68 Arabic Sciences and Philosophy, vol. 22 (2012) pp. 51 – 68 doi:10.1017/S0957423911000099 © 2012 Cambridge University Press
BETWEEN LOGIC AND MATHEMATICS: AL-KINDĪ’S APPROACH APPROA CH TO THE ARISTO ARISTOTELIAN TELIAN CATE CATEGORIES GORIES
AHMAD IGHBARIAH
The Cohn Institute for the History and Philosophy of Science and Ideas, Humanities Faculty, Tel Aviv University, Ramat Aviv, Tel Aviv 69978 Email: igbariaahmad@yahoo
[email protected] .com Abstract. What is the function of logic in al-Kind ī al-Kind ī’s corpus? What kind
of relation does it have with mathematics? This article tackles these questions by examining al-Kind ī al-Kind ī’s Numbe mberr of Ar Aris isto totl tlee’ s Bo Book okss theor th eory y of ca cate tego gori ries es as it was pr pres esen ente ted d in hi hiss epi epist stle le On the Nu ( F from om whi which ch we can le learn arn abo about ut hi hiss sp speci ecial al at atti titu tude de Fī ī Kammiyyat kutub Aristū), fr ˙ towards Aristotle theory of categories and his interpretation, as well. Al-Kind ī Al-Kind ī treats treats the Categories as a logical book, but in a manner different from that of the classical kam Aristotelia Arist otelian n tradi tradition. tion. He ascribes a special statu statuss to the categor categories ies Quant Quantity ity ( kammiyya) and Quality ( kayfiyya kayfiyya), whereas the rest of the categories are thought to be no more mo re th than an di diff ffer eren entt co comb mbin inat atio ions ns of th thes ese e tw two o ca cate tego gori ries es wi with th th the e ca cate teg gor ory y Substance. The discussion will pay special attention to the function of the categories of Quantity and Quality as mediators between logic and mathematics. ī?? Quel type de est la fonction de la logique dans le corpus d ’al-Kind al-Kind ī relation entretient-elle avec les mathématiques? Le présent article examine ces ques ī telle tions en étudiant la théorie des catégories d’al-Kind ī telle qu’on la trouve développée Sur la quantité des livres d Aristote Fī ī Kammiyyat kutub Aristū), dans son épît épître re ( F ’ ˙ e inst in stru ruct ctiv ive e qua quant nt à so son n rap rappor portt à la thé théori orie e ari arist stot otél élic icien ienne ne des ca catég tégori ories es et à sa pr propr opre ī tient les Catégories pour un traité logique, mais conception des catégories. Al-Kind ī d’une façon qui n’est pas celle de la tradition aristotélicienne classique. Il confère ainsi kammiyya) et à celle de la qualité ( kaykayun statut spécial à la catégorie de la quantité ( kammiyya fiyya) et tient toutes les autres catégories pour une simple combinaison de celles-ci avec la catégorie de la substance. On s’intéressera tout particulièrement à la fonction média méd iatri trice ce de la ca caté tégo gorie rie de la qu quant antit ité é et de la qu quali alité té en entr tre e lo logi giqu que e et ma math thém émat atiq iques ues.. Résumé. Quelle
After Aristotle’s death, and as a result of the various alternations of the logical corpus, many interpretations were written about it. 1 As for the Categories, it acquired a special focus since the first century, 2 but,, unf but unfort ortuna unately tely,, mos mostt of the int interp erpret retat ations ions tha thatt wer were e writ written ten 1
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See ex See exam ampl ples es in M. Fr Fred ede, e, “The tit title, le, un unity ity,, and aut authen hentic ticity ity of the Ari Aristo stotel telian ian Ca Categ tegori ories es”, in id., Essays in Ancient Philosophy (Minneapolis, 1987), pp. 11 – 28, 28, at pp. 24 – 5. 5. Frede, “The title, unity, and auth authenti enticity city”, p. 11 11.. Sor Sorabj abjii st state atess tha thatt bef befor ore e the age of Porphyry, and during the first and the second centuries, five interpretations were written on the Categories, non none e of wh which ich sur surviv vived ed exc except ept a nu numbe mberr of fra fragme gments nts tha thatt we were re pr prese eserv rved ed in Simplicius’ interpretation. See R. Sorabji, “The ancient commentators on Aristotle”, in R. Sorabji (ed.), Aristotle Transformed (Trowbridge, 1990), p. 1; Simplicius, On Aristotle’ s 18. Categories 1 – 4 4, tr. M. Chase (Ithaca, New York, 2003), pp. 17 – 18.
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about it did not survive,3 and the lucky extant interpretations were those written by Porphyry (d. 309),4 Dexippus (after 330),5 Ammonius (around 440 – 520),6 Simplicius (after 529),7 Olympiodorus (around 495 – 570),8 and Philoponus (around 490 – 570).9 Many discussions were held among the ancient commentators about the subject matter of the Categories,10 including the question of the book’s authenticity and purpose. In general, the ancient commentators tended toward a logical interpretation, which became the dominant one in the late antiquity. This interpretation placed the Categories at the head of Aristotle’s logical corpus and viewed it as a book that deals with utterances as indicators of concepts. This interpretation was established by Porphyry, who found it fitting to compose an introduction to logic ( Isagoge) which was later read as an introduction to the Categories.11 This approach became part of the Peripatetic tradition, and it continued to be dominant even after Simplicius’ time. It is not my aim here to claim that this was the only available interpretation of the nature of the Categories at that time, but rather that it was the most dominant one. In the Islamic world, the Categories was translated into Arabic first by the younger Ibn al-Muqaffa (d. 815)12 and then by Ishāq ibn ˙ Hunayn (d. 910), 13 and during that time it received considerable ʿ
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For more details about these interpretations see Frede, “ The title, unity, and authenticity ”, pp. 24 – 5. Simplicius enumerates all the commentators of the Categories up to his time: Simplicius, Categories, pp. 17 – 18. 4 See Porphyry, On Aristotle’ s Categories, tr. S. K. Strange (Ithaca, New York, 1992). 5 See Dexippus, On Aristotle’ s Categories, tr. John Dillon (London, 1990). 6 See Ammonius, On Aristotle’ s Categories, tr. S. M. Cohen and G. B. Matthews (London, 1991). 7 See Simplicius, Categories. 8 See Olympiodorus, Olympiodorii Prolegomena et in Categorias commentarium, ed. A. Busse, Commentaria in Aristotelem Graeca, XII.1 (Berlin, 1902). 9 See Philoponus, in Aristotelis Categorias commentarium, ed. A. Busse, Commentaria in Aristotelem Graeca, XIII.1 (Berlin, 1898). 10 See for example Simplicius, Categories, pp. 17 – 18. In a special chapter about the purpose of the Categories, Simplicius mentions three different opinions: the first claims that it deals with entities, the second with words, while the third with concepts ( ibid., pp. 24 – 5). Simplicius adds that for Alexander of Aphrodisias, Porphyry and others, this book deals with logic, and he himself adopts the same position ( ibid., pp. 25, 27 – 9, 35). 11 K. Gyekye, Arabic Logic: Ibn al-T ayyib’ s Commentary on Porphyry’ s Eisagoge (Albany, ˙ 1979), p. 7. 12 The Categories was translated along with the Isagoge, De Interpretatione and the Prior Analytics. For the debate concerning the identity of the translator see P. Kraus, “ Al-tarā jim al-Aristūtāliyya ilā Ibn al-Muqaffa ”, in al-Turāth al-yūnānī f ī al-h ad ā ra ˙ al-isl āmiyya, Dirāsā˙ t ˙li-kibār al-mustashriqī n, tr. A. Badawi, 4th edn (Kuwait and ˙Beirut, 1980), vol. 4, pp. 101 – 20. Cf. N. Rescher, The Development of Arabic Logic (London, 1964), p. 94; F. E. Peters, “The Greek and Syriac background ”, in S. H. Nasr and O. Leaman (eds.), History of Islamic Philosophy, 2 vols . (London and New York, 1997), vol. 1, p. 11. 13 See the prefaces in the two editions of the Arabic Categories: A. Badawi, Mantiq Aristū (Kuwait and Beirut, 1980), vol. 1, pp. 12 – 14; F. Jabir, al-Nass al-kāmil li-Mant˙ iq Arist˙ ū ˙˙ ˙ ˙ (Beirut, 1999), pp. 5 – 6. ʿ
