Problem of Simplicity of Muḥaddid al-Jihāt Sphere and Qūshchī's Challenge in it

The concept of “sphere” and its use for the description of the motions of heavenly bodies goes back to the ancient Greece. It was developed by the works of philosophers such as Plato and Aristotle and astronomers and mathematicians such as Euxoxus and Ptolemy. Philosophers and astronomers of the Islamic period extended this concpt and developed new philosophical concepts on its basis. They increased the number of the spheres from eight to nine, adding a last sphere called muḥaddid al-jihāt (the spheres which limits the directions). The idea of the simplicity of this sphere was emphasized by Ibn Sīnā and his followers, and this idea served as a basis for some philosophical-theological positions. In his commentary on Tajrīd al-ʿItiqād of Naṣir al-Dīn Ṭūsī, ʿAlī Qūshchī put into question this thesis. In this paper, we explain the concept of muḥaddid al-jihāt and we will discuss some of Qūshchī’s critiques.