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# EXISTENTIAL IMPORT IN AVICENNA'S MODAL LOGIC

Published online by Cambridge University Press:  02 February 2016

## Abstract

In this paper, I raise the following problem: what propositions have an import in Avicenna's modal logic? Which ones do not? Starting from the assumption that the singular and quantified propositions have an import if they require the existence of their subject's referent(s) to be true, I first discuss the import of the absolute propositions then I analyze the import of the modal propositions by considering Avicenna's definitions and the relations between these propositions. This leads to the following results: Avicenna's general opinion is that the affirmatives, be they assertoric or modal, have an import while the negatives do not. The possible affirmative propositions are given an import both in the externalist and the internalist post-Avicennan readings, provided that the subject is not impossible. However, the theory is not always clear, for the propositions containing ‘sometimes not’ are given an import, together with the negative necessaries containing ‘as long as it is P’, despite their negative character; the necessary affirmative propositions containing ‘as long as it is P’ are given an import, although they do not require it. In addition, Avicenna's analysis of the special assertorics E and O (containing the internal conditions ‘at some times but not always’) and their contradictories is erroneous, which does not help determine their import. But when correctly analyzed, these special E and O do not have an import, while their contradictories – I and A special assertorics respectively – have an import.

## Résumé

Dans cet article, je pose le problème suivant: quelles propositions ont un import dans la logique modale d'Avicenne? Lesquelles n'en ont pas? Partant de l'assomption que les propositions singulières et quantifiées ont un import si elles requièrent l'existence de leur sujet pour être vraies, j'analyse d'abord l'import des propositions absolues, ensuite celui des propositions modales en tenant compte des définitions d'Avicenne et des relations entre ces propositions. Cette analyse conduit aux résultats suivants: Avicenne défend l'opinion générale selon laquelle les affirmatives, qu'elles soient modales ou assertoriques, ont un import alors que les négatives n'en ont pas. Il attribue un import aux propositions possibles affirmatives aussi bien dans l'interprétation externaliste que dans l'interprétation internaliste des logiciens post-Avicenniens, pourvu que le sujet ne soit pas impossible. Toutefois, la théorie n'est pas toujours claire, car Avicenne attribue un import aux propositions contenant ‘parfois non’ et aux nécessaires négatives contenant ‘tant qu'il est P’ malgré leur caractère négatif; les propositions nécessaires affirmatives contenant ‘tant qu'il est P’ sont considérées comme ayant un import alors qu'elles ne l'exigent pas. De plus, l'analyse qu'il donne des assertoriques spéciales E et O (contenant les conditions internes ‘parfois mais pas toujours’) et de leurs contradictoires est erronée, ce qui ne permet pas de déterminer clairement leur import. Mais quand elles sont correctement analysées, ces propositions E et O n'ont pas d'import, alors que leurs contradictoires – les assertoriques spéciales I et A respectivement – ont un import.

Type
Research Article
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Arabic Sciences and Philosophy , March 2016 , pp. 45 - 71

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## References

1 Laurence Horn, A Natural History of Negation, The David Hume Series, CSLI Stanford (Chicago, 2001), p. 28.

2 Horn formalizes it as follows: “~∃xFx ∨ ∃x(Fx ∧ ~Gx)” (A Natural History of Negation, p. 27).

3 Ibid., p. 24.

4 I am indebted to one reviewer who drew my attention to that particular point.

5 See Saloua Chatti, “Logical oppositions in Arabic logic: Avicenna and Averroes”, in Jean-Yves Béziau, Dale Jacquette (eds.), Around and Beyond the Square of Opposition (Basel, 2012), pp. 21–40. The square is not drawn by Avicenna, however, for we do not find any figure in his texts.

6 Avicenna, al-Shifāʾ, al-Manṭiq 3: al-ʿIbāra, ed. Mahmud El Khodeiri, rev. and intr. by Ibrahim Madkour (Cairo, 1970), p. 47.