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attention from the Arabic philosophers and logicians, who commentated upon it extensively. In many cases the scholars did not deviate from the Aristotelian tradition, which understood the Categories as a book on logic and placed it within the Organon; however, there were also other approaches with regards to the work ’s subject matter and orientation.14 The present article discusses al-Kind ī’s unique approach to the theory of the categories, focusing on two elements of his intellectual persona that are reflected in it: the logical element and the mathematical element. In what follows I outline al-Kind ī’s interpretation of the Categories, showing how these two elements are reflected in it. AL-KINDĪ AS A LOGICIAN
Although al-Kind ī’s significant contribution to the editing and translating of several logical works from Greek and Syriac was recognized by the Arab biographers,15 his abilities as a logician per se were granted a rather ambiguous reception. Sā id al-Andalus ī, for instance, maintains al-Kind ī’s logical writings ˙ are of little scientific value ʿ
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Among the philosophers who maintained loyalty to the Aristotelian tradition, commentating on the Categories as a part of the logical corpus, one can name Ibn Rushd (see his Talkhī s Kitāb al-Maqūl āt, critical edition by M. Qāsim, with introduction and commentary by Ch.˙ Butterworth and A. Har īd ī [Cairo, 1980]). Among the philosophers who had deviated from the tradition one can name Ibn S īnā (see his al-Maqūl āt, in al-Shif ā , vol. 10, critical edition and introduction by I. Madkūr, edited by G. Anawāt ī, A. al-Ahwān ī, M. al-Khudayr ī and S. Zāyid [Cairo, 1959]). For a detailed discussion of this issue see ˙ The Development of the Theory of Categories in Islamic Philosophy Between A. Ighbariah, th the 9 and 13 th Centuries, PhD dissertation (University of Haifa, 2009). 15 A list of the works edited by al-Kind ī can be found in M. I. Moosa, “ Al-Kind ī’s role in the transmission of Greek knowledge to the Arabs”, Journal of the Pakistan Historical Society, 15 (1967): 1 – 1 8, at pp. 13 – 14; cf. P. Adamson, “Before essence and existence: Al-Kind ī’s conception of being ”, Journal of the History of Philosophy, 40 (2002): 297 – 312, at p. 297. Among the scholars who translated for al-Kind ī are Ibn Bihr īz, Ibn Nā ima, Ustāth and Yahyā ibn al-Bitr īq. See also Rescher, Development, pp. 100 – 1; D. Gutas, ʾ
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˙ Thought,˙ Arabic Culture: ˙ Greek The Graeco-Arabic Translation Movement in Baghdad nd th and Early Abbāsid Society (2 -4 /8 th-10 th Centuries) (London, 1998), pp. 117 – 18, 137 – 8. For al-Kind ī as a translator see Ibn Juljul, T abaqāt al-atibbā wa-al-h ukamā , ed. ˙ ˙ ā bi-akhbā˙r al-h ukamā ār al- ulam F. Sayyid (Cairo, 1955), pp. 73 – 4; al-Qift ī, Kit āb Ikhb (Beirut), p. 241; Ibn Ab ī Usaybi a, Uy˙ūn al-anbā f ī tabaqāt al-atibbā , ed. ˙N. Ridā ˙ ˙ ˙ (Beirut, 1965), p. 286; S ā id˙ al-Andalus ī, al-Ta rī f bi-tabaq , ed. Gh. Ūdhil āt al-umam ʿ
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˙ ˙ (Tehran, 1997), p. 192. See also R. Walzer, “Islamic philosophy ”, in S. Radhakrishnan et al. (eds.), History of Philosophy Eastern and Western (London, 1957), vol. 2, p. 125. M. Meyerhof, “Min al-Iskandariyya li-Baghdād: Bahth f ī ta r īkh al-ta l īm al-falsaf ī wa-al-t ibb ī inda al- Arab”, in al-Turāth al-yūnānī f ī˙ al-h ad ā ra al-isl āmiyya, vol. 4, ˙ 100. Some maintain that al-Kind ī did not translate˙ by˙ himself, since he had no pp. 37 – knowledge of Greek, but rather re-edited translations from Greek that were made by the translators in his circle. See P. Adamson, Al-Kindī (Oxford, 2007), p. 26; Moosa, “ Al-Kind ī’s role”; H. S. Wiesner, The Cosmology of al-Kindī , PhD Thesis (Harvard University, 1993), p. 11; M. Al-Ma sūm ī, “ Al-Kind ī as a thinker ”, in Abū Y ūsuf Ya qūb Ibn Ish āq al-Kindī : Islamic Philosophy˙ , vol. 5, collected and reprinted by F. Sezgin et al. ˙ (Frankfurt, 1999), p. 55. ʾ
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( qallam ā yuntafa u bihā f ī al- ul ūm).16 He further maintains that al-Kind ī’s logical works have no reference to the “art of analytics” ( sinā at al-tah l īl ) , whose function is to distinguish between truth ˙ and falsity.17˙ Whether the reason for this is ignorance of this art’s value or the need to hide it from the public, in both cases S ā id ˙ ascribes it to a deficiency in al-Kind ī’s learning.18 Al-Qift ī too is skep˙ to Sā id’s tical about al-Kind ī’s logical abilities, as he subscribes view.19 (In addition to these two historians, it seems as if al-F˙ ārāb ī had reservations towards al-Kind ī’s workings, since he completely ignores him in his survey of the scholars who took part in the transmission of Greek logic to the Arabic world.20) Ibn Ab ī Usaybi a tries to rectify this unfortunate state of affairs and accuses S ā˙ id of acting unjustly ( tah ā mala) toward al-Kind ī. He adds that S ā˙ id’s remarks ˙ ˙ will not undermine al-Kind ī’s proficiency in the sciences and will not discourage people from reading his works and benefit from them.21 Notwithstanding Sā id and al-Qift ī’s hostility, an examination of ˙ ˙ reveals a profound al-Kind ī’s list of works interest in logic, manifested in the many works he had written on the various fields of logic – including the Analytics ( al-Tah l ī l āt).22 Unfortunately, none of ʿ
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Sā id al-Andalus ī, al-Ta rif , p. 220. ˙ The term tah l ī l can be understood in two ways: ˙ 1 Sā id is referring to the book al-Tah l ī lā t al-thāniya / al-Burhān ( Posterior Analytics / The ˙ most important of the logical corpus, since its mas˙ Demonstration), whose function is the tering leads the logician to certainty. According to Sā id, the philosopher that followed ˙ al-Kind ī, namely al-Fārāb ī, is the one who took seriously the art of analytics ( sinā at ˙ al-tah l ī l ), which al-Kind ī had neglected (see ibid., pp. 220 – 1, 222). Cf. G. N. Atiyeh, ˙ Al-Kindī : the Philosopher of the Arabs (Rawalpindi, 1966), p. 36. Although the Analytics was one of the later books to be translated into Arabic, there is no doubt that al-Kind ī was acquainted with it (Rescher, Development, p. 101). For further discussion about al-Kind ī’s treatment of the Posterior Analytics in his writings, see J. Jolivet, “L’ Épître par al-Kind ī (une lecture), ” in R. Morelon and A. sur la quantité des livres d Aristote ’ Hasnawi (eds), De Zénon d’ Élée à Poincaré: Recueil d ’ études en hommage à Roshdi Rashed (Louvain, 2004), pp. 665 – 83, at pp. 669, 673. 2 Sā id is referring to the term tah l ī l, which is parallel to the term tarkī b, meaning that ˙ to compose dubious syllogisms, instead of founding ˙ al-Kind ī used uncertain premises the premises by the analytical method in order to distinguish between truth and falsity. Compare al-Fārāb ī, Kitāb al-Alf āz al-musta mala f ī al-mantiq, ed. M. Mahdi, 2nd edn ˙ ˙ ī , p. 18. (Beirut, 1986), ch. 7; Adamson, Al-Kind 18 Sā id al-Andalus ī, al-Ta rī f , p. 221. 19 ˙ Al-Qift ī, Akhbār, p. 241. 20 This is˙ preserved in Ibn Ab ī Us aybi a, ‘ Uyūn, pp. 604 – 5. 21 ˙ Ibid., p. 287. 22 The list first appears in Ibn al-Nad īm, and it contains about 300 titles: see his al-Fihrist (Beirut, 1978), pp. 358 – 65. The subsequent historians drew from his list (Adamson, Al-Kindī , p. 7). For al-Kind ī’s logical works see Ibn al-Nad īm, al-Fihrist, p. 358; al-Qift ī, ˙ Akhbār, p. 242; Ibn Ab ī Usaybi a, Uyūn, p. 289. Among his logical works whose titles ˙ suggest that they were written as summaries or commentaries on the Analytics, al-Qift ī ˙ mentions (p. 242) Kit āb f ī al-Burhān al-mantiqī ( Book on the Logical Demonstration); Ibn ˙ Ab ī Usaybi a (p. 289) mentions another work ( Risāla bi-ī jāz wa-ikhtisār f ī al-burhān ˙ ˙ iqī ; Summarized and Abridged Epistle on the Logical Demonstration ). See also al-mant 16
