The Philosophy of Mathematics

  • R. Rashed
Part of the Logic, Epistemology, and The Unity of Science book series (LEUS, volume 11)

Abstract

Is there a philosophy of mathematics in classical Islam? If so, what are the conditions and the scope of its presence? To answer these questions, hitherto left unnoticed, it is not sufficient to present the philosophical views on mathematics, but one should examine the interactions between mathematics and theoretical philosophy. These interactions are numerous, and mainly foundational. Mathematics has provided to theoretical philosophy some of its central themes, methods of exposition and techniques of argumentation. The aim of this chapter is to study some of these interactions, in an effort to give some answers to the questions raised above. The themes which will be successively discussed are mathematics as a model for the philosophical activity (al-Kindī, Maimonides), mathematics in the philosophical syntheses (Ibn Sīnā, Nasīr al-Dīn al-Tūsī), and finally the constitution of ars analytica (Thābit ibn Qurra, Ibn Sinān, al-Sijzī, Ibn al-Haytham).

Keywords

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References

I

  1. Al-Bayhaqī: 1946, Tārīkh ḥukamā’ al-Islām, ed. Muhammad Kurd Ali, Damascus.Google Scholar
  2. Al-Bīrūnī: 1954, Al-Qānūn al-mas’ūdī, ed. Hayderabad.Google Scholar
  3. Al-Fārābī: 1968, Ihṣā’ al-’ulūm, ed. ’Uthmān Amīn, Cairo.Google Scholar
  4. Al-Fārābī: 1970, Kitāb al-hurūf, ed. Muhsin Mahdi, Beirut.Google Scholar
  5. Ibn Abī Uṣaybi’a: 1965, Uyūn al-anbā’ fī ṭabaqāt al-atibbī’, ed. Nizīr Riḍā, Beirut.Google Scholar
  6. Ibn al-’Imād: Shadharāt al-dhahab fī akhbār man dhahab, vol. 3, Beirut (no date).Google Scholar
  7. Ibn Rushd: 1983, Faṣl al-maqāl fāmā bayna al-ḥikma wa-al-sharā’a min al-ittiṣāl, ed. M. ’Amāra, Cairo, Dār al-Ma’ārif.Google Scholar
  8. Ibn Sīnā: 1956, Al-Shifa’, al-Manṭiq, vol. V: al-Burhān, ed. Afifi, directed by Ibrāhīm Madhkour, Cairo.Google Scholar
  9. Ibn Sīnā: 1960a, Al-Shifā’, al-Ilāhiyyāt (I), ed. George Anawati and Sa’īd Zāyed, Cairo.Google Scholar
  10. Ibn Sīnā: 1960b, Al-Shifā’, al-Ilāhiyyāt (II), ed. Muhammad Y. Māsā, Sulaymān Dunyā and Sa’īd Zāyed, revised and introduced by Ibrāhīm Madkour, Cairo.Google Scholar
  11. Ibn Sīnā: 1964, Al-Shifā’, al-Manṭiq, vol. IV: al-Qiyās, éd. Sa’īd Zāyed, revised and introduced by Ibrāhīm Madkour, Cairo.Google Scholar
  12. Ibn Sīnā: 1975, Al-Shifā’, al-Ḥisāb, ed. ’Abd al-hāmid Lutfi Mażhar, revised and introduced by Ibrāhīm Madkour, Cairo.Google Scholar
  13. Ibn Khallikān: 1969,Wafayāt al-a’yān, vol. 2, ed. Ihsān ’Abbās, Beirut.Google Scholar
  14. Al-Kindī: 1950, Rasā’il al-Kindī al-falsafiyya, ed. Muhammad ’Abd al-Hādī Abū Rīda, Cairo.Google Scholar
  15. Maimonides: 1972, Dalālat al-ḥā’irīn(The Guide for the Perplexed), ed. Hüseyin Atay, Ankara üniversitesi, Ilâhîyat Fakültesî Yayinlari 93, Ankara.Google Scholar
  16. Al-Nadīm: 1971, Kitāb al-Fihrist, ed. Riḍā Tajaddud, Teheran.Google Scholar
  17. Nicomachus of Gerasa: 1958,Kitāb al-madkhal ilā ‘ilm al- ’adad, translated by Thābit ibn Qurra, ed. Wilhem Kutsch, Beirut.Google Scholar
  18. Al- Qifī: 1903, Ta’rīkh al-h1ukamā’, ed. Julius Lippert, Leipzig.Google Scholar
  19. Al-Tūsī (Naṣīr al-Dīn): 1971, al-Ishārāt wa-t-tanbīhāt, ed. Sulaymān Dunyā, Cairo.Google Scholar

