Home | Texts by category | | Quick Search:   
Works by Aristotle
Pages of Metaphysics

Previous | Next


also will be Ideas of some kind. And the same account applies to the
units; for the units in the first 2 generate the four in 4, so that
all the units come to be Ideas and an Idea will be composed of
Ideas. Clearly therefore those things also of which these happen to be
the Ideas will be composite, e.g. one might say that animals are
composed of animals, if there are Ideas of them.
In general, to differentiate the units in any way is an
absurdity and a fiction; and by a fiction I mean a forced statement
made to suit a hypothesis. For neither in quantity nor in quality do
we see unit differing from unit, and number must be either equal or
unequal-all number but especially that which consists of abstract
units-so that if one number is neither greater nor less than
another, it is equal to it; but things that are equal and in no wise
differentiated we take to be the same when we are speaking of numbers.
If not, not even the 2 in the 10-itself will be undifferentiated,
though they are equal; for what reason will the man who alleges that
they are not differentiated be able to give?
Again, if every unit + another unit makes two, a unit from the
2-itself and one from the 3-itself will make a 2. Now (a) this will
consist of differentiated units; and will it be prior to the 3 or
posterior? It rather seems that it must be prior; for one of the units
is simultaneous with the 3 and the other is simultaneous with the 2.
And we, for our part, suppose that in general 1 and 1, whether the
things are equal or unequal, is 2, e.g. the good and the bad, or a man
and a horse; but those who hold these views say that not even two
units are 2.
If the number of the 3-itself is not greater than that of the 2,
this is surprising; and if it is greater, clearly there is also a
number in it equal to the 2, so that this is not different from the
2-itself. But this is not possible, if there is a first and a second
Nor will the Ideas be numbers. For in this particular point they
are right who claim that the units must be different, if there are
to be Ideas; as has been said before. For the Form is unique; but if
the units are not different, the 2's and the 3's also will not be
different. This is also the reason why they must say that when we
count thus-'1,2'-we do not proceed by adding to the given number;
for if we do, neither will the numbers be generated from the
indefinite dyad, nor can a number be an Idea; for then one Idea will
be in another, and all Forms will be parts of one Form. And so with
a view to their hypothesis their statements are right, but as a
whole they are wrong; for their view is very destructive, since they
will admit that this question itself affords some
difficulty-whether, when we count and say -1,2,3-we count by
addition or by separate portions. But we do both; and so it is
absurd to reason back from this problem to so great a difference of

First of all it is well to determine what is the differentia of
a number-and of a unit, if it has a differentia. Units must differ
either in quantity or in quality; and neither of these seems to be
possible. But number qua number differs in quantity. And if the
units also did differ in quantity, number would differ from number,
though equal in number of units. Again, are the first units greater or
smaller, and do the later ones increase or diminish? All these are
irrational suppositions. But neither can they differ in quality. For
no attribute can attach to them; for even to numbers quality is said
to belong after quantity. Again, quality could not come to them either
from the 1 or the dyad; for the former has no quality, and the
latter gives quantity; for this entity is what makes things to be
many. If the facts are really otherwise, they should state this
quite at the beginning and determine if possible, regarding the
differentia of the unit, why it must exist, and, failing this, what

Previous | Next
Site Search