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al-Kind ī’s logical writings have come down to us, 23 so it is very difficult to establish a clear position about his contribution to the history of logic in general, and more specifically to the reception of the Categories . However, the Arab bibliographers mention several works on the Categories composed by al-Kind ī. Ibn al-Nad īm mentions His Epistle on the Ten Categories ( Kitāb Risālatihi f ī al-Maqūl āt al- ashr).24 Al-Qift ī lists a certain Book of the Ten Categories ( Kitāb ˙ ).25 Ibn Ab ī Usaybi a records a number of works al-Maqūl āt al- ashr on the subject: Book on Aristotle˙’ s Aim in the Categories ( Kitāb f ī Qasd Aristūtāl ī s f ī al-Maqūl āt),26 Epistle on the Ten Categories ˙ āla f ī al-Maq ˙ ˙ ūl āt al- ashr), and other works that probably treated ( Ris specific aspects of the theory of categories: Epistle on the Five Names that Accompany all of the Categories ( Risāla f ī al-Asmā al-khamsa al-l āh iqa li-kull al-Maq ūl āt) and Epistle on the Relative Quantity ( Risā˙la f ī al-Kammiyya al-mud ā fa).27 ˙ Luckily, we do possess al-Kind ī’s epistle On the Number of Aristotle’ s Books ( Fī Kammiyyat Kutub Aristū; hereafter: Kammiyya),28 which is quite indicative of his logical˙ skills. In this epistle al-Kind ī classifies Aristotle’s works as he understood them: 29 ʿ
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Aristotle’s ordered writings,30 which the student needs to go through successively, in their order and composition, so that he can be a philosopher
M. Abdarrāziq, “ Abū Y ūsuf Ya qūb Ibn Ish āq al-Kind ī: Islamic philosophy”, in Abū Y ūsuf ˙ Ya qūb Ibn Ish āq al-Kindī , p. 143. ˙ Atiyeh, Al-Kindī , p. 33; Adamson, Al-Kindī , p. 10. Ibn al-Nad īm, al-Fihrist, p. 358. Al-Qift ī, Akhbār, p. 242. ˙ Apparently this is the same book that appears in al-Qift ī’s list, but with a scribal error ( maqāl āt instead of maqūl āt): Kitāb f ī Qasd Aristūtāl ī˙ s f ī al-Maqāl āt ( ibid., p. 241). ˙ cases˙ al-Kind ī ˙ ’s historians and the editors Adamson ( Al-Kindī , p. 9) remarks that in many were the ones who gave titles to his works. Ibn Ab ī Us aybi a, ‘ Uyūn, p. 289. See also al-Qift ī, Akhbār, p. 359. The two men count this ˙ ˙ the arithmetical ( al-h isābiyyāt) rather epistle among than the logical works, since its discus˙ sion, as implied by its title, focuses on the category of Quantity. This category is obviously relevant to arithmetic. Al-Kind ī, F ī Kammiyyat kutub Arist ū, in Rasā il al-Kindī al-falsafiyya, ed. M. Abū R īda ˙ (Cairo, 1950), pp. 363 – 84. Partial English translation in N. Rescher, “ Al-Kind ī’s sketch of Aristotle’s Organon”, in Studies in the History of Arabic Logic (Liverpool and London, 1963), pp. 32 – 8. For an elaborate presentation of this epistle, see Jolivet, “L’ Épître”, pp. 665 – 83. Elsewhere, al-Kind ī writes that he has no intention to simply survey the works of the ancient philosophers (notably Aristotle), but also to “ complete their incomplete statements” ( Kitāb al-Kindī f ī al-Falsafa al-ūl ā, in his Rasā il , p. 103), implicating his intention to add to and interpret the writings of the ancients. It should be noted that in the Kammiyya al-Kind ī also refers to a different kind of science than Aristotle’s, which is characterized by man ’s search for knowledge. The other kind of science is the prophetic science ( ilm al-rusul ), which is characterized by being attained without being sought after. The first science is a human science ( ilm insānī ), while the other is a divine/metaphysical science ( ilm il āhī ). According to al-Kind ī, the divine science is loftier than the human science since it is the science of the things that are eternally true ʿ
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through them – after the science of mathematics – are four kinds of books: the first of the four is the logical [works] ( al-mantiqiyyāt); the second kind ˙ [discusses] that which is the physical [works] ( al-tabī iyyāt); the third kind ā can do without physics and˙ exists by itself, having no need for bodies ( f īm ʿ
kāna mustaghniyān an al-tabī a, qā imān bi-dhātihi ghayr muh tā j il ā ˙ a ceral-ajs ām), [although] it exists˙ with bodies, connected to them through ʿ
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tain connection; the forth kind [discusses] that which has no need for bodies and is not connected to them at all ( f ī mā l ā yah tā j il ā al-ajs ām wa-l ā ˙ yuwāsiluhā al-batta).31
˙ According to al-Kind ī, after the student of philosophy acquires the mathematical science he must study four kinds of Aristotelian writings: logical,32 physical,33 writings on things that do no need bodies for their existence (although they are able to exist attached to bodies),34 and metaphysical writings.35 Al-Kind ī also mentions Aristotle’s writings on ethics36 and other topics, but does not elaborate.37 In the Aristotelian tradition, the four kinds of writings that al-Kind ī enumerated belong to the theoretical sciences, while ethics is among the practical sciences. 38 Al-Kind ī views his classification
( al-ashyā al-haqqiyya al-thābita), that only the prophet can attain by revelation ˙ 372 – 6). Ibn al-Nad īm mentions a work by al-Kind ī entitled Kit āb Aqsām ( Kammiyya, pp. al- ilm al-insī ( Book of the Divisions of the Human Science ). 31 Al-Kind ī, Kammiyya, pp. 364 – 5. See Jolivet’s comments on this passage: Jolivet, “ L’ Épître”, p. 667. 32 Al-Kind ī enumerates the eight logical books ( ibid., pp. 365 – 8): Categories ( Qā tī ghūriyās wa-huwa al ā al-maqūl āt), De Interpretatione ( Bāriyārmāniās wa-ma nāhu: al ā˙ al-tafsī r), Prior Analytics ( Anāl ūtī qī
wa-ma nāhu: al- aks min al-ra s), Posterior Analytics ( Anāl ūtī qī al-Thāniya˙ wa-hiya al-makhsūs bi-ism Af ūdhiqt ī qā wa-ma nāhu al-ī d āh ), ˙ ˙ Topics ˙ ( T ū bī qā wa-ma anāhu: al-mawā˙ d i˙ , ya nī mawād i˙ al-qawl ), De Sophisticis ˙ ˙ ˙ Elenchis ( Sū fistī qā wa-ma nāhu: al-mansūb f ī al-sū fistā iyī n , wa-ma nā al-sū fistā ī al-mutah akkim),˙ Rhetoric (Rī tūrī qā wa-ma nāhu al-bal ˙ā ghī ), and Poetics ( Bū yī t˙ī qā ˙ ˙ wa-ma n˙āhu al-shi rī ). 33 According to al-Kind ī, there are seven physical works ( ibid., p. 368): Physics ( al-Khabar al-tabī ī ), De Caelo ( al-Samā ), De Generatione et Corruptione ( al-Kawn wa-al-fasād), ˙ ( Ah dāth al-jaww), On Minerals ( al-Ma ādin), On Plants (al-Nabāt), On Meteorology ˙ ān). Animals (al-H ayaw 34 ˙ These works are four ( ibid.): De Anima ( al-Nafs), Sense and Sensibilia ( al-H iss ˙ wa-al-mah sūs), On Sleep and Waking ( al-Nawm wa-al-yaqaz a), On Length and Shortness ˙ of Life ( T ū ˙ l al- umr wa-qisaruhu). 35 ˙ that deals with ˙these existents is the Metaphysics ( Mā The book warā al-tabī iyyāt) ( ibid.). ˙ On the difference between physics and metaphysics al-Kind ī writes: “the science of physics is the science of every thing that moves, hence metaphysics [is the science of every thing] that does not move” ( Fī al-Falsafa al-ūl ā, p. 111). 36 Among Aristotle’s ethical works al-Kind ī mentions the Nicomachean Ethics ( al-Akhl āq il ā N īq ūmākhus) and another work not mentioned by name. The editor of the Kammiyya ( ibid., p. 369, n. 5) claims that he is referring to the Eudemian Ethics ( Kitāb al-Akhl āq il ā Ū ydī mūs). 37 Al-Kind ī does not mention the titles of these works, but remarks that they deal with particular things ( ashyā juz iyya) ( ibid., p. 369). See the lists of his ethical works in Ibn al-Nad īm ( al-Fihrist, p. 363) and al-Qift ī ( Akhbār, p. 245). 38 ˙ al-khamsa ( Book of the Five Substances) in Rasā’ il al-Kindī See al-Kind ī’s Kitāb al-Jawāhir al-falsafiyya , ed. Abū R īda,pp. 8 – 35. See also Atiyeh, Al-Kindī , pp.38 – 40; Adamson, “Before ʾ
