḫaṭāba, ed. Sālim, M. Salīm (Cairo, 1976), p. 47.10–15Google Scholar. Hereafter, I will cite this work as follows: Alfarabi, Ḫaṭāba.

83 Alfarabi, Rhétorique, p. 97.6–9; id., Ḫaṭāba, p. 48.6–9.

84 Alfarabi, Rhétorique, p. 97.4–6; id., Ḫaṭāba, p. 48.4–6.

85 Black, Logic and Aristotle's Rhetoric and Poetics, p. 112: ‘Since rhetorical assent is a form of decisive adherence to one contrary, in the face of an equally strong objective probability that the rejected contrary is the true one, the logician is left without any explanation of why the mind does indeed incline one way, rather than the other. The production of rhetorical assent cannot, therefore, be due solely, or even primarily, to the truth and modality of rhetorical propositions. The very nature of rhetorical acceptance is that it is primary and unhesitating, and thus able to subsist despite the awareness of the possibility that it is false, or that not everyone accepts it as true. As soon as doubts regarding these rhetorical premises reach the point that they make the believer feel the need for investigation, his assent has lost its innocence, the very innocence that made it rhetorical belief. Thus, as soon as the opposite of which the holder of a rhetorical belief is aware becomes an active force, the believer is thrust into the realm of dialectical investigation’. For more details on the ‘locus of opposition (mawḍiʿ al-ʿinād)’, see ibid., pp. 111–13.

86 Alfarabi, Rhétorique, pp. 95.14–96.3; id., Ḫaṭāba, pp. 47.16–48.3.

87 Black, Logic and Aristotle's Rhetoric and Poetics, pp. 170f. Cf. Evans and Over, If, p. 32.

88 Jonathan Evans and David Over (If, p. 38) note that when conditionals are used in natural language environments, people ‘do not expect a “true” conditional to apply universally’ which gives further evidence in the authors' view that people tend to ‘interpret “all” fuzzily or vaguely to mean “nearly all”’.

89 For Muʿtazilite ideas about the syllogism, see van Ess, J., Die Erkenntnislehre des ʿAḍuaddīn al-Īcī (Wiesbaden, 1966), pp. 382–94Google Scholar. For Muʿtazilite influence on the classical Islamic philosophers, see Adamson, P., ‘Al-Kindī and the Muʿtazila: Divine attributes, creation and freedom’, Arabic Sciences and Philosophy, 13 (2003): 4577CrossRefGoogle Scholar.

90 Alfarabi, Rhétorique, p. 85.4–11; id., Ḫaṭāba, pp. 41.14–42.3.

91 This does not entail, however, that the argument with the same premise set and the contradiction of the conclusion would be valid in a demonstrative context, since there is clearly a difference between refusing to give assent to P on the one hand, and affirming not-P on the other. For a similar distinction between assertion and rejection, see Smiley, T., ‘Rejection’, Analysis, 56/1 (1996): 19CrossRefGoogle Scholar.

92 Adams, E., The Logic of Conditionals: An Application of Probability to Deductive Logic (Dordrecht/Boston, 1975)CrossRefGoogle Scholar.

93 Evans and Over, If, p. 25.

94 According to Adams, the probability of our belief in the indicative conditional P(A → B) = P(A&B)/P(A). Obviously, if we believe that A is false, then we believe that A has 0% chance of coming about. P(A) thus equals 0, and the probability of ‘A → B’ is indeterminate (since a fraction with a denominator of numerical value 0 is undefined).

95 Prior Analytics A44 50a16–28; quoted in Lear, Aristotle and Logical Theory, p. 40. The translation is Lear's.

96 Smith, R., Notes to Aristotle, Prior Analytics, trans. Smith, R. (Indianapolis, Cambridge, 1989), p. 175Google Scholar. Smith also notes (ibid.) that the context of the passage is dialectical. I am not sure that I agree with Smith's interpretation of this passage in important respects. Like earlier interpreters, Smith appears to take the agreed-upon proposition to be a conditional “if there is not a single potentiality […] for a pair of contraries, then there is not a single science of them either”. I have indicated in many places above why I believe Lear is right to say that this approach to Aristotle's text is wrong.

97 Robin Smith notes (ibid.) that this second portion of the argument is in the form of a reductio.

98 In a previous version I misunderstood Aristotle's argument. I am grateful to Stephen Menn for bringing this error to my attention.

99 Black does note (Logic and Aristotle's Rhetoric and Poetics, pp. 54f) that, at times, Alfarabi does seem to entertain that there is a sense in which non-assertives, viz. non-apophantic discourses, might be said to be true or false. However, Alfarabi's position is clear: only apophantic statements are true and false in a genuine sense.