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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."
Objection 2: Further, no opposite thing is constituted by its
opposite. But "multitude" is constituted by "one." Therefore it
is not opposed to "multitude."
Objection 3: Further, "one" is opposed to "one." But the idea
of "few" is opposed to "many." Therefore "one" is not opposed to
"many."
Objection 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 convertible with "being" is opposed to
"multitude" by way of privation; as the undivided is to the thing
divided.
Reply to Objection 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 to Objection 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 to Objection 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 to Objection 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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