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as pedagogical; its aim is to make it easier for the student of philosophy to acquire them. Although metaphysics is mentioned last, it is the most important science. 39 The first thing that stands out when examining the Kammiyya is that al-Kind ī’s position regarding logic seems unclear. It is unclear whether or not he accepted the traditional Peripatetic view of logic as a tool for truth and certainty.40 The same occurs in al-Kind ī’s Epistle on the Definitions and Descriptions of the Things ( Risālat al-Kindī f ī H ud ūd al-ashyā wa-rusūmihā; hereafter: H ud ūd);41 ˙ ˙ define although he refers to a few logical concepts,42 al-Kind ī does not the term mantiq (logic). ˙ This ambiguity is also reflected when examining al-Kind ī’s position concerning mathematics: as we have seen, he places mathematics before the study of the Aristotelian corpus. If one wishes to be a philosopher, one must be taught in the four kinds of sciences found in Aristotle’s books. But before that, one must know mathematics. Does al-Kind ī substitute mathematics for logic as a preliminary science? The Arab biographers mention many mathematical works written by al-Kind ī.43 Among others, he composed an epistle entitled That Philosophy cannot be Attained without the Mathematical Science ( Risāla f ī annahu l ā tunāl al-falsafa ill ā bi- ilm al-riyād iyyāt).44 From this title it is clear that al-Kind ī held mathemat˙ the preliminary science one should learn. The position that ics to be ʾ
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essence and existence”, p. 30; A. F. El-Ehwany, “ Al-Kind ī”, in M. M. Sharif (ed.), A History of Muslim Philosophy, 2 vols. (Wiesbaden, 1963) vol. 1, p. 424. On the superiority of metaphysics ( al-falsafa al-ūl ā) over the rest of the sciences al-Kind ī writes: “ the most lofty philosophy of all, which is ranked the highest, is the first philosophy, namely the science of the primary truth that is the cause of every truth, hence the most perfect and lofty philosopher must be a man who is taught in this lofty science ” ( Fī al-Falsafa al-ūl ā, pp. 98, 101). See also Atiyeh, Al-Kindī , p. 45; Adamson, Al-Kindī , chapter 3; A. L. Ivry, “ Al-Kind ī as philosopher: The Aristotelian and Neoplatonic dimensions ”, in S. M. Stern, A. Hourani and V. Brown (eds.), Islamic Philosophy and the Classical Tradition (Oxford, 1972), pp. 118, 124 – 5, 133. The term “Logic” started pointing at the logical corpus only by Alexander. See W. Kneale and M. Kneale, The Development of Logic, 3rd edn (Oxford, 1966), p. 23. See also H. B. Gottschalk, “ The earliest Aristotelian commentators”, in Aristotle Transformed, p. 59. See Rasā’ il al-Kindī al-falsafiyya, ed. Abū R īda, pp. 165 – 79. For the importance of this treatise for the development of philosophical terminology in Islam see S. M. Stern, “Notes on al-Kind ī’s Treatise on Definitions”, in Abū Y ūsuf Ya qūb Ibn Ish ā q al-Kindī , pp. 422 – 33. ˙ ” ( al-jawhar), “quantity” Note the definitions of the following concepts: “substance ( al-kammiyya), “quality” ( al-kayfiyya ), “relation ” ( al-id ā fa), “truth” ( al-sidq), “falsity” ˙ ūd, pp. 166, ( al-kadhib), “doubt” ( al-z ann), and “certainty” ( al-yaqī n˙). See al-Kind ī, H ud ˙ ˙ 167, 169, 171. See for example Ibn al-Nad īm, al-Fihrist, pp. 358 – 61. Ibid., p. 358; cf. al-Qift ī, Akhbār, p. 241. See also Atiyeh, Al-Kindī , pp. 33, 37. The historian ˙ ī describes al-Kind ī as a geometrician ( kāna muhandisān) because of Zah īr al-D īn al-Bayhaq ˙his extensive activity in that field. See his Ta rī kh h ukamā al-Isl ām, ed. M. H. Muhammad ˙ (Cairo, 1996), p. 52. ʿ
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al-Kind ī adopts seems closer to the Platonic tradition.45 After classifying the sciences, he writes: These are the enumerations of his [ i.e., Aristotle’s] writings that we have mentioned earlier; the complete philosopher needs to acquire their knowledge after the science of mathematics. [. . .] For if one lacks the knowledge of the mathematical sciences – which consists of arithmetic ( ilm al- adād), geometry ( al-handasa), astronomy ( al-tanjī m), and [musical] composition ) – and then studies (lit. uses) those [ i.e., Aristotelian books] all his ( al-ta l ī f life, he shall not complete the knowledge of any of them, and his effort will earn him nothing but [the ability] to recite them verbally, [and that] if he is of good memory; but acquiring their profound knowledge is not at all possible (lit. does not exist) if one lacks the knowledge of mathematics. 46 ʿ
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Al-Kind ī adopts the traditional Pythagorean fourfold classification of mathematics into arithmetic, geometry, astronomy, and musical composition.47 His remarks on mathematics are similar to what the Peripatetics before and after him have to say about logic: 48 acquiring mathematics is a preliminary condition for understanding the rest of the sciences; the starting point for all of the sciences – including logic – must be mathematical, otherwise there is no guarantee that these
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Al-Ma sūm ī, “ Al-Kind ī”, pp. 380 – 1. See also al-Fārāb ī’s description of the Platonists: “ As for ˙ the science one should begin with before studying philosophy, the followers of Plato say that it is the science of geometry, quoting Plato, who wrote in the gate of his academy [lit., “building” – haykal ]: ‘whoever does not know geometry will not enter ’, since the demonstration employed by geometry are the most correct’” (Al-Fārāb ī, Ma yanbaghī an yuqaddam qabla ta allum falsafat Aristū, in Alf ārābī ’ s Philosophische Abhandlungen, ed. F. Dieterici [Leiden, 1890], pp. 49 – 55).˙ See also T. Heath, A History of Greek Mathematics, 3rd edn (Oxford, 1965), vol. 1, p. 284. Al-Kind ī, Kammiyya, pp. 369 – 70. See also p. 376. This classification was adopted by Plato and the Platonists with certain adaptations (see G. Endress, “Mathematics and philosophy in Medieval Islam”, in J. P. Hogendijk and A. I. Sabra [eds.], The Enterprise of Science in Islam [London, 2003], pp. 124 – 5; Heath, History, vol. 1, p. 284; A. Wesberg, Plato’ s Philosophy of Mathematics [Stockholm, 1955], p. 21). Jolivet (pp. 673, 676) identifies two different orders of the classifications of mathematical sciences in al-Kind ī’s Kammiyya; the first is a Platonic and a pedagogical one (al-Kind ī, Kammiyya, p. 369: arithmetic, geometry, astronomy, and [musical] composition); and the second is a Pythagorean and an epistemological one ( ibid., p. 370: arithmetic, [musical] composition, geometry, and astronomy). Al-Kind ī was exposed to Pythagoreanism and Neopythagoreanism through the connection between the schools of Baghdad and the scholars who worked in H arrān or came from there. For instance, Thābit ibn Qurra, who moved ˙ from H arrān to Baghdad, had significant influence on Baghdadian schools, including ˙ al-Kind ī’s circle (Gutas, Greek Thought, p. 104). Logic was taken to be a tool for examining the validity of arguments, constructing a syllogism, and arrival at certainty. This view is expressed in the Aristotelian Commentators, especially Alexander of Aphrodisias, who viewed logic as a tool (organon) for philosophy and not as an independent science. Hence this tool functions as a method that aids man in attaining true knowledge in all of the aforementioned sciences, and one needs to control it before one approaches other sciences. See Kneale and Kneale, Development, p. 23. For the period after al-Kind ī see, for instance, al-Fārāb ī, Ih sā al- ul ūm (Beirut, 1991), pp. 13 – 15; ˙˙ Ibn S īnā, al-Ishārāt wa-al-tanbī hāt, ed. S. Dunyā (Cairo, 1983), vol. 1, p. 117; Ibn Rushd, Risālat mā ba d al-tabī a, ed. R. al- Ajam and J. Jihām ī (Beirut, 1994), p. 60. ʿ
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sciences will be studied correctly.49 Indeed, a quick survey of al-Kind ī’s writings exhibits his interest in mathematics. 50 II. SUBJECT AND PREDICATE: LOGIC OR ONTOLOGY?
