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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.
It is clear therefore that the same will hold good of number, if
number is a synthesis of units, as is said by some; for two is
either not one, or there is no unit present in it in complete reality.
But our result involves a difficulty. If no substance can consist of
universals because a universal indicates a 'such', not a 'this', and
if no substance can be composed of substances existing in complete
reality, every substance would be incomposite, so that there would not
even be a formula of any substance. But it is thought by all and was
stated long ago that it is either only, or primarily, substance that
can defined; yet now it seems that not even substance can. There

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