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BETWEEN LOGIC AND MATHEMATICS: AL-KINDĪ'S APPROACH TO THE ARISTOTELIAN CATEGORIES

Published online by Cambridge University Press:  27 February 2012

Ahmad Ighbariah
Ahmad Ighbariah*
Affiliation:
The Cohn Institute for the History and Philosophy of Science and Ideas, Humanities Faculty, Tel Aviv University, Ramat Aviv, Tel Aviv 69978
*
Email: [email protected]
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Abstract

What is the function of logic in al-Kindī's corpus? What kind of relation does it have with mathematics? This article tackles these questions by examining al-Kindī's theory of categories as it was presented in his epistle On the Number of Aristotle's Books (Fī Kammiyyat kutub Arisṭū), from which we can learn about his special attitude towards Aristotle theory of categories and his interpretation, as well. Al-Kindī treats the Categories as a logical book, but in a manner different from that of the classical Aristotelian tradition. He ascribes a special status to the categories Quantity (kammiyya) and Quality (kayfiyya), whereas the rest of the categories are thought to be no more than different combinations of these two categories with the category Substance. The discussion will pay special attention to the function of the categories of Quantity and Quality as mediators between logic and mathematics.

Résumé

Quelle est la fonction de la logique dans le corpus d'al-Kindī? Quel type de relation entretient-elle avec les mathématiques? Le présent article examine ces questions en étudiant la théorie des catégories d'al-Kindī telle qu'on la trouve développée dans son épître Sur la quantité des livres d'Aristote (Fī Kammiyyat kutub Arisṭū), instructive quant à son rapport à la théorie aristotélicienne des catégories et à sa propre conception des catégories. Al-Kindī tient les Catégories pour un traité logique, mais d'une façon qui n'est pas celle de la tradition aristotélicienne classique. Il confère ainsi un statut spécial à la catégorie de la quantité (kammiyya) et à celle de la qualité (kayfiyya) 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 médiatrice de la catégorie de la quantité et de la qualité entre logique et mathématiques.

Type
Research Article
Information
Arabic Sciences and Philosophy , Volume 22 , Issue 1 , March 2012 , pp. 51 - 68
Copyright
Copyright © Cambridge University Press 2012

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References

1 See examples in Frede, M., “The title, unity, and authenticity of the Aristotelian Categories”, in id., Essays in Ancient Philosophy (Minneapolis, 1987), pp. 11–28, at pp. 24–5Google Scholar.

2 Frede, “The title, unity, and authenticity”, p. 11. Sorabji states that before the age of Porphyry, and during the first and the second centuries, five interpretations were written on the Categories, none of which survived except a number of fragments that were preserved in Simplicius' interpretation. See Sorabji, R., “The ancient commentators on Aristotle”, in Sorabji, R. (ed.), Aristotle Transformed (Trowbridge, 1990), p. 1Google Scholar; Simplicius, On Aristotle's Categories 1–4, tr. Chase, M. (Ithaca, New York, 2003), pp. 17–18Google Scholar.

3 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. Strange, S. K. (Ithaca, New York, 1992)Google Scholar.

5 See Dexippus, On Aristotle's Categories, tr. Dillon, John (London, 1990)Google Scholar.

6 See Ammonius, On Aristotle's Categories, tr. Cohen, S. M. and Matthews, G. B. (London, 1991)Google Scholar.

7 See Simplicius, Categories.

8 See Olympiodorus, Olympiodorii Prolegomena et in Categorias commentarium, ed. Busse, A., Commentaria in Aristotelem Graeca, XII.1 (Berlin, 1902)Google Scholar.

9 See Philoponus, in Aristotelis Categorias commentarium, ed. Busse, A., Commentaria in Aristotelem Graeca, XIII.1 (Berlin, 1898)Google Scholar.

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 Gyekye, K., Arabic Logic: Ibn al-Ṭayyib's Commentary on Porphyry's Eisagoge (Albany, 1979), p. 7Google Scholar.