7 Avicenna, al-Ishārāt wa-al-tanbīhāt, with the commentary of Naṣīr al-Dīn al-Ṭūsī, intr. by Sulayman Dunya, Part 1, 3rd edn (Cairo, 1971), p. 305.

8 Avicenna, al-Shifāʾ, al-Manṭiq 2: al-Maqūlāt, ed. George Anawati, Mahmud El Khodeiri, Fu'ad El-Ahwani, Saʿid Zayed, rev. and intr. by Ibrahim Madkour (Cairo, 1959), p. 259, 12–13.

9 Avicenna, al-Maqūlāt, p. 259, 11–12.

10 Avicenna, al-Maqūlāt, p. 258, 17.

11 “[…] li-anna al-salba yaṣuḥḥu ʿan mawḍūʿin maʿdūmin wa-al-ījābu, kāna maʿdūlan aw muḥaṣṣalan, fa-lā yaṣuḥḥu illā ʿalā mawḍūʿin mawjūdin; fa-yaṣuḥḥu an taqūla inna al-ʿanqā laysa huwa baṣīran wa-lā yaṣuḥḥu an taqūla inna al-ʿanqā huwa ghayru baṣirun” (Avicenna, al-Najāt, edited by Muḥyī al-Dīn Sabrī al-Kurdī, 2nd edn [Cairo, 1938], p. 16, 3–6).

12 Wilfrid Hodges, “Affirmative and negative in Ibn Sīnā”, in Catarina Dutilh Novaes & Ole Hjortland Thomassen (eds.), Insolubles and Consequences, Essays in Honour of Stephen Read (Milton Keynes, UK, 2012), pp. 119–34, at p. 120.

13 Avicenna, al-ʿIbāra, p. 54, 5.

14 Avicenna, al-Ishārāt wa-al-tanbīhāt, p. 309, 2.

15kull [B] [A] maʿnāhu kull wāḥid wāḥid mimmā yūṣafu wa-yufraḍu annahu bi-al-fiʿli [B], dāʾiman aw ghayru dāʾimin, fa-innahu mawṣūfun ayḍan bi-annahu [A] min ghayri an yaltafita ilā matā dhālika, wa-min ayyi al-aqsāmi kāna” (Avicenna, al-Shifāʾ, al-Manṭiq 4: al-Qiyās, ed. Saʿid Zayed, rev. and intr. by Ibrahim Madkour [Cairo, 1964], p. 26, 18– p. 27, 2).

16 Avicenna, al-Qiyās, p. 32, 3.

17 For instance, al-ʿIbāra, pp. 79–80; see also Hodges “Affirmative and negative in Ibn Sīnā”, p. 127.

18kull wāḥid wāḥid mimmā yūṣafu bi-[J]- fī al-faraḍi al-dhihnī aw fī al-wujūdi al-khārijī, wa-kāna mawṣūfan bi-dhālika dāʾiman aw ghayru dāʾimin, bal kayfa ittafaqa; fa-dhālika al-shayʾu mawṣūfun bi-annahu [B] min ghayri ziyādati annahu mawṣūfun bihi fī waqti kadhā aw ḥāli kadhā aw dāʾiman” (Avicenna, al-Ishārāt wa-al-tanbīhāt, pp. 280–2; part of the translation reported by Paul Thom, “Logic and metaphysics in Avicenna's modal syllogistic”, in Shahid Rahman, Tony Street and Hassan Tahiri [eds.], The Unity of Science in the Arabic Tradition [Dordrecht, 2008], pp. 361–376, at p. 362).

19 Ibid., p. 362.

20 Ibid.

21 Ibid.

22 Avicenna, al-ʿIbāra, p. 79, 13–15, p. 80, 1, 6–10; translation Hodges in “Affirmative and negative in Ibn Sīnā”, p. 132.

