Between Philosophy and Mathematics: Examples of Interactions in Classical Islam

Abstract

In this paper the author raises the question of the existence and the extension of philosophy of mathematics in classical Islam. He considers three types of interactions between mathematics and theoretical philosophy. The first is that used by al-Kindi who uses the means and methods of mathematics to reconstruct his philosophical system. The second type emerges when the mathematician al-Tusi tries to solve a philosophical question: the emanation of the multiplicity. The third type is comes from the mathematician al-Sijzi, who philosophically solves a mathematical problem but does not yet have the means to do so mathematically. Keywords: Philosophy and mathematics in Islamic tradition; links between philosophy and science; history of Islamic science; al-Kindi; al-Tusi; al-Sijzi; Islamic scientific tradition; science, religion and philosophy. ********** Historians of Islamic philosophy have a keen interest in what is often readily called falsafa. According to their understanding, it deals with the doctrines of Being and the Soul, as developed by the authors of the Islamic culture, without any consideration for other fields of knowledge and independent of all determination, if it were not for the link these doctrines may have with religion. Thus, Islamic philosophers are perceived to be evolving within the Aristotelian tradition of neo- Platonism, and to be no more than heirs of late Antiquity, albeit with an Islamic 'touch'. This kind of historical understanding appears to assure us that from the ninth century onwards, the passage of Aristotle, Plotinus, and Proclus, among others, to the Islamic philosophers had taken place safely, without the slightest trouble. But this historical account is advanced not without some serious consequences: not only does it paint for us a very pale and an impoverished picture of philosophical activity, it also transforms the historian into an archaeologist whose skills he happens to lack. Indeed, it is not at all rare that historians set themselves the task of rummaging through the terrain of Islamic philosophy in search of vestiges of Greek works whose originals are lost but are thought to be preserved in the Arabic translations, or that, for lack of better resources, they are at least satisfied with the traces of writings of the philosophers of Antiquity, often studied with the competence and talent characteristic of the historians of Greek philosophy. It is in this manner that the history of Islamic philosophy is transformed into archaeology, so to speak. It is true that aside from the Greek heritage some historians have recently turned their attention to doctrines developed in other disciplines, such as philosophy of law, masterly developed by the jurists; philosophy of kalam, which reached important depths and stages of refinement; the Sufism of the great masters like al-Hallaj and Ibn 'Arabi, and so on. There is no doubt that studies of this sort go a long way towards enriching and rectifying our vision and better reflecting the philosophical activity of the time. Science and mathematics, however, are far from having received the same favourable attention given to law, kalam, linguistics, or Sufism. Furthermore, the examining of the relationships, which we regard as essential, between the sciences and philosophy, and notably between mathematics and philosophy, is completely disregarded. This serious lacuna is not the sole responsibility of the historians of philosophy; it is that of the historians of science as well. It is true that the examination of these relationships requires various competencies and an in-depth knowledge of these areas: in addition to a linguistic knowledge which goes beyond that called for in geometry (there one might do with elementary syntax and a poor lexicon), one is also asked to have a grasp of the history of philosophy itself. If we realize these requirements are not often met, and on top of that the conception of the relationships between science and philosophy is inherited from an oft-ambient positivism, we may come to better appreciate the profound indifference exhibited by the historians of science vis-a-vis the kind of examination we are calling for. …