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 Kraus, P., “Al-tarājim al-Arisṭūṭāliyya ilā Ibn al-Muqaffaʿ”, in al-Turāth al-yūnānī fī al-ḥaḍāra al-islāmiyya, Dirāsāt li-kibār al-mustashriqīn, tr. Badawi, A., 4th edn (Kuwait and Beirut, 1980), vol. 4, pp. 101–20Google Scholar. Cf. Rescher, N., The Development of Arabic Logic (London, 1964), p. 94Google Scholar; Peters, F. E., “The Greek and Syriac background”, in Nasr, S. H. and Leaman, O. (eds.), History of Islamic Philosophy, 2 vols. (London and New York, 1997), vol. 1, p. 11Google Scholar.

13 See the prefaces in the two editions of the Arabic Categories: Badawi, A., Manṭiq Arisṭū (Kuwait and Beirut, 1980), vol. 1, pp. 12–14Google Scholar; Jabir, F., al-Naṣṣ al-kāmil li-Manṭiq Arisṭū (Beirut, 1999), pp. 5–6Google Scholar.

14 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 Talkhīṣ Kitāb al-Maqūlāt, critical edition by M. Qāsim, with introduction and commentary by Ch. Butterworth and A. Harīdī [Cairo, 1980]). Among the philosophers who had deviated from the tradition one can name Ibn Sīnā (see his al-Maqūlāt, in al-Shifāʾ, vol. 10, critical edition and introduction by I. Madkūr, edited by G. Anawātī, A. al-Ahwānī, M. al-Khuḍayrī and S. Zāyid [Cairo, 1959]). For a detailed discussion of this issue see Ighbariah, A., The Development of the Theory of Categories in Islamic Philosophy Between the 9th and 13th Centuries, PhD dissertation (University of Haifa, 2009)Google Scholar.

15 A list of the works edited by al-Kindī can be found in Moosa, M. I., “Al-Kindī's role in the transmission of Greek knowledge to the Arabs”, Journal of the Pakistan Historical Society, 15 (1967): 1–18, at pp. 13–14Google Scholar; cf. Adamson, P., “Before essence and existence: Al-Kindī's conception of being”, Journal of the History of Philosophy, 40 (2002): 297–312CrossRefGoogle Scholar, at p. 297. Among the scholars who translated for al-Kindī are Ibn Bihrīz, Ibn Nāʿima, Usṭāth and Yaḥyā ibn al-Biṭrīq. See also Rescher, Development, pp. 100–1; Gutas, D., Greek Thought, Arabic Culture: The Graeco-Arabic Translation Movement in Baghdad and Early ʿAbbāsid Society (2nd-4th/8th-10th Centuries) (London, 1998), pp. 117–18, 137–8Google Scholar. For al-Kindī as a translator see Juljul, Ibn, Ṭabaqāt al-aṭibbāʾ wa-al-ḥukamāʾ, ed. Sayyid, F. (Cairo, 1955), pp. 73–4Google Scholar; al-Qifṭī, Kitāb Ikhbār al-ʿulamāʾ bi-akhbār al-ḥukamāʾ (Beirut), p. 241; Uṣaybiʿa, Ibn Abī, ʿUyūn al-anbāʾ fī ṭabaqāt al-aṭibbāʾ, ed. Riḍā, ʿN. (Beirut, 1965), p. 286Google Scholar; al-Andalusī, Ṣāʿid, al-Taʿrīf bi-ṭabaqāt al-umam, ed. Ūdhil, Gh. (Tehran, 1997), p. 192Google Scholar. See also Walzer, R., “Islamic philosophy”, in Radhakrishnan, S. et al. (eds.), History of Philosophy Eastern and Western (London, 1957), vol. 2, p. 125Google Scholar. M. Meyerhof, “Min al-Iskandariyya li-Baghdād: Baḥth fī taʾrīkh al-taʿlīm al-falsafī wa-al-ṭibbī ʿinda al-ʿArab”, in al-Turāth al-yūnānī fī al-ḥaḍāra al-islāmiyya, vol. 4, pp. 37–100. Some maintain that al-Kindī did not translate by himself, since he had no knowledge of Greek, but rather re-edited translations from Greek that were made by the translators in his circle. See Adamson, P., Al-Kindī (Oxford, 2007), p. 26Google Scholar; Moosa, “Al-Kindī's role”; Wiesner, H. S., The Cosmology of al-Kindī, PhD Thesis (Harvard University, 1993), p. 11Google Scholar; Al-Maʿṣūmī, M., “Al-Kindī as a thinker”, in Abū Yūsuf Yaʿqūb Ibn Isḥāq al-Kindī: Islamic Philosophy, vol. 5, collected and reprinted by Sezgin, F. et al. (Frankfurt, 1999), p. 55Google Scholar.