23 Avicenna, al-ʿIbāra, p. 82; translation Hodges in “Affirmative and negative in Ibn Sīnā”, p. 134.

24 This distinction is reported and analyzed by Tony Street in the following articles: Street, Tony, “Appendix: Readings of the subject term”, Arabic Sciences and Philosophy, 20 (2010), pp. 119–24CrossRefGoogle Scholar; id.,Afḍal al-Dīn al-Khunājī (d. 1248) on the conversion of modal propositions”, ORIENS, 42 (2014): 454513CrossRefGoogle Scholar; id.,“Kātibī, Taḥtānī and the Shamsiyya”, forthcoming, and by Thom, Paul in “Abharī on the logic of conjunctive terms”, Arabic Sciences and Philosophy, 20 (2010): 105–17CrossRefGoogle Scholar.

25idhā qulta [B] [J] fa-maʿnāhu anna mā yūsafu bi-annahu [B] wa-yufraḍu annahu [B] sawāʾan kāna mawjūdan aw laysa bi-mawjūdin, mumkina al-wujūdi aw mumtanaʿa al-wujūdi, baʿda an yujʿala mawṣūfan bi-al-fiʿli annahu [B] min ghayri ziyādati kawnihi dāʾiman [B] aw ghayra dāʾimin  fa-dhālika al-shayʾu mawṣufun bi-annahu [J]. Wa-ʿalā qiyāsihi fī al-salbi” (Avicenna, Manṭiq al-mashriqiyyīn, ed. Muḥyī al-Dīn al-Khatīb and ʿAbdelfattāḥ al-Qatlane [Cairo, 1910], p. 64, 1–4).

26 Avicenna, al-Qiyās, p. 82, 4.

27 Avicenna, al-Qiyās, p. 82, 2.

28 Avicenna, al-Qiyās, p. 49, 2–4. These propositions are stated with a different symbolism in Tony Street, “Arabic logic”, in Dov Gabbay & John Woods (eds.), Handbook of the History of Logic, vol. 1 (Elsevier BV, 2004), pp. 523–96, p. 590.

29 Avicenna, al-Qiyās, p. 47, 2–4.

30 Avicenna, al-Qiyās, p. 48, 4–5.

31 Chatti, Saloua & Schang, Fabien, “The cube, the square and the problem of existential import”, History and Philosophy of Logic, 34.2 (2013): 101–32CrossRefGoogle Scholar.

32(4) fa-idhā qulnā fīhā: ‘Kull [J] [B]’ ay ʿalā al-wajhi alladhī dhakarnāhu, kāna naqīḍuhu ‘laysa innama bi-al-wujūdi Kull [J] [B], ay immā bi-al-ḍarūrati dāʾiman baʿḍu [J] [B] aw [B] maslūbun ʿanhā kadhālika’ ” (Avicenna, al-Ishārāt, p. 310, 1–5). See also al-Qiyās, p. 46, 11, where Avicenna says: “Kull [B] [A] ay waqtan wa-ḥālan lā dāʾiman” and “fa-naqūlu Laysa Kull [B] [A], waqtan bi-ʿaynihi, lā dāʾiman, bal immā baʿḍuhu dāʾiman aw baʿḍuhu lā al-battata” (p. 47, 1–2).

33 “(6) wa-naqīḍu qawlinā: baʿḍu [J] [B] bi-hādhā al-wajhi, lā shayʾa min [J] innamā huwa bi-al-wujūdi [B], bal immā Kull [J] [B] dāʾiman, aw lā shayʾa min [J] [B] dāʾiman” (Avicenna, al-Ishārāt, p. 311, 3–5).

34(5) wa-idhā qulnā fīhā: laysa wa-lā shayʾa min [J] [B] ay ʿalā al-wajhi alladhī dhakarnāhu, kāna al-naqīḍu al-muqābilu lahu mā yufhamu min qawlinā: baʿḍu [J] dāʾiman lahu ījābu [B] aw salbuhu ʿanhu; li-annahu idhā sabaqa al-ḥukmu anna Kull [J] yunfā ʿanhu [B] waqtan mā lā dāʾiman, fa-innamā yuqābiluhu an yakūna nafyun dāʾiman aw ithbātun dāʾiman” (Avicenna, al-Ishārāt, p. 310, 6–11).

