knowledge of Him and worship of Him—with love and humility—as has been set out in its proper place.

For this reason, when the philosophers attain a measure of divine guidance, the furthest point they reach is only the starting point of the Jews and Christians who persist in unbelief, let alone of the Muslims, the nation of Muḥammad—may God’s blessings and peace be upon him. Indeed, even after abrogation and distortion, what the Jews and Christians still possess that pertains to the soul’s perfection surpasses—by type, quantity, and quality—what is found among the philosophers.

Fourth Point
Mathematical knowledge does not perfect the soul, even though the intellect may find it pleasing.

Their division of the sciences into natural, mathematical, and metaphysical, and their ranking of mathematics above natural science and metaphysics above mathematics, is one of the ways they have turned the truth on its head. Natural science—knowledge of the bodies that actually exist outside the mind, the origins of their motions, their transformations from one state to another, and the natures they contain—is nobler than the mere conception of abstract magnitudes and numbers. If a person’s comprehension extends no further than a circle, a triangle, or a square—even embracing everything in Euclid—or no further than abstract numbers, he has acquired no knowledge of anything that exists in the external world, nor is that perfection of the soul. Were it not that such study seeks knowledge of external things that are counted and measured—bodies and their attributes—it would not even be deemed a science.

They made geometry the gateway to astronomy so that they could employ it in astronomical proofs or use it for the affairs of worldly construction; yet their syllogistic demonstrations yield a constant, certain, unassailable indication only within these mathematical materials.

For arithmetic—knowledge of discrete quantity—and geometry—knowledge of continuous quantity—constitute sure knowledge that admits no contradiction whatsoever, as in the addition or division of numbers.