16 Ṣāʿid al-Andalusī, al-Taʿrif, p. 220.

17 The term taḥlīl can be understood in two ways:

  1. 1

    1 Ṣāʿid is referring to the book al-Taḥlīlāt al-thāniya / al-Burhān (Posterior Analytics / The Demonstration), whose function is the most important of the logical corpus, since its mastering leads the logician to certainty. According to Ṣāʿid, the philosopher that followed al-Kindī, namely al-Fārābī, is the one who took seriously the art of analytics (ṣināʿat al-taḥlīl), which al-Kindī had neglected (see ibid., pp. 220–1, 222). Cf. Atiyeh, G. N., Al-Kindī: the Philosopher of the Arabs (Rawalpindi, 1966), p. 36Google Scholar. Although the Analytics was one of the later books to be translated into Arabic, there is no doubt that al-Kindī was acquainted with it (Rescher, Development, p. 101). For further discussion about al-Kindī's treatment of the Posterior Analytics in his writings, see Jolivet, J., “L'Épître sur la quantité des livres d'Aristote par al-Kindī (une lecture),” in Morelon, R. and Hasnawi, A. (eds), De Zénon d'Élée à Poincaré: Recueil d'études en hommage à Roshdi Rashed (Louvain, 2004), pp. 665–83, at pp. 669, 673Google Scholar.

  2. 2

    2 Ṣāʿid is referring to the term taḥlīl, which is parallel to the term tarkīb, meaning that al-Kindī used uncertain premises to compose dubious syllogisms, instead of founding the premises by the analytical method in order to distinguish between truth and falsity. Compare al-Fārābī, Kitāb al-Alfāẓ al-mustaʿmala fī al-manṭiq, ed. Mahdi, M., 2nd edn (Beirut, 1986), ch. 7; Adamson, Al-Kindī, p. 18Google Scholar.

18 Ṣāʿid al-Andalusī, al-Taʿrīf, p. 221.

19 Al-Qifṭī, Akhbār, p. 241.

20 This is preserved in Ibn Abī Uṣaybiʿa, ‘Uyūn, pp. 604–5.

21 Ibid., p. 287.

22 The list first appears in Ibn al-Nadīm, 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-Kindī's logical works see Ibn al-Nadīm, al-Fihrist, p. 358; al-Qifṭī, Akhbār, p. 242; Ibn Abī Uṣaybiʿa, ʿUyūn, p. 289. Among his logical works whose titles suggest that they were written as summaries or commentaries on the Analytics, al-Qifṭī mentions (p. 242) Kitāb fī al-Burhān al-manṭiqī (Book on the Logical Demonstration); Ibn Abī Uṣaybiʿa (p. 289) mentions another work (Risāla bi-ījāz wa-ikhtiṣār fī al-burhān al-manṭiqī; Summarized and Abridged Epistle on the Logical Demonstration). See also M. ʿAbdarrāziq, “Abū Yūsuf Yaʿqūb Ibn Isḥāq al-Kindī: Islamic philosophy”, in Abū Yūsuf Yaʿ qūb Ibn Isḥāq al-Kindī, p. 143.

23 Atiyeh, Al-Kindī, p. 33; Adamson, Al-Kindī, p. 10.

24 Ibn al-Nadīm, al-Fihrist, p. 358.

25 Al-Qifṭī, Akhbār, p. 242.

26 Apparently this is the same book that appears in al-Qifṭī's list, but with a scribal error (maqālāt instead of maqūlāt): Kitāb fī Qaṣd Arisṭūṭālīs fī al-Maqālāt (ibid., p. 241). Adamson (Al-Kindī, p. 9) remarks that in many cases al-Kindī's historians and the editors were the ones who gave titles to his works.

27 Ibn Abī Uṣaybiʿa, ‘Uyūn, p. 289. See also al-Qifṭī, Akhbār, p. 359. The two men count this epistle among the arithmetical (al-ḥisābiyyāt) rather than the logical works, since its discussion, as implied by its title, focuses on the category of Quantity. This category is obviously relevant to arithmetic.

