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.