Abstract
Like his Greek and Arab predecessors, Avicenna’s research in mathematics concerned the development of methods of exposition, proof procedures and analytical tools. But Avicenna belonged to a new era of mathematics, and the question that this paper seeks to examine is how Avicenna applied this new mathematical knowledge in his philosophy. A treatment of the subject of Avicenna and mathematics cannot, then, confine itself to generalities, important as these are, but must start from the degree of knowledge he had of the various branches and the use he actually made of them. I shall restrict myself here to a number of examples which seem to me to possess evidential value and which all reveal a new conception of the connections between philosophy and mathematics. It will turn out that what Avicenna in fact did was to develop an analytical philosophy of mathematical concepts.
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- 1.
- 2.
Letter to Kiyā, in ‘A. Badawī, Aristū ‘inda al-’Arab (Kuwait, 1978), p. 121:
- 3.
Ibn Sīnā, al-Shifā’, al-Mantiq, 5. al-Burhān, ed. A. ‘Afifi (Cairo, 1956), pp. 194–195:
- 4.
Al-Shifā’. al-Ilāhiyyāt (1) (The Metaphysics), Text established and edited by G. C. Anawati and S. Zayed, revised and furnished with an introduction by I. Madkour (Cairo, 1960), p. 145.
- 5.
This is found particularly in the discussion of Atomism by the theologian-philosophers (al-Mutakallimūn); cf. M. Rashed, ‘Kalām e filosofia naturale’, in Storia della scienza, vol. III: La civiltà islamica, Enciclopedia Italiana (Rome, 2002), pp. 49–72.
- 6.
Al-Shifā’. Al-Ilāhiyyāt (1) (Metaphysics), ed. G. C. Anawati and S. Zayed, revised and preceded by an introduction by I. Madkour (Cairo, 1960), p. 118, 14–15:
- 7.
Al-Shifā’. Al-Mantiq—1. al-Madkhal, al-Maqūlāt, ed. G. C. Anawati, M. Khudayrī and F. al-Ahwānī, p. 156, 1–3:
- 8.
Ibid., p. 225, 7–8:
- 9.
Al-Shifā’. Al-Mantiq—1. al-Madkhal, al-Maqūlāt, ed. G. C. Anawati, M. Khudayrī and F. al-Ahwānī, p. 129, 2:
- 10.
Ibid., p. 250, 15–16:
- 11.
- 12.
Al-Najāt, ed. M. Kurdī (1938), p. 123:
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Rashed, R. (2018). Avicenna: Mathematics and Philosophy. In: Tahiri, H. (eds) The Philosophers and Mathematics. Logic, Epistemology, and the Unity of Science, vol 43. Springer, Cham. https://doi.org/10.1007/978-3-319-93733-5_11
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