28 Al-Kindī, Fī Kammiyyat kutub Arisṭū, in Rasāʾil al-Kindī al-falsafiyya, ed. Abū Rīda, M. (Cairo, 1950), pp. 363–84Google Scholar. Partial English translation in Rescher, N., “Al-Kindī's sketch of Aristotle's Organon”, in Studies in the History of Arabic Logic (Liverpool and London, 1963), pp. 32–8Google Scholar. For an elaborate presentation of this epistle, see Jolivet, “L’Épître”, pp. 665–83.

29 Elsewhere, al-Kindī 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 fī al-Falsafa al-ūlā, in his Rasāʾil, p. 103), implicating his intention to add to and interpret the writings of the ancients.

30 It should be noted that in the Kammiyya al-Kindī 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 (ʿilm al-rusul), which is characterized by being attained without being sought after. The first science is a human science (ʿilm insānī), while the other is a divine/metaphysical science (ʿilm ilāhī). According to al-Kindī, the divine science is loftier than the human science since it is the science of the things that are eternally true (al-ashyāʾ al-ḥaqqiyya al-thābita), that only the prophet can attain by revelation (Kammiyya, pp. 372–6). Ibn al-Nadīm mentions a work by al-Kindī entitled Kitāb Aqsām al-ʿilm al-insī (Book of the Divisions of the Human Science).

31 Al-Kindī, Kammiyya, pp. 364–5. See Jolivet's comments on this passage: Jolivet, “L'Épître”, p. 667.

32 Al-Kindī enumerates the eight logical books (ibid., pp. 365–8): Categories (Qāṭīghūriyās wa-huwa ʿalā al-maqūlāt), De Interpretatione (Bāriyārmāniās wa-maʿnāhu: ʿalā al-tafsīr), Prior Analytics (Anālūṭīqī <al-Ūlā> wa-maʿnāhu: al-ʿaks min al-raʾs), Posterior Analytics (Anālūṭīqī al-Thāniya wa-hiya al-makhṣūṣ bi-ism Afūdhiqṭīqā wa-maʿnāhu al-īḍāḥ), Topics (Ṭūbīqā wa-maʿanāhu: al-mawāḍiʿ, yaʿnī mawāḍiʿ al-qawl), De Sophisticis Elenchis (Sūfisṭīqā wa-maʿnāhu: al-mansūb fī al-sūfisṭāʾiyīn, wa-maʿnā al-sūfisṭāʾī al-mutaḥakkim), Rhetoric (Rīṭūrīqā wa-maʿnāhu al-balāghī), and Poetics (Būyīṭīqā wa-maʿnāhu al-shiʿrī).

33 According to al-Kindī, there are seven physical works (ibid., p. 368): Physics (al-Khabar al-ṭabīʿī), De Caelo (al-Samāʾ), De Generatione et Corruptione (al-Kawn wa-al-fasād), Meteorology (Aḥdāth al-jaww), On Minerals (al-Maʿādin), On Plants (al-Nabāt), On Animals (al-Ḥayawān).

34 These works are four (ibid.): De Anima (al-Nafs), Sense and Sensibilia (al-Ḥiss wa-al-maḥsūs), On Sleep and Waking (al-Nawm wa-al-yaqaẓa), On Length and Shortness of Life (Ṭūl al-ʿumr wa-qiṣaruhu).

35 The book that deals with these existents is the Metaphysics (Mā warāʾ al-ṭabīʿiyyāt) (ibid.). On the difference between physics and metaphysics al-Kindī 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-ūlā, p. 111).

36 Among Aristotle's ethical works al-Kindī mentions the Nicomachean Ethics (al-Akhlāq ilā Nīqūmākhus) 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-Akhlāq ilā Ūydīmūs).

37 Al-Kindī does not mention the titles of these works, but remarks that they deal with particular things (ashyāʾ juzʾiyya) (ibid., p. 369). See the lists of his ethical works in Ibn al-Nadīm (al-Fihrist, p. 363) and al-Qifṭī (Akhbār, p. 245).

38 See al-Kindī's Kitāb al-Jawāhir al-khamsa (Book of the Five Substances) in Rasā'il al-Kindī al-falsafiyya, ed. Abū Rīda, pp. 8–35. See also Atiyeh, Al-Kindī, pp. 38–40; Adamson, “Before essence and existence”, p. 30; El-Ehwany, A. F., “Al-Kindī”, in Sharif, M. M. (ed.), A History of Muslim Philosophy, 2 vols. (Wiesbaden, 1963) vol. 1, p. 424Google Scholar.

