The objection that unity, without itself experiencing anything, by the
mere addition of something else, is no longer one, but becomes double,
is a mistake.[32] The one has not become two, and is not that which
has been added to it, nor that to which something has been added. Each
of them remains one, such as it was; but two can be asserted of their
totality, and one of each of them separately. Two therefore, not any
more than "pair," is by nature a relation. If the pair consisted in
the union (of two objects), and if "being united" were identical with
"to duplicate," in this case the union, as well as the pair, would
constitute two. Now a "pair" appears likewise in a state contrary (to
that of the reunion of two objects); for two may be produced by the
division of a single object. Two, therefore, is neither reunion nor
division, as it would have to be in order to constitute a relation.
OBJECTS PARTICIPATE IN NUMBERS JUST AS THEY PARTICIPATE IN ALL
INTELLIGIBLE ENTITIES.
What then is the principal cause (by virtue of which objects
participate in numbers)? A being is one by the presence of one; double,
because of the presence of the pair; just as it is white because of the
presence of whiteness; beautiful, because of the presence of beauty;
and just by that of justice. If that be not admitted, we shall be
reduced to asserting that whiteness, beauty and justice are nothing
real, and that their only causes are simple relations; that justice
consists in some particular relation with some particular being; that
beauty has no foundation other than the affection that we feel; that
the object which seems beautiful possesses nothing capable of exciting
this affection either by nature, or by acquirement. When you see an
object that is one, and that you call single, it is simultaneously
great, beautiful, and susceptible of receiving a number of other
qualifications. Now why should unity not inhere in the object as
well as greatness and magnitude, sweetness and bitterness, and other
qualities? We have no right to admit that quality, whatever it be,
forms part of the number of beings, whilst quantity is excluded; nor
to limit quantity to continuous quantity, while discrete quantity is
excluded from the conception of quantity; and that so much the less as
continuous quantity is measured by discrete quantity. Thus, just as
an object is great because of the presence of magnitude, as it is one
by the presence of unity; so is it double because of the presence of
being a pair, and so forth.[33]