Metaphysics and Mathematics in Classical Islamic Culture: Avicenna and His Successors
For seven centuries, advanced mathematical research was carried out in Arabic in the urban centers of Islam. We are justified in wondering whether philosophers found themes for reflection in this work, and if they were incited to seek models in mathematics for the elaboration of their systems, or if, on the contrary, they fell back upon what historians like to call falsafa, that is, a doctrine o f Being and o f the Soul which was indifferent to other branches of knowledge, and independent o f every determination save that o f religion (in brief, an inheritance from Late Antiquity under the sign of Islam). Such a question might be o f interest both to the historian of philosophy and to the historian o f sciences. Indeed, how can we imagine that, in the face o f the unprecedented flourishing of mathematical disciplines and results - algebra, algebraic geometry, Diophantean analysis, the theory of parallels, and methods o f projection - philosophers could have remained indifferent? It is even more difficult to believe that they could have failed to react when, before their very eyes, brand-new epistemological questions were being raised by the new mathesis. Among these was the question o f the applicability o f mathematics: never before had the mathematical disciplines been applied to one another; never had the need been conceived o f applying mathematics to physics, as a condition o f the latter’s apodicticity; finally, never had it occurred to anyone to invent a discipline able to express its results by positional geometry as well as by metrical geometry; in other words, a topology avant la lettre. These epistemic events were far from being the only ones; and it would be
astonishing if all o f them had escaped the attention o f the philosophers, some o f whom were themselves mathematicians, and most o f whom were up to date in the field. It is not, o f course, necessary that a discipline or scientific activity should have the philosophy it deserves, nor that the philosopher should play any kind of a role in the development of mathematics and of science. There is, in other words, no a priori necessity in the relations between mathematics and theoretical philosophy; but this is one more reason to raise the question and return to the writings of both philosophers and mathematicians, in order to try to elucidate these relations. One result already seems established: having attacked this task on several occasions, I believe I have shown the hitherto-unsuspected wealth of the philosophy of mathematics in classical Islam in mathematicians such as al-SijzI, Ibn Sinan, Ibn al-Haytham, etc., and that o f philosophers like al-Kindl, al-Farabl, and Ibn Slna.