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feathers and one is featherless (if we do this we do it through
incapacity); we must divide it only into cloven-footed and not cloven;
for these are differentiae in the foot; cloven-footedness is a form of
footedness. And the process wants always to go on so till it reaches
the species that contain no differences. And then there will be as
many kinds of foot as there are differentiae, and the kinds of animals
endowed with feet will be equal in number to the differentiae. If then
this is so, clearly the last differentia will be the substance of
the thing and its definition, since it is not right to state the
same things more than once in our definitions; for it is
superfluous. And this does happen; for when we say 'animal endowed
with feet and two-footed' we have said nothing other than 'animal
having feet, having two feet'; and if we divide this by the proper
division, we shall be saying the same thing more than once-as many
times as there are differentiae.
If then a differentia of a differentia be taken at each step,
one differentia-the last-will be the form and the substance; but if we
divide according to accidental qualities, e.g. if we were to divide
that which is endowed with feet into the white and the black, there
will be as many differentiae as there are cuts. Therefore it is
plain that the definition is the formula which contains the
differentiae, or, according to the right method, the last of these.
This would be evident, if we were to change the order of such
definitions, e.g. of that of man, saying 'animal which is two-footed
and endowed with feet'; for 'endowed with feet' is superfluous when
'two-footed' has been said. But there is no order in the substance;
for how are we to think the one element posterior and the other prior?
Regarding the definitions, then, which are reached by the method of
divisions, let this suffice as our first attempt at stating their
nature.
13
Let us return to the subject of our inquiry, which is substance.
As the substratum and the essence and the compound of these are called
substance, so also is the universal. About two of these we have
spoken; both about the essence and about the substratum, of which we
have said that it underlies in two senses, either being a 'this'-which
is the way in which an animal underlies its attributes-or as the
matter underlies the complete reality. The universal also is thought
by some to be in the fullest sense a cause, and a principle; therefore
let us attack the discussion of this point also. For it seems
impossible that any universal term should be the name of a
substance. For firstly the substance of each thing is that which is
peculiar to it, which does not belong to anything else; but the
universal is common, since that is called universal which is such as
to belong to more than one thing. Of which individual then will this
be the substance? Either of all or of none; but it cannot be the
substance of all. And if it is to be the substance of one, this one
will be the others also; for things whose substance is one and whose
essence is one are themselves also one.
Further, substance means that which is not predicable of a
subject, but the universal is predicable of some subject always.
But perhaps the universal, while it cannot be substance in the way
in which the essence is so, can be present in this; e.g. 'animal'
can be present in 'man' and 'horse'. Then clearly it is a formula of
the essence. And it makes no difference even if it is not a formula of
everything that is in the substance; for none the less the universal
will be the substance of something, as 'man' is the substance of the
individual man in whom it is present, so that the same result will
follow once more; for the universal, e.g. 'animal', will be the
substance of that in which it is present as something peculiar to
it. And further it is impossible and absurd that the 'this', i.e.
the substance, if it consists of parts, should not consist of
substances nor of what is a 'this', but of quality; for that which
is not substance, i.e. the quality, will then be prior to substance
and to the 'this'. Which is impossible; for neither in formula nor
in time nor in coming to be can the modifications be prior to the
substance; for then they will also be separable from it. Further,
Socrates will contain a substance present in a substance, so that this
will be the substance of two things. And in general it follows, if man
and such things are substance, that none of the elements in their
formulae is the substance of anything, nor does it exist apart from
the species or in anything else; I mean, for instance, that no
'animal' exists apart from the particular kinds of animal, nor does
any other of the elements present in formulae exist apart.
If, then, we view the matter from these standpoints, it is plain
that no universal attribute is a substance, and this is plain also
from the fact that no common predicate indicates a 'this', but
rather a 'such'. If not, many difficulties follow and especially the
'third man'.
The conclusion is evident also from the following consideration. A
substance cannot consist of substances present in it in complete
reality; for things that are thus in complete reality two are never in
complete reality one, though if they are potentially two, they can
be one (e.g. the double line consists of two halves-potentially; for
the complete realization of the halves divides them from one another);
therefore if the substance is one, it will not consist of substances
present in it and present in this way, which Democritus describes
rightly; he says one thing cannot be made out of two nor two out of
one; for he identifies substances with his indivisible magnitudes.
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