Unusual Syllogisms: Avicenna and Najm al-Dīn al-Kātibī on per impossibile Syllogisms and Implication (luzūm)

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In his proofs of article image e- and article image e-conversion in Logic for Shams al-Dīn, Najm al-Dīn al-Kātibī (d. 1276/7) accepts syllogisms that have redundant premises as theses. Similarities in Avicenna’s and Kātibī’s doctrines of the per impossibile syllogism suggest that Avicenna could have adopted such proofs and remained consistent with the principles of his syllogistic. However, analysis of their modal syllogistic and their ideas about the nature of implication (luzūm) reveals that Avicenna could not employ the type of per impossibile syllogism that Kātibī does and remain faithful to his modal theory, or to the Aristotelian vision of the theory of syllogistic as a theory of reasoning. In his commentary on Afḍal al-Dīn al-Khūnajī’s (d. 1248) Disclosure of Secrets Kātibī offers a second analysis of per impossibile syllogisms. Kātibī envisions a generic sense of logical necessitation that accommodates the sense in which an antecedent implies a consequent and premises imply a conclusion. This evidence may explain why Kātibī admitted redundantly concluding syllogisms as theses. If Avicenna was committed to a strict distinction between these senses, this may partially account for why Avicenna does not adopt Kātibī’s unusual syllogisms.

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References

1

Tony Street, “Faḫraddīn al-Rāzī’s Critique of Avicennan Logic,” in Logik und Theologie: Das Organon im Arabischen und im Lateinischen Mittelalter, eds. Dominik Perler and Ulrich Rudolph (Leiden: Brill, 2005), 106. For ease of reference, translations of texts from Arabic have been assigned markers “T1”, “T2”, “T3”, etc. Block quotes from secondary sources are unmarked.

3

Street, “Rāzī’s Critique,” 106. Avicenna uses the “upgrade” method of supposing the possible actual in Pointers and Reminders (Avicenna, Remarks and Admonitions, trans. S. Inati (Toronto: Pontifical Institute, 1984), 115). He also says that ecthesis can be used (ibid., 116). Avicenna gives another proof in Salvation (Kitāb al-Najāt), which is, again, unlike the one in T1; Tony Street, “An Outline of Avicenna’s Syllogistic,” Archiv für Geschichte der Philosophie 84 (2002): 144.

5

Alexander, On Aristotle’s Prior Analytics 1.1–7, 90.

6

Ibid., 86.

7

Street, “Rāzī’s Critique,” 106.

9

See Tony Street, “Arabic Logic,” in Handbook of the History of Logic, vol. 1, John Woods and Dov Gabbay eds. (Amsterdam: Elsevier, 2004), 546f.

18

E.g. Paul Thom, Medieval Modal Systems: Problems and Concepts (Aldershot: Ashgate, 2003), 65–80. For a lucid discussion of the virtues of this interpretation, see Paul Thom, “Logic and Metaphysics in Avicenna’s Modal Syllogitic,” in The Unity of Science in the Arabic Tradition, Shahid Rahman, Tony Street, and Hasan Tahiri eds. (Dordrecht: Springer, 2008), 361–376, esp. 362–365.

20

Street, “Outline of Avicenna’s Syllogistic,” 134.

21

Thom, “Logic and Metaphysics in Avicenna’s Modal Syllogistic,” 374. See also Khaled El-Rouayheb, “Post-Avicennan Logicians on the Subject Matter of Logic: Some Thirteenth- and Fourteenth-Century Discussions,” Arabic Sciences and Philosophy 22 (2012): 80.

23

Street, “Rāzī’s Critique,” 106.

24

See Paul Thom, “Abharī on the Logic of Conjunctive Terms,” Arabic Sciences and Philosophy 20 (2010): 108 for an illuminating discussion of this way of defining the ampliation of the subject term. It seems that in the later tradition, Arabic logicians may have used Avicenna’s notion of implication (luzūm) in order to characterize what objects fall under the subject term. This is an important topic that requires greater attention.