39 On the superiority of metaphysics (al-falsafa al-ūlā) over the rest of the sciences al-Kindī 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-ūlā, pp. 98, 101). See also Atiyeh, Al-Kindī, p. 45; Adamson, Al-Kindī, chapter 3; Ivry, A. L., “Al-Kindī as philosopher: The Aristotelian and Neoplatonic dimensions”, in Stern, S. M., Hourani, A. and Brown, V. (eds.), Islamic Philosophy and the Classical Tradition (Oxford, 1972), pp. 118, 124–5, 133Google Scholar.

40 The term “Logic” started pointing at the logical corpus only by Alexander. See Kneale, W. and Kneale, M., The Development of Logic, 3rd edn (Oxford, 1966), p. 23Google Scholar. See also Gottschalk, H. B., “The earliest Aristotelian commentators”, in Aristotle Transformed, p. 59Google Scholar.

41 See Rasā'il al-Kindī al-falsafiyya, ed. Abū Rīda, pp. 165–79. For the importance of this treatise for the development of philosophical terminology in Islam see S. M. Stern, “Notes on al-Kindī's Treatise on Definitions”, in Abū Yūsuf Yaʿqūb Ibn Isḥāq al-Kindī, pp. 422–33.

42 Note the definitions of the following concepts: “substance” (al-jawhar), “quantity” (al-kammiyya), “quality” (al-kayfiyya), “relation” (al-iḍāfa), “truth” (al-ṣidq), “falsity” (al-kadhib), “doubt” (al-ẓann), and “certainty” (al-yaqīn). See al-Kindī, Ḥudūd, pp. 166, 167, 169, 171.

43 See for example Ibn al-Nadīm, al-Fihrist, pp. 358–61.

44 Ibid., p. 358; cf. al-Qifṭī, Akhbār, p. 241. See also Atiyeh, Al-Kindī, pp. 33, 37. The historian Żahīr al-Dīn al-Bayhaqī describes al-Kindī as a geometrician (kāna muhandisān) because of his extensive activity in that field. See his Taʾrīkh ḥukamāʾ al-Islām, ed. Muhammad, M. H. (Cairo, 1996), p. 52Google Scholar.

45 Al-Maʿṣūmī, “Al-Kindī”, pp. 380–1. See also al-Fārābī'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-Fārābī, Ma yanbaghī an yuqaddam qabla taʿallum falsafat Arisṭū, in Alfārābī's Philosophische Abhandlungen, ed. F. Dieterici [Leiden, 1890], pp. 49–55). See also Heath, T., A History of Greek Mathematics, 3rd edn (Oxford, 1965), vol. 1, p. 284Google Scholar.

46 Al-Kindī, Kammiyya, pp. 369–70. See also p. 376.

47 This classification was adopted by Plato and the Platonists with certain adaptations (see Endress, G., “Mathematics and philosophy in Medieval Islam”, in Hogendijk, J. P. and Sabra, A. I. [eds.], The Enterprise of Science in Islam [London, 2003], pp. 124–5Google Scholar; Heath, History, vol. 1, p. 284; Wesberg, A., Plato's Philosophy of Mathematics [Stockholm, 1955], p. 21)Google Scholar. Jolivet (pp. 673, 676) identifies two different orders of the classifications of mathematical sciences in al-Kindī's Kammiyya; the first is a Platonic and a pedagogical one (al-Kindī, 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-Kindī was exposed to Pythagoreanism and Neopythagoreanism through the connection between the schools of Baghdad and the scholars who worked in Ḥarrān or came from there. For instance, Thābit ibn Qurra, who moved from Ḥarrān to Baghdad, had significant influence on Baghdadian schools, including al-Kindī's circle (Gutas, Greek Thought, p. 104).

48 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-Kindī see, for instance, al-Fārābī, Iḥṣāʾ al-ʿulūm (Beirut, 1991), pp. 13–15; Ibn Sīnā, al-Ishārāt wa-al-tanbīhāt, ed. Dunyā, S. (Cairo, 1983), vol. 1, p. 117Google Scholar; Rushd, Ibn, Risālat mā baʿd al-ṭabīʿa, ed. al-ʿAjam, R. and Jihāmī, J. (Beirut, 1994), p. 60Google Scholar.

