 Now that we know what mathematical objects are not for Muslim philosophers, we must thus ask what they are. In his Metaphysics (VI.1, 1026a13–19) Aristotle classifies different theoretical sciences based on the ontological status of the objects they study (Cleary 1994). Aristotle’s main criteria for distinguishing different sciences from each other are the extent and qualification of the association of the subject-matter of the sciences with movement and materiality. Employing a similar approach, in his The Aims of Aristotle’s Metaphysics (Maqāla fī aghrāḍ kitāb mā baʿd al-ṭabīʿa), al-Fārābī (d. 950) argues that the subject matters of mathematics—i.e., mathematical objects—are abstracted (mujarrad) from matter in estimation (wahm) but not in the extramental world. On the one hand, mathematical objects are different from the objects that metaphysics studies because the latter objects are fully detached from matter both in estimation and in the extramental world. On the other hand, mathematical objects are different from the sensible physical objects because they cannot be separated from matter, either in estimation or in the extramental world. Thus, mathematics occupies an intermediate position between metaphysics and physics. The association of mathematical objects with matter is stronger than that of the objects of metaphysics but weaker than that of the objects of physics. (The original Arabic of al-Fārābī’s book can be found in al-Fārābi 1890: 34–38, and Kiankhah 2015: 147–57. For two English translations, see Bertolacci 2006: 66–72, and McGinnis &amp; Reisman 2007: 78–81.)