Suppose someone objects: “Multiplicity can be made up of things other than units—of people, livestock, and the like.” We reply: just as those things are not themselves pluralities but entities to which plurality is ascribed, so too each of them is an individual thing, not a unit; and they are many, but not multiplicity itself.

Those who imagine that, by defining number as “a discrete quantity provided with order,” they have escaped this difficulty have in fact not escaped it at all. For the very idea of quantity cannot be grasped unless the mind already knows either part, division, or equality. Now, part and division can be conceived only through multiplicity; and equality is less obvious to a sound intellect than quantity itself, because equality is one of the specific accidents of quantity and therefore must already include quantity in its definition—one says, “equality is the sameness of two things in quantity.” As for the “order” included in the definition of number, that too cannot be understood until number has first been understood.

It must therefore be realized that all such statements are no more than pointers—devices akin to analogies, illustrative examples, or synonymous names. The meanings in question are apprehended, wholly or in part, in and of themselves; these devices merely call attention to them and distinguish them, nothing more.

I say: The discussion Ibn Sīnā records here has been received from him with approval; Abū Ḥāmid al-Ghazālī, Fakhr al-Dīn al-Rāzī, al-Suhrawardī, and others report similar remarks.

It may thus be said: what they have noted about the definitions of these matters is present, upon reflection and careful consideration, in everything they attempt to elucidate by means of their definitions. Some of it is evident to everyone—as with the most general notions—while some of it is evident only to particular people, just as those skilled in certain crafts and disciplines know matters unknown to others. In relation to such specialists, the definitions of those matters stand much as the definitions of general notions do in relation to the wider public.