Among the various books of Aristotle’s Organon, al-Kind ī took special interest in the Categories. In the Kammiyya a modest discussion is devoted to the eight books of Aristotle ’s Organon. It opens with the Categories : The first among them [ i.e., the logical works] is called Q ātī ghūriyās and it is about the categories, namely, the subject ( al-h ā mil ) ˙and the predicate ˙ ” ( jawhar), and the pre( al-mah mūl ). The subject is what is called “substance dicate ˙is what is called “accident ” ( arad ), which is predicated of the substance without giving it its name or ˙its definition ( ghayr mu tin lahu ˙ ismahu wa-l ā h addahu).51 ʿ
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˙ According to al-Kind ī, there are eight books in Aristotle’s logic. He does not mention Porphyry ’s Isagoge,52 which traditionally opened
In his F ī al-Falsafa al-ūl ā (p. 112), al-Kind ī states that in mathematics one must provide demonstration rather than persuasion: “if we were to employ persuasion ( iqnā ) in the science of mathematics, our learning in it would be of surmise ( z anniyya) and not scientific ˙ ( ilmiyya ).” 50 The mathematical method appears in many of al-Kind ī’s epistles. See, for instance, his treatment of the problem of infinity: F ī al-Falsafa al-ūl ā, pp. 114 – 16; Ris ālat al-Kindī f ī Ī d ā h tanāhī jurum al- ālam, in his Rasā’ il , pp. 186 – 92; Risālat al-Kindī f ī M ā iyyat mā l ā ˙ ˙ yumkin an yakūna l ā nihā ya lahu wa-mā alladhī yuqāl l ā nihā ya lahu, pp. 194 – 8; Risālat al-Kindī f ī Wah dāniyyat Allah wa-tanāhī jurum al- ālam, pp. 201 – 7 . De Boer ˙ notes that al-Kind ī applied the mathematical method also to medicine (T. J. De Boer, The History of Philosophy in Islam, tr. E.R. Jones [New York, 1967], pp. 100 – 1). See also Adamson, Al-Kindī , ch. 7, which is dedicated to a discussion of the mathematical method in medicine (pp. 161 – 6 ), optics (pp. 166 – 7 2), and music (pp. 172 – 80); Gutas, Greek Thought, p. 120; Y. T. Langermann, “ Another Andalusian revolt? Ibn Rushd’s critique of al-Kind ī’s pharmacological computus”, in The Enterprise of Science in Islam , pp. 351 – 72, pp. 351 – 2. For al-Kind ī’s works in the four mathematical sciences (arithmetic, geometry, astronomy, and musical composition) see the long list that is reproduced by a number of historians: Ibn al-Nad īm, al-Fihrist, pp. 358 – 61; al-Qift ī, Akhbār, pp. 242 – 3; Ibn Ab ī Us aybi a, Uyūn, ˙ quotes a Kindian anecdote about ˙ the reason p. 289-91. Sā id al-Andalus ī ( al-Ta rī f , p. 179) ˙ for the composition of Euclid ’s Elements ( al-Arkān). For al-Kind ī’s works that are related to the Elements see Ibn al-Nad īm, Al-Fihrist, p. 360 (cf. al-Qift ī, Akhbār, p. 243): His is), His Epistle on Epistle on the Aims of Euclid ’ s Book ( Risālatihi f ī Aghrād Kitāb ˙Uql īd the Correction of Euclid’ s Book ( Risālatihi f ī Isl āh Kitāb Uql ī dis). Ibn Ab ī Usaybi a adds ˙ ˙of the Fourteenth and Fifteenth ˙ Books of another works, entitled Epistle on the Correction Euclid’ s Treatise ( Risāla f ī Isl āh al-maqāla al-rābi a ashrata wa-al-khāmisa ashrata min ˙ is). For Euclid’s ˙influence on al-Kind ī see Adamson, Al-Kindī , p. 27. Kitāb Uql īd 51 Al-Kind ī, Kammiyya, p. 365. Cf. his definition in H ud ūd, p. 166. See also F. W. ˙ Zimmermann, Al-Farabi’ s Commentary and Short Treatise on Aristotle’ s De Interpretatione (Oxford, 1987), p. xxvii. 52 The Isagoge was popular in the Muslim world since the early period of translation, and al-Kind ī was undoubtedly familiar with it. Ibn al-Nad īm ( al-Fihrist, p. 358) and al-Qift ī ˙ ( Akhbār, p. 242) list two books – an abridgement and a commentary – on the Introduction to Logic ( al-Madkhal al-mantiqī ) , which is an Arabic title for the Isagoge. Ibn Ab ī 49
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the Organon, but rather approaches the Categories immediately. While the other books are surveyed briefly, the discussion of the Categories is broader, exhibiting al-Kind ī’s personal interest in it.53 Near the end of the discussion he introduces the threefold division of the Categories in a manner indicative of his familiarity with the work.54 The view that al-Kind ī had a special interest in the Categories is reinforced by the fact that the translator Ibn Bihr īz (d. c. 860) wrote a summary of the book especially for him. 55 Al-Kind ī treats the Categories as a logical book, and he views the ten categories as the basic elements from which propositions can be made, thus he connects between the Categories and On Interpretation ( Al ā al-tafs ī r) by saying that the former is entitled On Interpretation since it aims at “interpreting what is said in the Categories and connecting them [i.e., the categories] in order to make propositions [which consist of] subject and what can be said about it, namely from subject and predicate. ”56 Al-Kind ī adopts the traditional Aristotelian division of substance and accident, 57 and clarifies the nature of their relationship: the accident is said of the substance “without giving it its name or its definition.”58 He later explains himself: ʿ
Usaybi a ( Uyūn, p. 289) explicitly uses the Greek title in his list: Abridgement of the Book ˙ Isagoge by Porphyry ( Ikhtisār Kitāb Ī saghū jī li-Farf ūryūs). ˙ the Christians ( al-Radd al ā al-Nasārā) he explicitly mentions In his epistle on Refuting ˙ the Isagoge and employs it in his attack on the trinity. See R. Rashed and J. Jolivet, Œ uvres philosophiques et scientifiques d’ al-Kindī , vol. II: Métaphysique et cosmologie (Leiden, 1998), p. 123. It is possible that al-Kind ī does not mention the Isagoge here because he knew it was not composed by Aristotle. In his F ī al-Falsafa al-ūl ā, al-Kind ī surveys the universals in a manner similar to Porphyry, discussing the genus ( al-jins), the species (al-Kind ī uses the term sūra – “form” – rather than the more common naw . See ibid., pp. 125, 126, 130. In other ˙places he uses naw – see ibid., pp. 153, 160. In the H ud ūd, p. 166, he uses the term s ūra ˙ ˙ is in a manner parallel to “matter”: “the form [is] the thing through which a certain thing what it is.” For the different meaning of s ūra in al-Kind ī see Rashed and Jolivet, Œ uvres, ˙ l ) , the property ( al-khāssa), and the accident vol. 2, pp. 19 – 22), the differentia ( al-fas ˙ concept to the discussion, ˙ ˙ namely the individ( al- arad al- āmm). However, he adds another ˙ ual ( al-shakhs ; see F ī al-Falsafa al-ūl ā, pp. 124 – 30, esp. pp. 126 – 7, 128 for the individual). ˙ ā also add the individual to the five universals of the Isagoge. See Ras ā il Ikhwān al-Saf ˙ af ā (Beirut, n.d.), vol. 1, p. 395. Ikhwān al-S 53 ˙ See al-Kind ī, Kammiyya, pp. 365 – 6, 370 – 2, 377 – 9. See also Jolivet, “L’ Épître”, pp. 670 – 1. 54 Ibid., p. 379. 55 Rescher, Development, p. 100; T. Street, “ Arabic logic”, in D. M. Gabbay and J. Woods (eds.), Handbook of the History of Logic, vol. I: Greek, Indian and Arabic (Amsterdam, 2004), p. 531. 56 Al-Kind ī, Kammiyya, p. 366. 57 Al-Kind ī, F ī al-Falsafa al-ūl ā, p. 126. Aside from the individual, al-Kind ī divides the universals here into essential (genus, species, differentia), and accidental (property, accident). 58 Al-Kind ī, Kammiyya, p. 365. For a parallel discussion in Aristotle about the different relations that can exist between the subject and the predicate, see Aristotle, “Categoriae”, in The Works of Aristotle, ed. W. D. Ross (Oxford, 1950), vol. 1, Chapters: 1, 2, 5. ʿ