35wa-naqīḍu qawlinā: laysa baʿḍu [J] [B] ay laysiya bi-hādhā al-maʿnā, huwa qawlunā: Kull [J] immā dāʾiman [B] wa-immā dāʾiman laysa bi-[B] ” (Avicenna, al-Ishārāt, pp. 311, 8–11). In al-Qiyās, Avicenna does not provide formulas as clear as the ones cited above, although he evokes the special absolutes and their opposites in section 5, part 1, pp. 38–50.

36fa-in kānatā muṭlaqatayni bi-al-maʿnā al-khāṣṣ, lam yajib an yakūna muqābiluhumā shayʾan bi-ʿaynihi, bal kāna al-ḍarūrī al-muwāfiq fī al-kayf wa-al-dāʾim al-mukhālif fī al-kayf, baʿda an yukhālifa fī al-kamm, dākhilīna fī naqīḍihi” (al-Qiyās, p. 49, 4–6).

37 Street, “Arabic logic”, p. 551. We use “w” because “descriptional” is the translation of “waṣfī”.

38 Avicenna, al-ʿIbāra, p. 80; translation Hodges in “Affirmative and negative in Ibn Sīnā”, p. 132.

39 Avicenna says that “The griffin is not a thing that can see” is true while “The griffin is a thing that cannot see” is false (al-ʿIbāra, p. 82; translation Hodges in “Affirmative and negative in Ibn Sīnā”, p. 134).

40Kull mā yūṣafu bi-annahu [B], fa-innahu bi-al-ḍarūrati wa-dāʾiman mā dāma dhātuhu mawjūdatan yūṣafu bi-annahu [A], mā dāma alifan, wa-yakūnu al-alifu laysa huwa al-maḥmūlu bal juzʾan min al-maḥmūli” (Avicenna, al Qiyās, p. 42, 3–5).

41wa-kadhālika naqīḍuhu, wa-huwa annahu laysa kull [B] [A] fī al-waqti alladhī huwa [A], fa-inna hādhā al-sāliba lā yaṣduqu al-battata” (Avicenna, al-Qiyās, p. 41, 16–p. 42, 1).

42 Wilfrid Hodges, “Ibn Sīnā on modes”, ‘Ibāra ii.4, http://wilfridhodges.co.uk/arabic07.pdf, p. 11.

43 Avicenna, al-ʿIbāra, p. 118, 6–7.

44 Avicenna, al-Najāt, pp. 20–1.

45 For instance al-Qiyās, p. 32, 11–13, al-Ishārāt, p. 265, 8–10.

46 Avicenna, al-ʿIbāra, p. 113, 4–5, 7–8.

47 They are all stated in Chatti, Saloua, “Avicenna on possibility and necessity”, History and Philosophy of Logic, 35.4 (2014): 332–53, pp. 342–3CrossRefGoogle Scholar.

48 ◊: possibly and □: necessarily.

49 Avicenna, al-ʿIbāra, p. 114, 5–7.

50 Avicenna, al-ʿIbāra, p. 80, 1–3; translation Hodges in “Affirmative and negative in Ibn Sīnā”, p. 132.

51 Avicenna, al-ʿIbāra, p. 115, 9.

52fa-inna min al-nāsi man yaqūlu: muḥālun an yakūna kullu annāsi kātibin ay muḥālun an yūjada anna kull insānun huwa kātibun” (Avicenna, al-ʿIbāra, p. 115, 9–10).

