^{1}For it is possible either (a) that any one unit is inaddible to any other, or (b) that the units in the Ideal 2 are inaddible to those in the Ideal 3, and thus that the units in each Ideal number are inaddible to those in the other Ideal numbers.

Now if all units are addible and do not
differ in kind, we get one type of number only, the mathematical, and
the Ideas cannot be the numbers thus produced;for how can we regard the Idea of Man
or Animal, or any other Form, as a number? There is one Idea of each
kind of thing: e.g. one of Humanity and another one of Animality; but
the numbers which are similar and do not differ in kind are infinitely
many, so that this is no more the Idea of Man than any other 3 is. But
if the Ideas are not numbers, they cannot exist at all;for from what principles can
the Ideas be derived? Number is derived from Unity and the
indeterminate dyad, and the principles and elements are said to be the
principles and elements of number, and the Ideas cannot be placed
either as prior or as posterior to numbers.^{2}

But if the units are inaddible in the
sense that any one unit is inaddible to any other, the number so
composed can be neither mathematical number (since mathematical number
consists of units which do not differ,
[20]
and the facts demonstrated of it fit in with this
character) nor Ideal number. For on this view 2 will not be the first
number generated from Unity and the indeterminate dyad, and then the
other numbers in succession, as they^{3} say 2, 3, because the
units in the primary 2 are generated at the same time,^{4} whether,
as the originator of the theory held, from unequals^{5}(coming into being when these were
equalized), or otherwiseâ€” since if we regard the one unit as prior to
the other,^{6} it will be prior
also to the 2 which is composed of them; because whenever one thing is
prior and another posterior, their compound will be prior to the
latter and posterior to the former.^{7}

Further, since the Ideal 1 is first, and then comes a particular 1 which is first of the other 1's but second after the Ideal 1, and then a third 1 which is next

after the second
but third after the first 1, it follows that the units will be prior
to the numbers after which they are called; e.g., there will be a
third unit in 2 before 3 exists, and a fourth and fifth in 3 before
these numbers exist.^{8}

It is true that nobody has represented the units of numbers as inaddible in this way; but according to the principles held by these thinkers even this view is quite reasonable,