On The Parts Of Animals   

solid hoofs. Now even with differentiae capable of this specific
subdivision it is difficult enough so to make the classification, as
that each animal shall be comprehended in some one subdivision and in
not more than one; but far more difficult, nay impossible, is it to do
this, if we start with a dichotomy into two contradictories. (Suppose
for instance we start with the two contradictories, Feathered and
Unfeathered; we shall find that the ant, the glow-worm, and some other
animals fall under both divisions.) For each differentia must be
presented by some species. There must be some species, therefore,
under the privative heading. Now specifically distinct animals cannot
present in their essence a common undifferentiated element, but any
apparently common element must really be differentiated. (Bird and Man
for instance are both Two-footed, but their two-footedness is diverse
and differentiated. So any two sanguineous groups must have some
difference in their blood, if their blood is part of their essence.)
From this it follows that a privative term, being insusceptible of
differentiation, cannot be a generic differentia; for, if it were,
there would be a common undifferentiated element in two different
groups.
Again, if the species are ultimate indivisible groups, that is, are
groups with indivisible differentiae, and if no differentia be common
to several groups, the number of differentiae must be equal to the
number of species. If a differentia though not divisible could yet be
common to several groups, then it is plain that in virtue of that
common differentia specifically distinct animals would fall into the
same division. It is necessary then, if the differentiae, under which
are ranged all the ultimate and indivisible groups, are specific
characters, that none of them shall be common; for otherwise, as
already said, specifically distinct animals will come into one and the
same division. But this would violate one of the requisite conditions,
which are as follows. No ultimate group must be included in more than
a single division; different groups must not be included in the same
division; and every group must be found in some division. It is plain
then that we cannot get at the ultimate specific forms of the animal,
or any other, kingdom by bifurcate division. If we could, the number
of ultimate differentiae would equal the number of ultimate animal
forms. For assume an order of beings whose prime differentiae are
White and Black. Each of these branches will bifurcate, and their
branches again, and so on till we reach the ultimate differentiae,
whose number will be four or some other power of two, and will also be
the number of the ultimate species comprehended in the order.
(A species is constituted by the combination differentia and matter.
For no part of an animal is purely material or purely immaterial; nor
can a body, independently of its condition, constitute an animal or
any of its parts, as has repeatedly been observed.)
Further, the differentiae must be elements of the essence, and not
merely essential attributes. Thus if Figure is the term to be divided,
it must not be divided into figures whose angles are equal to two
right angles, and figures whose angles are together greater than two
right angles. For it is only an attribute of a triangle and not part
of its essence that its angles are equal to two right angles.
Again, the bifurcations must be opposites, like White and Black,
Straight and Bent; and if we characterize one branch by either term,
we must characterize the other by its opposite, and not, for example,
characterize one branch by a colour, the other by a mode of
progression, swimming for instance.
Furthermore, living beings cannot be divided by the functions common
to body and soul, by Flying, for instance, and Walking, as we see them
divided in the dichotomies already referred to. For some groups, Ants
for instance, fall under both divisions, some ants flying while others
do not. Similarly as regards the division into Wild and Tame; for it
also would involve the disruption of a species into different groups.
For in almost all species in which some members are tame, there are
other members that are wild. Such, for example, is the case with Men,