49 In his Fī al-Falsafa al-ūlā (p. 112), al-Kindī states that in mathematics one must provide demonstration rather than persuasion: “if we were to employ persuasion (iqnāʿ) in the science of mathematics, our learning in it would be of surmise (ẓanniyya) and not scientific (ʿilmiyya).”

50 The mathematical method appears in many of al-Kindī's epistles. See, for instance, his treatment of the problem of infinity: Fī al-Falsafa al-ūlā, pp. 114–16; Risālat al-Kindī fī Īḍāḥ tanāhī jurum al-ʿālam, in his Rasā'il, pp. 186–92; Risālat al-Kindī fī Māʾiyyat mā lā yumkin an yakūna lā nihāya lahu wa-mā alladhī yuqāl lā nihāya lahu, pp. 194–8; Risālat al-Kindī fī Waḥdāniyyat Allah wa-tanāhī jurum al-ʿālam, pp. 201–7. De Boer notes that al-Kindī applied the mathematical method also to medicine (Boer, T. J. De, The History of Philosophy in Islam, tr. Jones, E.R. [New York, 1967], pp. 100–1Google Scholar). See also Adamson, Al-Kindī, ch. 7, which is dedicated to a discussion of the mathematical method in medicine (pp. 161–6), optics (pp. 166–72), and music (pp. 172–80); Gutas, Greek Thought, p. 120; Langermann, Y. T., “Another Andalusian revolt? Ibn Rushd's critique of al-Kindī's pharmacological computus”, in The Enterprise of Science in Islam, pp. 351–72, pp. 351–2Google Scholar.

For al-Kindī'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-Nadīm, al-Fihrist, pp. 358–61; al-Qifṭī, Akhbār, pp. 242–3; Ibn Abī Uṣaybiʿa, ʿUyūn, p. 289-91. Ṣāʿid al-Andalusī (al-Taʿrīf, p. 179) quotes a Kindian anecdote about the reason for the composition of Euclid's Elements (al-Arkān). For al-Kindī's works that are related to the Elements see Ibn al-Nadīm, Al-Fihrist, p. 360 (cf. al-Qifṭī, Akhbār, p. 243): His Epistle on the Aims of Euclid's Book (Risālatihi fī Aghrād Kitāb Uqlīdis), His Epistle on the Correction of Euclid's Book (Risālatihi fī Iṣlāḥ Kitāb Uqlīdis). Ibn Abī Uṣaybiʿa adds another works, entitled Epistle on the Correction of the Fourteenth and Fifteenth Books of Euclid's Treatise (Risāla fī Iṣlāḥ al-maqāla al-rābiʿa ʿashrata wa-al-khāmisa ʿashrata min Kitāb Uqlīdis). For Euclid's influence on al-Kindī see Adamson, Al-Kindī, p. 27.

51 Al-Kindī, Kammiyya, p. 365. Cf. his definition in Ḥudūd, p. 166. See also Zimmermann, F. W., Al-Farabi's Commentary and Short Treatise on Aristotle's De Interpretatione (Oxford, 1987), p. xxviiGoogle Scholar.

52 The Isagoge was popular in the Muslim world since the early period of translation, and al-Kindī was undoubtedly familiar with it. Ibn al-Nadīm (al-Fihrist, p. 358) and al-Qifṭī (Akhbār, p. 242) list two books – an abridgement and a commentary – on the Introduction to Logic (al-Madkhal al-manṭiqī), which is an Arabic title for the Isagoge. Ibn Abī Uṣaybiʿa (ʿUyūn, p. 289) explicitly uses the Greek title in his list: Abridgement of the Book Isagoge by Porphyry (Ikhtiṣār Kitāb Īsaghūjī li-Farfūryūs).

In his epistle on Refuting the Christians (al-Radd ʿalā al-Naṣārā) he explicitly mentions the Isagoge and employs it in his attack on the trinity. See Rashed, R. and Jolivet, J., Œuvres philosophiques et scientifiques d'al-Kindī, vol. II: Métaphysique et cosmologie (Leiden, 1998), p. 123Google Scholar.

