The rational sciences stand apart. Arabic, by contrast, is a customary practice of a people: it can only be learned by hearing, and its rules are discovered solely through induction. This differs from the instruments by which one determines the quantities of what is measured by volume, weight, what is planted, or what is counted, for such matters generally do require instruments. Nevertheless, designating a particular implement or standard by which something is to be measured or weighed is itself a conventional affair—just as people agree upon the conventions of language.

Muslim scholars have also disagreed over what is meant by the terms dirham and dinar: are they fixed by the Sacred Law, or does their meaning revert to common usage? There are two opinions, the sounder being the latter. Upon that issue hinges the legal ­niṣâb: is it two hundred dirhams of a specified weight, or two hundred dirhams of whatever coinage people are currently using, according to what is firmly established among them?

As for the so-called “craft of definition,” there is no doubt that they themselves invented it; they admit that its author was Aristotle, whom they venerate on that account. They claim that no one before him encompassed all the branches of logic, though they differ—holding two views—over whether some of those branches had been anticipated by others.

The divisions of logic, they say, are eight:

1. Simple elements, namely the single intelligible predicables;
2. The first composition, the composition of propositions;
3. The second composition, the composition of a syllogism from propositions;
4. The demonstrative (al-Burhânî);
5. The dialectical (al-Jadalî);
6. The rhetorical (al-Khiṭâbî);
7. The poetic (al-Shiʿrî);
8. The sophistical (al-Safsaṭa).

They call the first part the Isagoge, and some say that Porphyry introduced this section of logic after Aristotle. At times they treat “syllogism” and “demonstration” as one, reducing the divisions to seven and saying