The Inconsistency between Geometrical Continuism and Kalam Atomism In Fakhr al-Din Razi

Kalām Atomism defended by Ash’arī and Mu’tazila both, also includes the geometrical Atomism. Geometrical Atomism considers lines and geometrical shapes consisting of indivisible things. In other words, from this view, line is made up of points. This view conflicts with the definitions in Euclid’s Elements and subsequently classical geometry. Fakhr al-Din Razi who defended Atomism in the last decades of his lifespan was aware of this inconsistency. Through the arguments relevant to Atomism, he tried to resolve the inconsistency. Although his efforts do not result in developing a new geometry consistent with Atomism, his arguments contain subtle points which are significant from the view of the history and philosophy of Mathematics. In this paper, I will investigate several arguments from al-Maṭālib al-‘Alīyah in modern mathematical notation. And I will analyze the theoretical background of the arguments to achieve a frame to see their significance from the history of mathematics point of view. It is to show how Razi examined another geometrical structure other than the classical Geometry of his age. Furthermore, I suggest that Razi’s arguments should be considered in the history of infinitesimals as a possibility