It is possible that al-Kindī does not mention the Isagoge here because he knew it was not composed by Aristotle. In his Fī al-Falsafa al-ūlā, al-Kindī surveys the universals in a manner similar to Porphyry, discussing the genus (al-jins), the species (al-Kindī uses the term ṣūra – “form” – rather than the more common nawʿ. See ibid., pp. 125, 126, 130. In other places he uses nawʿ – see ibid., pp. 153, 160. In the Ḥudūd, p. 166, he uses the term ṣūra in a manner parallel to “matter”: “the form [is] the thing through which a certain thing is what it is.” For the different meaning of ṣūra in al-Kindī see Rashed and Jolivet, Œuvres, vol. 2, pp. 19–22), the differentia (al-faṣl), the property (al-khāṣṣa), and the accident (al-ʿaraḍ al-ʿāmm). However, he adds another concept to the discussion, namely the individual (al-shakhṣ; see Fī al-Falsafa al-ūlā, pp. 124–30, esp. pp. 126–7, 128 for the individual). Ikhwān al-Ṣafāʾ also add the individual to the five universals of the Isagoge. See Rasāʾil Ikhwān al-Ṣafāʾ (Beirut, n.d.), vol. 1, p. 395.

53 See al-Kindī, 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; Street, T., “Arabic logic”, in Gabbay, D. M. and Woods, J. (eds.), Handbook of the History of Logic, vol. I: Greek, Indian and Arabic (Amsterdam, 2004), p. 531Google Scholar.

56 Al-Kindī, Kammiyya, p. 366.

57 Al-Kindī, Fī al-Falsafa al-ūlā, p. 126. Aside from the individual, al-Kindī divides the universals here into essential (genus, species, differentia), and accidental (property, accident).

58 Al-Kindī, 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. Ross, W. D. (Oxford, 1950), vol. 1, Chapters: 1, 2, 5Google Scholar.

59 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-ūlā, 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-Kindī explains the difference between a similar name (mutashābih) and an agreed upon name (mutawāṭiʾ) in his description of the substance. The substance is “that which is [described in an] agreed upon description (naʿt mutawāṭiʾ) or a similar description (naʿt 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 fī annahu tūjad jawāhir lā ajsām, in al-Kindī, Rasā'il, p. 266).

60 Al-Kindī 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 Fī al-Falsafa al-ūlā, p. 128.

61 Al-Kindī, Kammiyya, pp. 365–6. See also Fī al-Falsafa al-ūlā, p. 125, and Jawāhir lā ajsām, pp. 266–7.

62 Al-Kindī, Kammiyya, p. 365.

63 This is al-Kindī's definition of color (Kammiyya, p. 366).

64 Ibid.

65 Editor's insertion.

66 See the definition of Substance in the Ḥudūd, p. 166.

67 See the definition of Quantity, ibid., p. 167.

68 See the definition of Quality, ibid.

69 See the definition of Relation, ibid.

70 Ḥudūd, p. 366.

71 Ibid., p. 370.

72 Ibid.

73 In the Ḥudūd (p. 167) al-Kindī provides the following definition for Quantity: “that which is subjected to equality and inequality” (mā iḥtamala al-musāwā wa-ghayr al-musāwā). The term musāwā here is interchangeable with mithl.

74 Al-Kindī, Kammiyya, p. 370. See also Fī al-Falsafa al-ūlā, pp. 106, 160; Ḥudūd, p. 167.

75 Al-Kindī uses the term ṭīna instead of hayūlī. See Ḥudūd, p. 166, and n. 2 there.

76 Al-Kindī 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 Fī al-Falsafa al-ūlā, pp. 109, 138. This is how place is defined in the Ḥudūd (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 iltiqāʾ ufuqay al-muḥīṭ wa-al-muḥāṭ bihi).

77 This is how action is defined in the Ḥudūd (p. 167): “Action is the influence on a subject that can be influenced. Some say: it is the movement [whose principle is] from the mover himself. Compare al-Kindī's Epistle al-Fāʿil al-ḥaqq al-awwal al-tāmm wa-al-fāʿil al-nāqiṣ alladhī huwa bi-al-majāz (The First True and Perfect Actor and the Defective Actor [which is an Actor] Metaphorically), in al-Kindī, Rasāʾil, pp. 182–4.