II

  1. Ahmad, S. and R. Rashed: 1972, Al-Bahir en Algébre d’As-Samaw’al, Presses de l’Universitè de Damas, Damascus.Google Scholar
  2. Davison, H. A.: 1987,Proofs for Eternity Creation and the Existence of God in Medieval Islamic and Jewish Philosophy, New York-Oxford.Google Scholar
  3. Druart, T. A.: 1987, “Al-Fārābī and Emanationism”, in John F. Wippell (ed.), Studies in Medieval Philosophy, The Catholic University of America Press, Washington, pp. 23–43.Google Scholar
  4. Druart, T.A.: 1992, “Al-Fārābī, Emanation and Metaphysics”, in Parviz Morewedge (ed.), Neoplatonism and Islamic Philosophy, State University of New York Press, Albany, pp. 127–148.Google Scholar
  5. Gardet, L.: 1951, “En l’honneur du millènaire d’Avicenne”, in Revue Thomiste, LIXe annèe, t. li, n 2, 333–345.Google Scholar
  6. Goichon, A. M.: 1957, La Distinction entre existence et essence, Paris.Google Scholar
  7. Hasnawi, A.: 1990, “Fayd(èpanchement, èmanation)”, in A. Jacob (ed.), Encyclopèdie philosophique universelle, vol. II, Paris, pp. 966–972.Google Scholar
  8. Heer, N.: 1992, “Al-Rāzī and al-Ṭūsī on Ibn Sīnā’s Theory of emanation”, in P. Morewedge (ed.), Neoplatonism and Islamic Philosophy, State University of New York Press, Albany, pp. 111–125.Google Scholar
  9. Marmura, M. E.: 1992, “Quiddity and Universilaty in Avicenna”, in P. Morewedge (ed.), Neoplatonism and Islamic Philosophy, State University of New York Press, Albany, pp. 77–87.Google Scholar
  10. Morewedge P.: 1972, “The Logic of emanationism and Ṣūfism in the Philosophy of Ibn Sīnā (Avicenna)”, Part II, Journal of the American Oriental Society 92, 1–18.Google Scholar
  11. Morewedge, P.: 1992, “The Neo-platonic Structure of Some Islamic Mystical Doctrines”, in Parviz Morewedge (ed.), Neo-Platonism and Islamic Philosophy, State University of New York Press, Albany, pp. 51–75.Google Scholar
  12. Owens, J.: 1992, “The Relevance of Avicennian Neo-Platonism”, in P. Morewedge (ed.), Neoplatonism and Islamic Philosophy, State University of New York Press, Albany, pp. 41–50.Google Scholar
  13. Rashed, R.: 1980, “Ibn al-Haytham et le thèoréme de Wilson”, in Archive for History of Exact Science, vol. 22, n 4, 305–321.Google Scholar
  14. Rashed, R.: 1984a, “Mathèmatiques et philosophie chez Avicenne”, in Ètudes sur Avicenne, dirigèes par J. Jolivet et R. Rashed, Collection sciences et philosophie arabes, Ètudes et reprises, Paris, Les Belles Lettres, pp. 29–39.Google Scholar
  15. Rashed, R.: 1984b, Entre arithmètique et algébre: Recherches sur l’histoire des mathèmatiques arabes, Collection Sciences et philosophie arabes, Ètudes et reprises, Paris, Les Belles Lettres, 1984. English translation in Boston Studies in Philosophy of Science, 1994, The Development of Arabic Mathematics: Between Arithmetic and Algebra, Kluwer.Google Scholar
