In general one might raise the question why after all, besides
perceptible things and the intermediates, we have to look for
another class of things, i.e. the Forms which we posit. If it is for
this reason, because the objects of mathematics, while they differ
from the things in this world in some other respect, differ not at all
in that there are many of the same kind, so that their first
principles cannot be limited in number (just as the elements of all
the language in this sensible world are not limited in number, but
in kind, unless one takes the elements of this individual syllable
or of this individual articulate sound-whose elements will be
limited even in number; so is it also in the case of the
intermediates; for there also the members of the same kind are
infinite in number), so that if there are not-besides perceptible
and mathematical objects-others such as some maintain the Forms to be,
there will be no substance which is one in number, but only in kind,
nor will the first principles of things be determinate in number,
but only in kind:-if then this must be so, the Forms also must
therefore be held to exist. Even if those who support this view do not
express it articulately, still this is what they mean, and they must
be maintaining the Forms just because each of the Forms is a substance
and none is by accident.

    But if we are to suppose both that the Forms exist and that the
principles are one in number, not in kind, we have mentioned the
impossible results that necessarily follow.

    (13) Closely connected with this is the question whether the
elements exist potentially or in some other manner. If in some other
way, there will be something else prior to the first principles; for
the potency is prior to the actual cause, and it is not necessary
for everything potential to be actual.-But if the elements exist
potentially, it is possible that everything that is should not be. For
even that which is not yet is capable of being; for that which is
not comes to be, but nothing that is incapable of being comes to be.

    (12) We must not only raise these questions about the first
principles, but also ask whether they are universal or what we call
individuals. If they are universal, they will not be substances; for
everything that is common indicates not a "this" but a "such", but
substance is a "this". And if we are to be allowed to lay it down that
a common predicate is a "this" and a single thing, Socrates will be
several animals-himself and "man" and "animal", if each of these
indicates a "this" and a single thing.

    If, then, the principles are universals, these universal.
Therefore if there is to be results follow; if they are not universals
but of knowledge of the principles there must be the nature of
individuals, they will not be other principles prior to them, namely
those knowable; for the knowledge of anything is that are
universally predicated of them.