78 Later on, these two categories were known as an yafʿala and an yanfaʿila. See for instance al-Fārābī, Kitāb al-Maqūlāt, in al-Manṭiq ʿinda al-Fārābī, vol. 1, ed. al-ʿAjam, R. (Beirut, 1985), pp. 113, 115Google Scholar.

79 Sometimes al-Kindī 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.

81 Except for the categories Having and Position, which are outcomes of the composition of two substances.

82 Ibid., p. 372.

83 Compare with Iamblichus' position which is quoted in Simplicius, p. 83.

84 See Jolivet, “L'Épître”, p. 674.

85 Atiyeh, Al-Kindī, p. 37. On the difference between the primary and secondary substances al-Kindī writes (Fī al-Falsafa al-ūlā, 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-Kindī's theory of substance see Atiyeh, Al-Kindī, pp. 88–90.

86 Al-Kindī, Kammiyya, p. 372.

87 Ibid., p. 377.

88 Taʿālīm and mathematics have the same meaning.

89 Ibid., p. 378.

90 Ibid.

91 To be precise, al-Kindī was interested in the category of Quantity even more than in the category of Quality. See the fourth section of Fī al-Falsafa al-ūlā (pp. 143–53), where al-Kindī devotes a full and detailed discussion to the Quantity and issues that stem from it.

92 The reference here is to the primary, not the secondary substance, since the latter can be known through the logical definition (al-ḥadd) 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 Fī al-Falsafa al-ūlā (pp. 124–5) al-Kindī remarks that philosophy aims at knowing the universal, and not the particular, which is infinite in number.

93 Jolivet states that while Aristotle's classification of sciences is based on ontological considerations, al-Kindī's classification is based on epistemological ones (Jolivet, “L'Épître”, p. 677). It should be mentioned that al-Kindī'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-Kindī explains that the latter do not employ neither mathematics nor logic, but receive their knowledge directly from God (al-Kindī, Kammiyya, pp. 372–3).

94 This is how al-Shahrastānī sums up Pythagoras' doctrine: “he said that the number is the principle of all of the existents” (al-Shahrastānī, al-Milal wa-al-niḥal, ed. Muhammad, A. F. [Beirut, 1992], p. 387Google Scholar; for Pythagoras and the Pythagoreans in the Islamic tradition see ibid., pp. 385–99).

One of the books that al-Kindī 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; Gow, J., A Short History of Greek Mathematics, 3rd edn (New York, 1968), pp. 88–95Google Scholar. Ḥabīb ibn Bihrīz translated the work from Syriac into Arabic, and al-Kindī edited and corrected the translation for a man named Ṭāhir ibn al-Ḥasan (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 Bahrīz, al-Kindī, 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 fī al-Madkhal ilā al-arithmāṭīqī: khams maqālāt). See Ibn al-Nadīm, al-Fihrist, p. 358; al-Qifṭī, Akhbār, p. 242; Ibn Abī Uṣaybiʿa, ʿUyūn, p. 289.

Another indication of al-Kindī's familiarity with the Pythagorean tradition is his intellectual connection with the Ṣābiʾans of Ḥarrān (Ṣābiʾat Ḥarrān, 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-Kindī and on their theories of soul see the introduction to his Rasāʾil, pp. 80(18)–80(21). On the influence of Platonic mathematics see Endress, “Mathematic”, pp. 127–31; Ibn al-Nadīm (al-Fihrist, p. 358) ascribes to al-Kindī a work entitled His Epistle on the Explanation of the Numbers that Plato Mentioned in the Republic (Risālatihi fī al-Ibāna ʿan al-aʿdād allatī dhakarahā Flāṭun fī Kitāb al-Siyāsa). Cf. al-Qifṭī, Akhbār, p. 242; Ibn Abī Uṣaybiʿa, ʿUyūn, p. 289.

96 For Aristotle's influence on al-Kindī see the introduction to his Rasā'il, pp. 80(13)–80(18).

97 One can find a proximate position in Ikhwān al-Ṣafāʾ, whose Rasāʾil opens with a group of mathematical treatises that aim at paving the way for prospective students of philosophy (Ikhwān al-Ṣafāʾ, Rasāʾil, pp. 21, 48, 75–6). However, unlike al-Kindī, 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 thand 13 thCenturies, 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.