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The predicate “said-of ” [is divided] to two species: one of them gives its sub ject its name and its definition, like the “living” that is said-of the man, for the man is called “living ” and is [also] defined by the definition of the living, that is “a sensing substance that moves toward a different thing exterior to it” ( jawhar h assās mutah arrik li-ghayr shay khārij anhu).
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[. . .] [The second species of the predicate] is what is said of its subject as a similar name ( ishtibāh al-ism)59 and not as an agreed upon ( tawātu ) ˙ ” [name],60 without giving its definition and its name, like “the whiteness that is predicated of “the white”, namely “the white body.”61 ʾ
Al-Kind ī’s distinction between two kinds of relations between the subject ( al-h ā mil ) and the predicate ( al-mah mūl ) is significant, and ˙ is subsequently developed in philosophers˙ as al-Fārāb ī, Ibn S īnā and Fakhr al-D īn al-Rāz ī. According to al-Kind ī, the relation between the subject and the predicate is such that the predicate is said of the subject when the latter can be called by its predicate, and when both of them share a definition. He exemplifies this by the relation between “man” and “animal”: the species “man” is included in the genus “animal”, and hence “man” can be named “animal” as well as be defined it, for the definition of “animal” ( “a substance with a sensory faculty that moves towards a different thing exterior to it”62) also applies to “man”. In this sense, “animal” can function both as a name for “man” and as his definition. Al-Kind ī calls this relation between subject and predicate a “synonym” ( al āqat tawātu ). Another possible relation that˙ can exist between the subject and the predicate is a homonym ( ishtibāh). In this kind of relation, the predicate expresses neither the subject’s name nor its definition. As an example, al-Kind ī gives the whiteness that is predicated of the white [body]. Though the terms “white” and “whiteness” are similar, “whiteness” cannot function as a name or a definition for the ʿ
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Here is a Kindian example for the similar name ( al-ism al-mutashābih): “the lion that is called ‘dog’ and the star that is [also] called ‘dog’ – we say that both of them are ‘one in name’, which is ‘dog’ ( Fī al-Falsafa al-ūl ā, p. 155). “Dog” is a similar name, since it is said of both the lion and the star but is all that they have in common. Al-Kind ī explains the difference between a similar name ( mutashābih) and an agreed upon name ( mutawāti ) in his ˙ agreed description of the substance. The substance is “that which is [described in an] upon description ( na t mutawāti ) or a similar description ( na t mutashābih); the agreed ˙ upon description gives the described [thing] both its name and its definition, while the similar description gives the described [thing] neither its name nor its definition. If it gives it its name, it does so through derivation ( ishtiqāq)” ( Risālat al-Kindī f ī annahu tū jad jawāhir l ā ajsām, in al-Kind ī, Rasā’ il , p. 266). Al-Kind ī exemplifies the agreed upon name through the terms “genus” and “species”: “genus” is said of all of the individuals that are included equally and in the same manner, for man is not more of an animal than the lion. The same applies for species. See F ī al-Falsafa al-ūl ā, p. 128. Al-Kind ī, Kammiyya, pp. 365 – 6. See also F ī al-Falsafa al-ūl ā, p. 125, and Jawāhir l ā ajsām, pp. 266 – 7. Al-Kind ī, Kammiyya, p. 365. ʾ
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white” (or, to be precise, “the white body ”) and the relation between them is of paronymity ( ishtiqāq): the term “white” is derived from the term “whiteness”. The “white body” is not identical to the “whiteness”, and when one says “whiteness” one does not mean “white body”. Therefore, in this case the predicate does not function as a name for the subject. Accordingly, the definition of “whiteness”, namely “a color [that] obstructs the vision ” ( lawn yu ī q al-basar),63 is not said ˙ “white” and the of the “white body”. Hence the relation between the “whiteness” is neither of name nor of definition, but rather of a linguistic derivation: the term “white” is derived linguistically from the term “whiteness”.64 Al-Kind ī finds the second type of relation between subject and predicate to be the one that fits into the theory of categories. In the Kammiyya he enumerates the ten categories: ʿ
The categories [i.e.,] the accidental predicates ( al-mah mūl āt al- arad iyya) of ˙ the “said-of ” subject ( al-maqūl al-h ā mil ) , 65 the Substance ( al-jawhar),66 are nine: Quantity ˙ ( kammiyya),67 Quality ( kayfiyya ),68 Relation ( id ā fa),69 Where ( ayn), When ( matā), Acting ( f ā il ), Being Acted ˙ il ), Having [=Property] ( lahu), Position ( wad ).70 Upon ( munfa ʿ
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˙ The categories are said of the substance in the manner of linguistic derivation. For instance, “whiteness” is included in the category of Quality, but one does not say “the table is whiteness”, but rather “the table is white ”. The term “white” is derived from the term “whiteness”, and the rest of the categories that are said of the substance undergo the same process of linguistic derivation. Al-Kind ī’s distinction between two kinds of relation is important and has far reaching ontological implications. In the case of “man is an animal”, the relation between the subject and the predicate is that of identification, so far as that the subject can be defined by the predicate as well as be named by it. On the other hand, one says “the table is white” and not “the table is whiteness ”. In this case, the relationship between the subject and the predicate is ontological, in the sense that the “white” is really present in the table. To sum up, in the first example the relation is logical, while in the second example the relation is ontological.
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This is al-Kind ī’s definition of color ( Kammiyya, p. 366). Ibid. Editor’s insertion. See the definition of Substance in the H ud ūd, p. 166. ˙ See the definition of Quantity, ibid., p. 167. See the definition of Quality, ibid. See the definition of Relation, ibid. H ud ūd, p. 366.