27

Thom, “Logic and Metaphysics in Avicenna’s Modal Syllogistic,” 365.

29

Ibid., from Avicenna, Remarks and Admonitions, 226.

30

Thom, “Logic and Metaphysics in Avicenna’s Modal Syllogistic,” 366.

32

Ibid., p. 374; idem, “Al-Fārābī on Indefinite and Privative Names,” Arabic Sciences and Philosophy 18 (2008): 198.

34

Thom, “Logic and Metaphysics in Avicenna’s Modal Logic,” 366.

35

Ibid., p. 369.

37

Thom, “Logic and Metaphysics in Avicenna’s Modal Syllogistic,” 366.

39

Kit Fine, “Aristotle’s Megarian Manoeuvres,” Mind 120 (2011): 993–1034; Fine’s discussion, which is based on Aristotle’s statement and argument for this rule, is based on Metaphysics Theta.4 (1047b14–b30). Rosen and Malink acknowledge their debt to Fine’s paper, but take An. Pr. 1.15 as their object of study: Jacob Rosen and Marko Malink, “A Method of Modal Proof in Aristotle,” in Oxford Studies in Ancient Philosophy, vol. 42, ed. Brad Inwood (Oxford: Oxford University Press, 2012), 179–261; idem, “Proof by Assumption of the Possible in Prior Analytics 1.15,” Mind 122 (2013): 953–986.

43

Thom, The Syllogism, 41. Aristotle states (An. Pr. A29 24–28) that “Deductions [syllogisms] which lead into an impossibility are also in the same condition as probative ones: for they too come about by means of what each term follows or is followed by, and there is the same inquiry in both cases. For whatever is proved probatively can also be deduced through an impossibility by means of the same terms, and whatever is proved through an impossibility can also be deduced probatively (Aristotle, Prior Analytics, Robin Smith trans. (Indianapolis: Hackett, 1989), 47 [italics added]).” See also An. Pr. 2.11–14.

44

Paul Thom, “Three Conceptions of Formal Logic,” Vivarium 48 (2010): 228–42.

46

Thom, The Syllogism, 196.

47

Thom, “Three Conceptions of Formal Logic,” 237.

50

Thom, The Syllogism, 216.

52

Thom, “Three Conceptions of Formal Logic,” 236.

53

Khaled El-Rouayheb, “Opening the Gate of Verfication: the Forgotten Arab–Islamic Florescence of the 17th-Century,” International Journal of Middle East Studies 38 (2006): 263–281. See also Robert Wisnovsky’s outstanding article on how the term “verification [taḥqīq]” was utilized by post-classical commentators on Avicenna’s Pointers and Reminders to convey a variety of meanings, and was deployed strategically to serve different exegetical ends: Robert Wisnovsky, “Avicennism and Exegetical Practice in Early Commentaries on the Ishārāt,” Oriens 41 (2013): 349–378.

55

See El-Rouayheb, “Impossible Antecedents and Their Consequents: Some Thirteenth-Century Arabic Discussions,” History and Philosophy of Logic 30 (2009): 211; Avicenna, Syllogism, v.1, 237, ll.13–16: “Let the conjunctive [hypothetical, al-muttaṣil] be absolute [ʿalā l-iṭlāq]—so that what is claimed in it is only that the consequent is true with [maʿa] the antecedent—or restricted [ʿalā taḥqīq]—in which case the truth of the consequent follows from the antecedent.” To my knowledge, “restricted” has been the standard translation in the field of Arabic logic for “ʿalā t-taḥqīq” since Shehaby’s translation of Qiyās, v–ix.

58

Ibid., 210.

63

El-Rouayheb, “Impossible Antecedents and Their Consequents,” 209.

65

Ibid., 213. Thus, Avicenna’s “strict” implication admits a qualified Rule of Expansion: if “strictly implies ” is true, then “, strictly implies ” provided that does not (restrictedly) imply .

67

Avicenna, Syllogism, v.4, 274, l.11–5, l.4.

70

El-Rouayheb, “Impossible Antecedents,” 215. Khūnajī accepts the truth of and , for any and .

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