^{1}Now it is obvious that it cannot be infinite, because infinite number is neither odd nor even, and numbers are always generated either from odd or from even number. By one process, when 1 is added to an even number, we get an odd number; by another, when 1 is multiplied by 2, we get ascending powers of 2; and by another, when powers of 2 are multiplied by odd numbers, we get the remaining even numbers.

Again, if every Idea is an Idea of
something, and the numbers are Ideas, infinite number will also be an
Idea of something, either sensible or otherwise. This, however, is
impossible, both logically^{2} and on their own
assumption,^{3} since they regard the Ideas as they
do.

If, on the other hand, number
is finite, what is its limit? In reply to this we must not only assert
the fact, but give the reason.Now if number only goes up to 10, as some
hold,^{4} in the
first place the Forms will soon run short. For example, if 3 is the
Idea of Man, what number will be the Idea of Horse? Each number up to
10 is an Idea; the Idea of Horse, then, must be one of the numbers in
this series, for they are substances or Ideas.But the fact remains that they will run
short, because the different types of animals will outnumber them. At
the same time it is clear that if in this way the Ideal 3 is the Idea
of Man, so will the other 3's be also (for the 3's in the same
numbers^{5} are
similar),
[20]
so that
there will be an infinite number of men; and if each 3 is an Idea,
each man will be an Idea of Man; or if not, they will still be
men.And if the
smaller number is part of the greater, when it is composed of the
addible units contained in the same number, then if the Ideal 4 is the
Idea of something, e.g. "horse" or "white," then "man" will be part of
"horse," if "man" is 2. It is absurd also that there should be an Idea
of 10 and not of 11, nor of the following numbers.

Again, some things exist and come into being of which there are no
Forms^{6}; why, then, are there not Forms of
these too? It follows that the Forms are not the causes of
things.

Again, it is absurd that
number up to 10 should be more really existent, and a Form, than 10
itself; although the former is not generated as a unity, whereas the
latter is. However, they try to make out that the series up to 10 is a
complete number;at least
they generate the derivatives, e.g. the void, proportion, the odd,
etc., from within the decad. Some, such as motion, rest, good and
evil, they assign to the first principles; the rest to numbers.^{7} Hence they identify the odd with Unity;
because if oddness depended on 3, how could 5 be odd?^{8}

Again, they hold that spatial magnitudes and the like have a certain limit;