MA. of History of Science, Mathematics in Islamic World, Iran.
Abstract
The finitude of dimensions is the dominant Paradigm in the Muslim World and the most important argument for it is perhaps the argument of “Collimation”, proposed by Avicenna in his book ‘Oyoon Al Hikam, Fountains of wisdom’. According to this argument, if we assume an infinite line and then draw another parallel one which crosses the center of a sphere, then, as a result of the circular motion of the sphere, Collimation will happen between these two lines instantly. But such Collimation in an instant is impossible. Among Muslim philosophers, ‘Abul Barakat Al-Baghdadi’, ‘Khaje Naṣīr al-Dīn Al-Ṭūsī’, and ‘Allameh al-Hilli’ have critiqued and refuted this arguement. And ‘Mulla Șadrā’ and 'Fakhr Al-Dīn Razi' have defended it against these criticisms. In this article, first the argument is elaborated. Then, Abul Barakat’s criticisms and Fakhr Al-Dīn Razi’s replies are explained. Khaje Naṣīr al-Dīn Al-Ṭūsī’s critique and Mulla Șadrā’s reply will come next. It will be shown that Mulla Șadrā’s reply is incomplete but Al Tusi’s criticism is reasonable. Therefore, the Collimation argument fails to prove true.