53 Avicenna, al-Qiyās, p. 172, 7.

54 Avicenna, al-Qiyās, p. 172, 12–p. 173, 2.

55 Avicenna, al-Qiyās, p. 141, 12–15.

56 Bäck, Allan, “Avicenna's conception of the modalities”, Vivarium XXX, 2 (1992): 217–55, p. 228CrossRefGoogle Scholar.

57fa-yakūnu kamā anna qawlunā: ‘kull ḥayawānun aw kull abyaḍun insānun’ bi-ḥasbi al-mustaqbali, huwa qaḍīya mumkina […]. fa-takūnu hādhihi al-qaḍāyā bi-ḥasbi i‘tibāri ḥaṣrihā mumkina an taṣduqa aw takdhiba fī al-mustaqbali, wa-hiya fī māddatihā ḍarūriyya […]” (Avicenna, al-Qiyās, p. 173, 12–15).

58 Thom, “Logic and metaphysics in Avicenna's modal syllogistic”, p. 291.

59 Chatti, “Avicenna on possibility and necessity”, p. 342.

60 Chatti, “Avicenna on possibility and necessity”, p. 343.

61 Ibid., p. 342.

62 Ibid., pp. 342–3.

63 Ibid.

64 Lagerlund, Henrik, “Avicenna and Ṭūsī on modal logic”, History and Philosophy of Logic, 30.3 (2009): 227–39, p. 233CrossRefGoogle Scholar.

65wa-ammā dawāmu kawni al-mawḍūʿu mawṣūfan bi-mā wuḍiʿa maʿahu, mithla qawlinā ‘kull mutaḥarrikun mutaghayirun’, fa-laysa maʿnāhu ʿalā al-iṭlaqi, wa-lā mā dāma mawjūda al-dhāti, bal mā dāma dhātu al-mutaḥarriki mutaḥarrikan” (Avicenna, al-Ishārāt, p. 265, 8–10; part of the translation in Street “Arabic logic”).

66 Avicenna, al-Qiyās, p. 32, 11–13.

67 Avicenna, al Qiyās, p. 42, 3–4.

68 Rāzī, Mulakhkhaṣ, pp. 141, 6–10, 142, 13–143, 1, cited and translated by Street, “Afḍal al-Dīn al-Khunājī on the conversion of modal propositions”, p. 461.

69 Ṭūsī, Asās al-iqtibās fī al-manṭiq, translation by Mullā Khusraw, edited by Ḥasan Shāfi‘ī and Sa‘īd Jamāl al-Dīn (Cairo, 2004), p. 110, 6–13; cited and translated by Tony Street, “Kātibī, Taḥtānī and the Shamsiyya”, p. 16. In that same Street's article, we can see that Kātibī also defends the same position, for according to him, the proposition “every square is a figure” is true in the essentialist reading, but not in the externalist reading “if there are no squares in external existence”, p. 15.

70 Street, “Kātibī, Taḥtānī and the Shamsiyya”, p. 16.

71 See, for instance, Afḍal al-Dīn al-Khunājī, Kashf al-Asrār ‘an Ghawāmiḍ al-Afkār, edited by Khaled El-Rouayheb (Tehran, 2010); cited in Street, “Kātibī, Taḥtānī and the Shamsiyya”, p. 18, and Thom, “Abharī on the logic of conjunctive terms”, p. 108.

72 Thom, “Abharī on the logic of conjunctive terms”, p.109.

73 Thom, “Abharī on the logic of conjunctive terms”, p. 115.

74 Avicenna, al-Qiyās, p. 172, 7, 15–p. 173, 2 (see the quotations in section 4 above).

75 Cited and translated by Street, “Appendix: Readings of the subject-term”, p. 119.

76 Thom, “Abharī on the logic of conjunctive terms”, p. 107.

77 Avicenna, al-Qiyās, p. 172, 15–17.

78 Taḥtānī, Taḥrīr, p. 94, 6–4; cited by Street, “Afḍāl al-Dīn al-Khunājī on the conversion of modal propositions”, p. 462.

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