for if they are finite, everything finite requires a determining cause and admits of increase and decrease, as he posited concerning magnitude. If they are not finite, this entails the existence of an infinite number of attributes. Positing an infinite attribute is like positing an infinite magnitude, for an attribute must have a subject in which it inheres, and its infinitude entails the infinitude of that subject.

Moreover, each attribute is distinct from the others, so the attributes have a number. Their number is therefore either finite or infinite. If it is finite, the former consequence follows; if it is infinite, the latter follows. If, then, the number of His attributes is infinite, this is comparable to an infinite magnitude. Thus, every argument advanced to establish the impossibility of an infinite magnitude can also be advanced to establish the impossibility of an infinite number of attributes. For whatever is supposed concerning alignment or its absence in magnitudes can likewise be supposed concerning correspondence or its absence in numbers.

This argument can be made binding on anyone, since one must acknowledge an existent possessing a distinctive property that sets it apart from everything else: an existent with no distinctive property is impossible. Even universals, though they exist in minds, are distinct in Zayd’s mind from those in ʿAmr’s mind, for they are attributes inhering in minds. Since every existent has a distinctive property that sets it apart, whether it exists necessarily in itself or is contingent, the argument concerning its having that particular property is the same as the argument concerning its having a particular magnitude.