On unity

Prima Pars - qu. 11
Article 1. Whether "one" adds anything to "being"?
Objection 1. It seems that "one" adds something to "being." For everything is in a determinate genus by addition to being, which penetrates all "genera." But "one" is a determinate genus, for it is the principle of number, which is a species of quantity. Therefore "one" adds something to "being."
Objection 2. Further, what divides a thing common to all, is an addition to it. But "being" is divided by "one" and by "many." Therefore "one" is an addition to "being."
Objection 3. Further, if "one" is not an addition to "being," "one" and "being" must have the same meaning. But it would be nugatory to call "being" by the name of "being"; therefore it would be equally so to call being "one." Now this is false. Therefore "one" is an addition to "being."
On the contrary, Dionysius says (Div. Nom. 5, ult.): "Nothing which exists is not in some way one," which would be false if "one" were an addition to "being," in the sense of limiting it. Therefore "one" is not an addition to "being."
I answer that, "One" does not add any reality to "being"; but is only a negation of division; for "one" means undivided "being." This is the very reason why "one" is the same as "being." Now every being is either simple or compound. But what is simple is undivided, both actually and potentially. Whereas what is compound, has not being whilst its parts are divided, but after they make up and compose it. Hence it is manifest that the being of anything consists in undivision; and hence it is that everything guards its unity as it guards its being.
Reply to Objection 1. Some, thinking that the "one" convertible with "being" is the same as the "one" which is the principle of number, were divided into contrary opinions. Pythagoras and Plato, seeing that the "one" convertible with "being" did not add any reality to "being," but signified the substance of "being" as undivided, thought that the same applied to the "one" which is the principle of number. And because number is composed of unities, they thought that numbers were the substances of all things. Avicenna, however, on the contrary, considering that "one" which is the principle of number, added a reality to the substance of "being" (otherwise number made of unities would not be a species of quantity), thought that the "one" convertible with "being" added a reality to the substance of beings; as "white" to "man." This, however, is manifestly false, inasmuch as each thing is "one" by its substance. For if a thing were "one" by anything else but by its substance, since this again would be "one," supposing it were again "one" by another thing, we should be driven on to infinity. Hence we must adhere to the former statement; therefore we must say that the "one" which is convertible with "being," does not add a reality to being; but that the "one" which is the principle of number, does add a reality to "being," belonging to the genus of quantity.
Reply to Objection 2. There is nothing to prevent a thing which in one way is divided, from being another way undivided; as what is divided in number, may be undivided in species; thus it may be that a thing is in one way "one," and in another way "many." Still, if it is absolutely undivided, either because it is so according to what belongs to its essence, though it may be divided as regards what is outside its essence, as what is one in subject may have many accidents; or because it is undivided actually, and divided potentially, as what is "one" in the whole, and is "many" in parts; in such a case a thing will be "one" absolutely and "many" accidentally. On the other hand, if it be undivided accidentally, and divided absolutely, as if it were divided in essence and undivided in idea or in principle or cause, it will be "many" absolutely and "one" accidentally; as what are "many" in number and "one" in species or "one" in principle. Hence in that way, being is divided by "one" and by "many"; as it were by "one" absolutely and by "many" accidentally. For multitude itself would not be contained under "being," unless it were in some way contained under "one." Thus Dionysius says (Div. Nom. cap. ult.) that "there is no kind of multitude that is not in a way one. But what are many in their parts, are one in their whole; and what are many in accidents, are one in subject; and what are many in number, are one in species; and what are many in species, are one in genus; and what are many in processions, are one in principle."
Reply to Objection 3. It does not follow that it is nugatory to say "being" is "one"; forasmuch as "one" adds an idea to "being."

Article 2. 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."
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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article 3
Reply to Objection 2. "One" which is the principle of number is not predicated of God, but only of material things. For "one" the principle of number belongs to the "genus" of mathematics, which are material in being, and abstracted from matter only in idea. But "one" which is convertible with being is a metaphysical entity and does not depend on matter in its being. And although in God there is no privation, still, according to the mode of our apprehension, He is known to us by way only of privation and remotion. Thus there is no reason why a certain kind of privation should not be predicated of God; for instance, that He is incorporeal and infinite; and in the same way it is said of God that He is one.
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art. 4
Reply to Objection 1. Although privation considered in itself is not susceptive of more or less, still according as its opposite is subject to more or less, privation also can be considered itself in the light of more and less. Therefore according as a thing is more divided, or is divisible, either less or not at all, in the degree it is called more, or less, or supremely, "one."
Reply to Objection 2. A point and unity which is the principle of number, are not supremely being, inasmuch as they have being only in some subject. Hence neither of them can be supremely "one." For as a subject cannot be supremely "one," because of the difference within it of accident and subject, so neither can an accident.
Reply to Objection 3. Although every being is "one" by its substance, still every such substance is not equally the cause of unity; for the substance of some things is compound and of others simple.
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Article 3. Whether the craving for unity is a cause of sorrow?
Objection 1. It would seem that the craving for unity is not a cause of sorrow. For the Philosopher says (Ethic. x, 3) that "this opinion," which held repletion to be the cause of pleasure, and division [Aristotle wrote endeian, 'want'; St. Thomas, in the Latin version, read 'incisionem'; should he have read 'indigentiam'?], the cause of sorrow, "seems to have originated in pains and pleasures connected with food." But not every pleasure or sorrow is of this kind. Therefore the craving for unity is not the universal cause of sorrow; since repletion pertains to unity, and division is the cause of multitude.
Objection 2. Further, every separation is opposed to unity. If therefore sorrow were caused by a craving for unity, no separation would be pleasant: and this is clearly untrue as regards the separation of whatever is superfluous.
Objection 3. Further, for the same reason we desire the conjunction of good and the removal of evil. But as conjunction regards unity, since it is a kind of union; so separation is contrary to unity. Therefore the craving for unity should not be reckoned, rather than the craving for separation, as causing sorrow.
On the contrary, Augustine says (De Lib. Arb. iii, 23), that "from the pain that dumb animals feel, it is quite evident how their souls desire unity, in ruling and quickening their bodies. For what else is pain but a feeling of impatience of division or corruption?"
I answer that, Forasmuch as the desire or craving for good is reckoned as a cause of sorrow, so must a craving for unity, and love, be accounted as causing sorrow. Because the good of each thing consists in a certain unity, inasmuch as each thing has, united in itself, the elements of which its perfection consists: wherefore the Platonists held that "one" is a principle, just as "good" is. Hence everything naturally desires unity, just as it desires goodness: and therefore, just as love or desire for good is a cause of sorrow, so also is the love or craving for unity.
Reply to Objection 1. Not every kind of union causes perfect goodness, but only that on which the perfect being of a thing depends. Hence neither does the desire of any kind of unity cause pain or sorrow, as some have maintained: whose opinion is refuted by the Philosopher from the fact that repletion is not always pleasant; for instance, when a man has eaten to repletion, he takes no further pleasure in eating; because repletion or union of this kind, is repugnant rather than conducive to perfect being. Consequently sorrow is caused by the craving, not for any kind of unity, but for that unity in which the perfection of nature consists.
Reply to Objection 2. Separation can be pleasant, either because it removes something contrary to a thing's perfection, or because it has some union connected with it, such as union of the sense to its object.
Reply to Objection 3. Separation from things hurtful and corruptive is desired, in so far as they destroy the unity which is due. Wherefore the desire for such like separation is not the first cause of sorrow, whereas the craving for unity is.