Since the celestial spheres are round, and their motions could not be calculated without knowledge of geometry and the properties of straight and curved lines, they studied “geometry” for this purpose and for worldly development. This is why they pursued it so extensively. Otherwise, if its only purpose had been the mere conception of numbers and magnitudes, that aim would not have warranted the effort described. Yet this may be an end in itself for some who take pleasure in it, for the pleasures of the soul are diverse. Some people take pleasure in chess, backgammon, and gambling until these distract them from what would benefit them more.

“Logic” originated in geometry. They called it “definitions,” drawing on the boundaries of those figures, so that they could pass from perceptible figures to intelligible ones. This was due to the weakness of their intellects and their inability to attain knowledge except by a circuitous route. Allah Most High has made knowledge, clear exposition, righteous deeds, and faith accessible to the Muslims, enabling them to surpass every other group of humankind. All praise belongs to Allah, Lord of all worlds.

As for “metaphysics,” which they regard as independent of matter both in the mind and in external reality, it has already become clear to you that it has no object of knowledge in external reality. Rather, it is general in scope, concerning unrestricted universals that exist as universals only in the mind. None of this contributes to the perfection of the soul.

If they know the Necessary Existent specifically, this is knowledge of a particular whose very conception precludes its applying to more than one individual. This is something that the syllogism they call “demonstration” does not establish. Their demonstration does not establish any specific particular, whether the Necessary Existent or anything else