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As we have seen, al-Kind ī’s surviving fragments on logic imply that he doesn’t see logic in its traditional Aristotelian role as a tool for certainty. This role is taken by mathematics insofar as it provides the aspiring student of philosophy the necessary skill of correct thought. Logic is to be studied only afterwards. In this section I will try to explain how al-Kind ī understands the transfer from mathematics to logic and the relation between the two. Al-Kind ī sees the “science of the substance ( ilm al-jawhar) and its predicates ( al-mah mūl āt)” as the most important science. 71 He divides the predicates into˙ simple ( mufrad) and composite ( murakkab), and the latter are divided on the basis of whether or not they have matter. 72 Accordingly, the categories are divided in the following manner: ʿ
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The categories Quantity and Quality differ from the rest as they are not composite. Each of the two is characterized by its special essential property: Quantity alone characterizes the substance as “equal” ( mithl ) or “non-equal” ( l ā mithl ),73 while Quality
Ibid., p. 370. Ibid. In the H ud ūd (p. 167) al-Kind ī provides the following definition for Quantity: “ that which is ˙ to equality and inequality ” ( mā ih tamala al-musāwā wa-ghayr al-musāwā). The subjected term musāwā here is interchangeable with˙ mithl .
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alone characterizes it as “similar” ( shabī h) or “non-similar” ( lā 74 shabī h). Composite categories are divided into two: 2.1 Composite without matter ( tī na):75 this is the category of ˙ Relation, for the relations between the father and the son, or the whole and the part – to take al-Kind ī’s examples – do not involve matter. 2.2 Categories which are composite with matter: 2.2.1 The composition of Quantity and Substance: if the substance exists ( kā in) in a certain place76 – place is a quantity – this is the category of Where ( ayn); if the substance exists in a certain time ( zamān) – time is a quantity as well – this is the category of When ( matā). 2.2.2 The composition of Quality and Substance: if the substance is in action – action77 being a quality – this is the category of Acting ( f ā il ) ; if the substance is being acted upon – the latter being a quality too – this is the category of Being Acted Upon ( munfa il ).78 2.2.3 The composition of Substance and Substance: if a certain substance is “with” ( ma a) another substance, this is the category of Having ( mulk),79 in which one of the substances has the other; if a certain substance is situated “on” another substance, this is the category of Position ( wad ).80 ʾ
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It seems thatal-Kind ī ascribes a special place to the categoriesof Quantity and Quality, while the rest of the categories are the result of the different Al-Kind ī, Kammiyya, p. 370. See also F ī al-Falsafa al-ūl ā, pp. 106, 160; H ud ūd, p. 167. Al-Kind ī uses the term t ī na instead of hayūl ī . See H ud ūd, p. 166, and n. ˙2 there. 76 ˙ ˙ Al-Kind ī follows the Aristotelian assumption according to which the place ( al-makān) and the object that is placed in it ( al-mutamakkin) exist simultaneously, so that there is no place that is not occupied by an object (in other words, there is no void), and there is no placed object without a place. See F ī al-Falsafa al-ūl ā, pp. 109, 138. This is how place is defined in the H ud ūd (p. 167): “the place [is] the edges of the body, and some say: it is ˙ the meeting points of two horizons – of the container and of that which it contains ” ( huwa iltiqā ufuqay al-muh ī t wa-al-muh āt bihi). 77 ˙ H ˙ ˙ ud ūd (p. 167): “ Action is the influence on a subject that This is how action is˙defined in the ˙ can be influenced. Some say: it is the movement [whose principle is] from the mover himself. Compare al-Kind ī’s Epistle al-F ā il al-h aqq al-awwal al-t āmm wa-al-f ā il al-nāqis alladhī ˙ is an huwa bi-al-majāz ( The First True and˙ Perfect Actor and the Defective Actor [which Actor] Metaphorically), in al-Kind ī, Rasā il , pp. 182 – 4. 78 Later on, these two categories were known as an yaf ala and an yanfa ila. See for instance al-Fārāb ī, Kit āb al-Maqūl āt, in al-Mantiq inda al-F ārābī , vol. 1, ed. R. al- Ajam (Beirut, ˙ 1985), pp. 113, 115. 79 Sometimes al-Kind ī uses the term lahu, which has the same meaning. See Kammiyya, p. 366. 80 Ibid., pp. 370 – 2. Compare with Simplicius’ division: Simplicius, pp. 82 – 3. 74 75
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combinations between the two and the category of Substance.81 He then adds another element to his understanding of the categories: The primary knowledge that encompasses every philosophical science is [the knowledge of] the substance, and [then that of] the quantity and the quality. The primary substance, namely the sensible, is also included in the knowledge of its primary predicates ( mah mūl āt). For the sense does not approach ˙ it through the mediation of the quantity [substance] directly, but approaches and the quality, and he who lacks the science of quantity [and] quality lacks the science of the substance. Within the science of philosophy, the science of the substance is the most unchangeable, true, and perfect. The secondary substances are those whose knowledge does not perish, because it is stationary and they are far from change and flowing. One approaches them through the science of the primary substance. 82
Not only are Quantity, Quality, and Substance the basis of the rest of the categories,83 the first two are epistemologically prior to Substance, the knowledge of which is dependent upon them.84 On the other hand, the knowledge of the unchanging secondary substances ( al-jawāhir al-thawānī ) is dependent upon the knowledge of the changing primary substances ( al-jaw āhir al-awwal ī ).85 In other words, although the knowledge of the secondary substance is superior given that it is the knowledge of the universal, it is dependent upon the knowledge of the primary substance, which, in turn, is dependent upon the knowledge of the categories of Quantity and Quality. Therefore, al-Kind ī asserts: “if someone lacks [. . .] the science of quantity and the science of quality, he lacks the science of the primary and secondary substances.”86 Elsewhere in the Kammiyya al-Kind ī enumerates the arts and sciences that belong to these two categories: Two arts study the quantity: The first is the art of number ( sinā at al-a dād), which studies the separate ˙ quantity, namely the counted quantity ( kammiyyat al-h isāb). [. . .] ʿ
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The other art is the science of [musical] composition, which is finding the relation between a [certain] number and [another] number. 81
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Except for the categories Having and Position, which are outcomes of the composition of two substances. Ibid., p. 372. Compare with Iamblichus’ position which is quoted in Simplicius, p. 83. See Jolivet, “L’ Épître”, p. 674. Atiyeh, Al-Kindī , p. 37. On the difference between the primary and secondary substances al-Kind ī writes ( Fī al-Falsafa al-ūl ā, p. 107): “The particular and material individuals fall under the senses, while the genera and the species do not fall under the senses, nor do they have a tangible existence, but rather fall under one of the faculties, of the perfect soul, namely the human [soul], and it is [the faculty] which is called ‘the human intellect’.” For al-Kind ī’s theory of substance see Atiyeh, Al-Kindī , pp. 88 – 90. Al-Kind ī, Kammiyya, p. 372.
