Whether "One" and "Many" Are Opposed to Each Other?
Objection 1: It seems that "one" and "many" are not mutually opposed.
For no opposite thing is predicated of its opposite. But every
_multitude_ is in a certain way _one,_ as appears from the preceding
article. Therefore "one" is not opposed to "multitude."
Obj. 2: Further, no opposite thing is constituted by its
opposite. But _multitude_ is constituted by _one._ Therefore it is not
opposed to "multitude."
Obj. 3: Further, "one" is opposed to "one." But the idea of "few"
is opposed to "many." Therefore "one" is not opposed to "many."
Obj. 4: Further, if "one" is opposed to "multitude," it is
opposed as the undivided is to the divided; and is thus opposed to it
as privation is to habit. But this appears to be incongruous; because
it would follow that "one" comes after "multitude," and is defined by
it; whereas, on the contrary, "multitude" is defined by "one." Hence
there would be a vicious circle in the definition; which is
inadmissible. Therefore "one" and "many" are not opposed.
_On the contrary,_ Things which are opposed in idea, are themselves
opposed to each other. But the idea of "one" consists in
indivisibility; and the idea of "multitude" contains division.
Therefore "one" and "many" are opposed to each other.
_I answer that,_ "One" is opposed to "many," but in various ways. The
_one_ which is the principle of number is opposed to _multitude_ which
is number, as the measure is to the thing measured. For "one" implies
the idea of a primary measure; and number is _multitude_ measured by
_one,_ as is clear from _Metaph._ x. But the _one_ which is convertible
with _being_ is opposed to _multitude_ by way of privation; as the
undivided is to the thing divided.
Reply Obj. 1: No privation entirely takes away the being of a thing,
inasmuch as privation means "negation in the subject," according to
the Philosopher (Categor. viii). Nevertheless every privation takes
away some being; and so in being, by reason of its universality, the
privation of being has its foundation in being; which is not the case
in privations of special forms, as of sight, or of whiteness and the
like. And what applies to being applies also to one and to good,
which are convertible with being, for the privation of good is
founded in some good; likewise the removal of unity is founded in
some one thing. Hence it happens that multitude is some one thing;
and evil is some good thing, and non-being is some kind of being.
Nevertheless, opposite is not predicated of opposite; forasmuch as
one is absolute, and the other is relative; for what is relative
being (as a potentiality) is non-being absolutely, i.e. actually; or
what is absolute being in the genus of substance is non-being
relatively as regards some accidental being. In the same way, what is
relatively good is absolutely bad, or vice versa; likewise what is
absolutely _one_ is relatively _many,_ and vice versa.
Reply Obj. 2: A _whole_ is twofold. In one sense it is homogeneous,
composed of like parts; in another sense it is heterogeneous,
composed of dissimilar parts. Now in every homogeneous whole, the
whole is made up of parts having the form of the whole; as, for
instance, every part of water is water; and such is the constitution
of a continuous thing made up of its parts. In every heterogeneous
whole, however, every part is wanting in the form belonging to the
whole; as, for instance, no part of a house is a house, nor is any
part of a man a man. Now multitude is such a kind of a whole.
Therefore inasmuch as its part has not the form of the multitude, the
latter is composed of unities, as a house is composed of not houses;
not, indeed, as if unities constituted multitude so far as they are
undivided, in which way they are opposed to multitude; but so far as
they have being, as also the parts of a house make up the house by
the fact that they are beings, not by the fact that they are not
houses.
Reply Obj. 3: "Many" is taken in two ways: absolutely, and in that
sense it is opposed to "one"; in another way as importing some kind
of excess, in which sense it is opposed to "few"; hence in the first
sense two are many but not in the second sense.
Reply Obj. 4: "One" is opposed to "many" privatively, inasmuch as the
idea of "many" involves division. Hence division must be prior to
unity, not absolutely in itself, but according to our way of
apprehension. For we apprehend simple things by compound things; and
hence we define a point to be, "what has no part," or "the beginning
of a line." "Multitude" also, in idea, follows on "one"; because we
do not understand divided things to convey the idea of multitude
except by the fact that we attribute unity to every part. Hence "one"
is placed in the definition of "multitude"; but "multitude" is not
placed in the definition of "one." But division comes to be
understood from the very negation of being: so what first comes to
mind is being; secondly, that this being is not that being, and thus
we apprehend division as a consequence; thirdly, comes the notion of
one; fourthly, the notion of multitude.
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