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their nature, their essence being just unity and being. But the
natural philosophers take a different line; e.g. Empedocles-as
though reducing to something more intelligible-says what unity is; for
he would seem to say it is love: at least, this is for all things
the cause of their being one. Others say this unity and being, of
which things consist and have been made, is fire, and others say it is
air. A similar view is expressed by those who make the elements more
than one; for these also must say that unity and being are precisely
all the things which they say are principles.
(A) If we do not suppose unity and being to be substances, it
follows that none of the other universals is a substance; for these
are most universal of all, and if there is no unity itself or
being-itself, there will scarcely be in any other case anything
apart from what are called the individuals. Further, if unity is not a
substance, evidently number also will not exist as an entity
separate from the individual things; for number is units, and the unit
is precisely a certain kind of one.
But (B) if there is a unity-itself and a being itself, unity and
being must be their substance; for it is not something else that is
predicated universally of the things that are and are one, but just
unity and being. But if there is to be a being-itself and a
unity-itself, there is much difficulty in seeing how there will be
anything else besides these,-I mean, how things will be more than
one in number. For what is different from being does not exist, so
that it necessarily follows, according to the argument of
Parmenides, that all things that are are one and this is being.
There are objections to both views. For whether unity is not a
substance or there is a unity-itself, number cannot be a substance. We
have already said why this result follows if unity is not a substance;
and if it is, the same difficulty arises as arose with regard to
being. For whence is there to be another one besides unity-itself?
It must be not-one; but all things are either one or many, and of
the many each is one.
Further, if unity-itself is indivisible, according to Zeno's
postulate it will be nothing. For that which neither when added
makes a thing greater nor when subtracted makes it less, he asserts to
have no being, evidently assuming that whatever has being is a spatial
magnitude. And if it is a magnitude, it is corporeal; for the
corporeal has being in every dimension, while the other objects of
mathematics, e.g. a plane or a line, added in one way will increase
what they are added to, but in another way will not do so, and a point
or a unit does so in no way. But, since his theory is of a low
order, and an indivisible thing can exist in such a way as to have a
defence even against him (for the indivisible when added will make the
number, though not the size, greater),-yet how can a magnitude proceed
from one such indivisible or from many? It is like saying that the
line is made out of points.
But even if ore supposes the case to be such that, as some say,
number proceeds from unity-itself and something else which is not one,
none the less we must inquire why and how the product will be
sometimes a number and sometimes a magnitude, if the not-one was
inequality and was the same principle in either case. For it is not
evident how magnitudes could proceed either from the one and this
principle, or from some number and this principle.

(14) A question connected with these is whether numbers and bodies
and planes and points are substances of a kind, or not. If they are
not, it baffles us to say what being is and what the substances of
things are. For modifications and movements and relations and
dispositions and ratios do not seem to indicate the substance of
anything; for all are predicated of a subject, and none is a 'this'.
And as to the things which might seem most of all to indicate
substance, water and earth and fire and air, of which composite bodies

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