The Divisions of the Philosophical Sciences (Part One: Mathematical Sciences)

Excerpt from Imam al-Ghazali's Deliverance from Error:

Know that the science of the philosophers, with reference to the aim we have in mind, include six divisions: mathematical, logical, physical, metaphysical, political, and moral.

The mathematical sciences deal with arithmetic, geometry, and astronomy. But nothing in them entails denial or affirmation of religious matters. On the contrary, they concern rigorously demonstrated facts which can in no ways be denied once they are known and understood. From them, however, two evils have been engendered.

One of these is that whoever takes up these mathematical sciences marvels at the fine precision of their details and the clarity of their proofs. Because of that, he forms a high opinion of the philosophers and assumes that all their sciences have the same lucidity and apodeictic solidity as this science of mathematics. Moreover, he will have heard the talk of the town about their unbelief, their negative attitude, and their disdain for the Law. Therefore he ceases to believe out of pure conformism, asserting: "If religion were true, this would not have been unknown to these philosophers, given their precision in this science of mathematics." Thus, when he learns through hearsay of their unbelief and rejection of religion, he concludes that it is right to reject and disavow religion. How many a man have I seen who strayed from the path of truth on this pretext and for no other reason!

One may say to such a man: "A person skilled in one field is not necessarily skilled in every field. Thus a man skilled in jurisprudence and kalaam is not necessarily skilled in medicine, nor is a man who is ignorant of the speculative and rational sciences necessarily ignorant of the science of the syntax. On the contrary, in each field there are men who have reached in it a certain degree of skill and preeminence, although they may be quite stupid and ignorant about other things. What the ancients had to say about mathematical topics was apodeictic, whereas their views on metaphysical questions were conjectural. But this is known only to an experienced man who has made a thorough study of the matter."

When such an argument is urged against one who has become an unbeliever out of mere conformism, he finds it unacceptable. Rather, caprice's sway, vain passion, and love of appearing to be clever prompt him to persist in his high opinion of the philosophers with regard to all their sciences. This, then, is a very serious evil, and because of it one should warn off anyone who would embark upon the study of those mathematical sciences. For even though they do not pertain to the domain of religion, yet, since they are among the primary elements of the philosophers' sciences, the student of mathematics will be insiduously affected by the sinister mischief of the philosophers.

The second evil likely to follow from the study of mathematical sciences derives from the case of an ignorant friend of Islam who supposes that our religion must be championed by the rejection of every science ascribed to the philosophers. So he rejects all their sciences, claiming that they display ignorance and folly in them all. He even denies their statements about eclipses of the sun and the moon and asserts that their views are contrary to the revealed Law. When such an assertion reaches the ears of someone who knows those things through apodeictic demonstration, he does not doubt the validity of his proof, but rather believes that Islam is built on ignorance and the denial of apodeictic demonstration. So he becomes all the more enamored of philosophy and envenomed against Islam. Great indeed is the crime against religion committed by anyone who supposes that Islam is to be championed by the denial of these mathematical sciences. For the revealed Law nowhere undertakes to deny or affirm these sciences, and the latter nowhere address themselves to religious matters.

The saying of Muhammad- God's blessings and peace be upon him!- "The sun and moon are two signs of God Most High: they are not eclipsed for the death or life of any man; so when you see an eclipse, fly in fear to the mention of God Most High," contains nothing demanding the denial of the science of calculation which apprises us of the course of the sun and the moon and their conjunction and their opposition in a specific way. As for his (alleged) saying- Peace be upon him!- "But when God manifests Himself to a thing, it humbles itself before Him," this addition is not found at all in sound tradition. This, then, is the judgment to be made on the character of mathematics and its evil consequences.