nor in external reality—his claim need only be fully understood for its falsity to become evident. These matters are discussed at length elsewhere. The point here is that this science admits of valid demonstrations, yet no soul attains perfection through it, escapes punishment by it, or achieves happiness through it. Hence Abū Hāmid al-Ghazālī and others said of these men’s sciences:
“They consist either of true sciences that yield no benefit—and we seek refuge in Allah from knowledge that brings no benefit—or of false conjectures that cannot be trusted—and indeed, some suspicion is sinful.”
By the former, they mean the mathematical sciences; by the latter, what these men say about metaphysics, astrology, and the like. Nevertheless, the soul may take pleasure in this, just as it takes pleasure in other things. A person enjoys learning what he did not know and hearing what he had not heard, provided he is not preoccupied with something he considers more important. Likewise, he may enjoy various activities that fall under amusement and play.
Moreover, through sustained study of these matters, the soul becomes accustomed to sound knowledge, correct and true propositions, and sound inference. This serves to refine the mind and its understanding. The soul also becomes accustomed to knowing and speaking the truth, thereby gaining assistance in attaining knowledge of a higher order. Hence it is said that the early philosophers would begin their children’s education with mathematics. Many of their masters eventually devote themselves exclusively to this, because, when they examined their methods and those of their opponents among the proponents of false speculative theology, they did not