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Two arts also study the quality: The first is the science of the unmoving quality ( ilm al-kayfiyya al-th ābita), which is the science of the area called “geometry” ( ilm al-misāh a ˙ al-musammā handasa). ʿ
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The other is the science of the moveable quality ( ilm al-kayfiyya al-mutah ārrika), and it is the science of the appearance of the all ( ilm ˙ hay at al-kull ) [i.e., the world and the heavens surrounding it], its shape, and its movements. [. . .] This is called the science of “astronomy”.87 ʿ
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Finally, al-Kind ī connects mathematics with the rest of the sciences and stresses that mathematics must be philosophy ’s starting point, and a preliminary condition for studying it correctly: He who lacks the four sciences that are called mathematics and ta āl ī m88 – which are the [sciences of] the number, the area, astronomy, and [musical] composition – lacks the science of the quantity and the quality, and lacks the science of the substance, that cannot persist without their mediation yaz ūlu ill ā bi-tawassutihimā). He who lacks the science of quantity, qual( lā ˙ science of philosophy. ity, and substance lacks the Indeed, he who wants the science of philosophy should precede [it] with the use of the mathematical writings according to their order which we have defined; and the logical [writings] according to their order that we have already defined; then the writings about the natural things in the manner we have already defined; and then the metaphysical [books]; and then the books on ethics and the governance of the soul according to the virtues; and then what is left of the sciences, that we have not defined, [which is] composed of what we have defined. 89 ʿ
Al-Kind ī broadens the boundaries of the discussion and connects mathematics with all of the sciences that belong to philosophy. Through the mediation of the categories of Quantity and Quality, mathematics leads the student of philosophy to a proper instruction of the latter. In al-Kind ī’s thought, the passage from mathematics to logic is not a sudden one; he knows how to connect the two without alienating logic from mathematics, and the passage doesn ’t seem like a leap. The overlapping of these sciences occurs thanks to the categories of Quantity and Quality: on the one hand, they belong to logic, being part of the discussion of the Categories; on the other, they possess the mathematical aspect, for the four mathematical sciences (arithmetic, geometry, musical composition, and astronomy) fall under them. Quantity and Quality do not act merely as mediators, but rather penetrate the rest of the categories as I showed in the above scheme. Their importance in the
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Ibid., p. 377. Ta āl ī m and mathematics have the same meaning. Ibid., p. 378. ʿ
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sciences is such that al-Kind ī states: “ he who lacks the science of quantity, quality, and substance lacks the science of philosophy. ”90 Besides Substance, Quantity, and Quality – the latter two receiving special attention – the rest of the categories are scarcely mentioned. 91 Quantity and Quality have epistemological prevalence over Substance,92 for according to al-Kind ī the knowledge of the latter is dependent upon the other two, which also function as the epistemological gateway to the rest of the sciences. 93 In al-Kind ī’s model mathematics is not only the tool that opens the philosophical corpus and trains the student for the study of the rest of the sciences; it is actually present in all of them, through the categories of Quantity and Quality. In a certain manner, one can say that al-Kind ī communicates with the Pythagorean, Platonic, and Aristotelian traditions. His treatment of the categories of Quantity and Quality, whichresults in the presence of mathematics in all of the sciences, has affinity to the Pythagorean idea of a universe all of whose phenomena can be expressed as mathematical relations.94 The Platonic influence is apparent in placing mathematics 90 91
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Ibid. To be precise, al-Kind ī was interested in the category of Quantity even more than in the category of Quality. See the fourth section of F ī al-Falsafa al-ūl ā (pp. 143 – 53), where al-Kind ī devotes a full and detailed discussion to the Quantity and issues that stem from it. The reference here is to the primary, not the secondary substance, since the latter can be known through the logical definition ( al-h add) or the descriptive definition ( rasm), while the former is always in a changing state so˙ it is difficult to grasp its essence. The knowledge is of the universal, not the particular. Furthermore, in F ī al-Falsafa al-ūl ā (pp. 124 – 5) al-Kind ī remarks that philosophy aims at knowing the universal, and not the particular, which is infinite in number. Jolivet states that while Aristotle’s classification of sciences is based on ontological considerations, al-Kind ī’s classification is based on epistemological ones (Jolivet, “ L’ Épître”, p. 677). It should be mentioned that al-Kind ī’s hierarchical classification, which starts with mathematics and proceeds to the rest of the sciences through the mediation of the categories Quantity and Quality, does not apply to the divine science, which is exclusive to the prophets. Al-Kind ī explains that the latter do not employ neither mathematics nor logic, but receive their knowledge directly from God (al-Kind ī, Kammiyya, pp. 372 – 3). This is how al-Shahrastān ī sums up Pythagoras ’ doctrine: “he said that the number is the principle of all of the existents” (al-Shahrastān ī, al-Milal wa-al-nih al , ed. A. F. Muhammad [Beirut, 1992], p. 387; for Pythagoras and the Pythagoreans ˙in the Islamic tradition see ibid., pp. 385 – 99). One of the books that al-Kind ī edited was an Arabic version of Nicomachus of Gerasa ’s (Pythagorean mathematician who flourished circa 100 AD) Introduction to Arithmetic (see Heath, History, vol.1, pp. 97 – 112; J. Gow, A Short History of Greek Mathematics , 3rd edn (New York, 1968), pp. 88 – 9 5. H ab īb ibn Bihr īz translated the work from Syriac into Arabic, and al-Kind ī edited and˙ corrected the translation for a man named T āhir ibn ˙ al-H asan (see Endress, “Mathematics”, p. 128). The Arabic version is lost, but is preserved in a˙ Medieval Hebrew translation ( partial edition in G. Freudenthal and T. Lévy, “De Gérase à Bagdad: Ibn Bahr īz, al-Kind ī, et leur recension arabe de L’ introduction arithmétique de Nicomaque, d ’après la version hébraïque de Qalonymos ben Qalonymos d’ Arles”, in De Zénon d’ Elée à Poincaré , pp. 479 – 544, at pp. 514 – 44: “Le premier traité du Livre d’ arithmétique”). The work is mentioned in the bibliographic literature under the title His Epistle on the Introduction to Arithmetic: Five Tracts ( Risālatihi f ī al-Madkhal il ā al-arithmātī qī : khams maqāl āt). See Ibn al-Nad īm, al-Fihrist, p. 358; al-Qift ī, Akhbār, ˙ ˙ p. 242; Ibn Ab ī Us aybi a, Uyūn, p. 289. ʿ
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as a prior condition for studying the sciences and in maintaining that mathematics rather than logic is the tool for correct thought.95 Finally, the Aristotelian influence is apparent from the adoption of the categories as the basis for the entire discussion. 96 What we arrive at is a systematic attempt for the mathematization of the categories. 97 IV. CONCLUSION
A study of al-Kind ī’s approach to the theory of categories reveals that it is closely connected to his pedagogical prioritization of mathematics over logic and serves as a bridge between the two disciplines. Mathematics and logic are connected through the mediation of the categories of Quantity and Quality, which belong to logic insofar as they are part of the Categories, but possess a mathematical aspect as well. Without further explanation, al-Kind ī maintains that these two categories penetrate the rest of the categories and the sciences, as well. Furthermore, they have a key role in the theory of knowledge as they are an epistemological condition for the knowledge of the substance. Finally, all of the remaining categories are derived from different relations between Substance, Quantity, and Quality. Belonging to the early Abbāsid era, when the pursuit for knowledge focused more on the sciences that on philosophy, al-Kind ī was more of a scientist than a philosopher. In this sense, it comes as no surprise that his understanding of the categories is directed towards a scientific use of them, though his model is still a theoretical one.* ʿ
Another indication of al-Kind ī’s familiarity with the Pythagorean tradition is his intellectual connection with the Sābi ans of H arrān ( S ā bi at H arr ān, most of whom were Pagans, ˙ ˙ ˙ ˙ who incorporated Pythagorean, Platonic, and Neoplatonic elements in their thought; see Endress, “Mathematics ”, p. 127). Thābit ibn Qurra wrote an Arabic abridgement of Proclus’ commentary on the Introduction to Arithmetic. See Gutas, Greek Thought, p. 104. 95 For Plato’s influence on al-Kind ī and on their theories of soul see the introduction to his Rasā il , pp. 80(18) – 80(21). On the influence of Platonic mathematics see Endress, “Mathematic ”, pp. 127 – 31; Ibn al-Nad īm ( al-Fihrist, p. 358) ascribes to al-Kind ī a work entitled His Epistle on the Explanation of the Numbers that Plato Mentioned in the Republic ( Risālatihi f ī al-Ibāna an al-a dād allatī dhakarahā Fl ātun f ī Kitāb al-Siyāsa). ˙ Cf. al-Qift ī, Akhbār, p. 242; Ibn Ab ī Us aybi a, Uyūn, p. 289. 96 ˙ ’s influence on al-Kind ī see ˙ the introduction to his Rasā’ il , pp. 80(13) – 80(18). For Aristotle 97 One can find a proximate position in Ikhwān al-Saf ā , whose Rasā il opens with a group of ˙ for prospective students of philosophy mathematical treatises that aim at paving the way (Ikhwān al-Saf ā , Rasā il , pp. 21, 48, 75 – 6). However, unlike al-Kind ī, they do not offer an explanation˙for the affinity between mathematics and logic. * This paper is an expansion of a discussion in chapter 3.2 of my doctoral dissertation: A. Ighbariah, The Development of the Theory of Categories in Islamic Philosophy Between the 9 th and 13 th Centuries, PhD dissertation, University of Haifa, 2009. I would like to express my deepest gratitude to my teacher Ilai Alon, to my friend Yoav Meyrav, and to the consulting board of Arabic Sciences and Philosophy for their useful notes, which improved this article considerablely. ʾ
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