  16. Rashed, R.: 1987, “Al-Sijzī et Maïmonide : Commentaire mathèmatique et philosophique de la proposition II-14 des Coniques d’Apollonius”, Archives Internationales d’Histoire des Sciences , n 119, vol. 37, 1987, pp. 263–296. English translation Fundamenta Scientiae, vol. 8, n 3/4, 1987, 241–256.Google Scholar
  17. Rashed, R.: 1991, “La philosophie mathèmatique d’Ibn al-Haytham, I: L’analyse et la synthése”, in Mèlanges de l’Institut Dominicain d’Etudes Orientales du Caire, 20, 31–231.Google Scholar
  18. Rashed, R.: 1993a, “Al-Kindī’s commentary on Archimedes’ The Measurement of the Circle”, Arabic Sciences and Philosophy, vol. 3.1, 7–53.Google Scholar
  19. Rashed, R.: 1993b,Les Mathèmatiques infinitèsimales du IXeau XIesiécle,Vol. II: Ibn al-Haytham, al-Furqān Islamic Heritage Foundation, London.Google Scholar
  20. Rashed, R.: 1993c, “La philosophie mathèmatique d’Ibn al-Haytham, II: Les Connus” in Mèlanges de l’Institut Dominicain d’Etudes Orientales du Caire(MIDEO), 21, 87–275.Google Scholar
  21. Rashed, R.: 1996,Œuvres philosophiques et scientifiques d’al-Kindī, Vol. I: L’Optique et la Catoptrique, E.J. Brill, Leiden.Google Scholar
  22. Rashed, R.: 1999, “Combinatoire et mètaphysique : Ibn Sīnā, al-Ṭūsī et al-Halabī” in R. Rashed et J. Biard (eds.), Les Doctrines de la science de l’antiquitè á l’âge classique, Ancient and Classical Sciences and Philosophy, Leuven, Peeters, pp. 61–86. German translation in Rüdiger Thiele (Hrg.),Mathesis, Festschrift siebzigsten Geburtstag von Matthias Schramm, 2000, Kombinatorik und Metaphysik : Ibn Sīnā, al-Ṭūsī und al-Ḥalabī, Berlin, Diepholz, pp. 37–54.Google Scholar
  23. Rashed, R.: 2000, Les Mathèmatiques infinitèsimales du IXeau XIesiécle, vol. III:Ibn al-Haytham. Thèorie des coniques, constructions gèomètriques et gèomètrie pratique, London.Google Scholar
  24. Rashed, R.: 2002, Les Mathèmatiques infinitèsimales du XIeauXIesiécle, vol.IV:Mèthodes gèomètriques, transformations ponctuelles et philosophie des mathèmatiques, London.Google Scholar
  25. Rashed, R., H. Bellosta: 2000, Ibrāhīm ibn Sinān. Logique et gèomètrie au Xesiécle, E.J. Brill, Leiden.Google Scholar
  26. Rashed, R., J. Jolivet: 1998, Œuvres philosophiques et scientifiques d’al-Kindī, Vol. II: Mètaphysique et Cosmologie, E.J. Brill, Leiden.Google Scholar
  27. Saliba, D.: 1926, Sur la Mètaphysique d’Avicenne, Pau.Google Scholar
  28. Verbeke, G.: 1977, “Le statut de la mètaphysique, Introduction to Simone Van Riet’s edition”, Avicenna Latinus, Liber de Philosophia Prima, Louvain – Leiden.Google Scholar
  29. Wiedemann, E.: 1970, “über al-Fārābīs Aufzählung der Wissenschaften (De Scientiis)”, in Aufsätze zur arabischen Wissenschafts-Geschichte, G. Olms.Google Scholar

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© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • R. Rashed
    • 1
  1. 1.CNRS

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