LESSON 1

The Kinds of Unity and the Common Meaning of Unity

  Chapter 1: 1052a 15-1052b 19

             814. It was pointed out before (423), where we distinguished the different meanings of terms, that the term one is used in many senses. But while this is true, there are four principal senses in which things are said to be one primarily and essentially and not accidentally. For that is said to be one which is continuous, either in an unqualified sense, or in the fullest sense by nature and not by contact or by a binding. And of these, that is one to a greater degree and before all else whose motion is more indivisible and simpler (415).

             815. And not only is that which is such said to be one, but so also and to a greater degree that which is a whole and has some form or specifying principle; and a thing is one to the greatest degree if it is such by nature and not by force (as those things which are united by glue or by a nail or by being tied together) and has in itself the cause of its own continuity.

             816. And a thing is such because its motion is one and indivisible as to place and to time; so that if a thing has by nature a first principle of the primary kind of motion--I mean circular motion--it is evident that it is a primary continuous quantity. Some things are one, then, in the sense that they are continuous or whole.

             817. And other things are one if their intelligible structure is one; and such are those whose concept is one, that is, whose concept is indivisible; and it is indivisible if the thing is specifically or numerically indivisible. Now what is numerically indivisible is the singular thing, and what is specifically indivisible is what is knowable and is the object of scientific knowledge. Hence whatever causes the unity of substances must be one in the primary sense.

             818. The term one, then, is used of all these things, namely, of what is continuous by nature, of a whole, of the singular thing, and of the universal. And all these are one because they are indivisible. And some are indivisible in motion, and others in their concept or intelligible structure.

             819. Now it must be borne in mind that the questions as to what sort of things are one, and what the essence of oneness is, and what its intelligible structure is, should not be assumed to be the same; for the term one is used in these various senses, and each of the things to which some one of these senses applies will be one. But the essence of oneness will apply sometimes to one of these senses, and sometimes to something else (819), which is nearer to the meaning of the word; but the others are potentially one. This is like what is found in regard to element and cause by anyone who has to designate them in things and define terms. For in a sense fire is an element (and perhaps this is true of the indeterminate itself or something else of this sort), and in a sense it is not; for the essence of fire and that of an element are not the same, but fire is an element inasmuch as it is a thing and a nature. But the term signifies something which is accidental to it, namely, that something is composed of it as a primary constituent. The same is also true of cause and of one and of all such terms. Hence the essence of oneness consists in being indivisible, i.e., in being an individual thing, and in being inseparable [i.e., not separated from itself] either as to place or to form or to thought, or to being a whole and something determinate.

COMMENTARY

             1920. Above in Book IV of this work the Philosopher showed (301:C 548) that this science has for its subject being and the kind of unity which is interchangeable with being. Therefore, having drawn his conclusions about accidental being (544:C 1172) and about the kind of being which signifies the truth of a proposition, which he does in Book VI (556:C 1223), and about essential being as divided into the ten categories, which he does in Books VII (561:C 1245) and VIII (691:C 1681), and as divided into potency and actuality, which he does in Book IX (742:C 1768), his aim in this tenth book is to settle the issue about unity or oneness and the attributes which naturally accompany it. This is divided into two parts. In the first (814:C 1920) he establishes what is true of unity in itself; and in the second (833:C 1983) he considers unity in relation to plurality ("One and many").

             The first part is divided into two members. In the first he explains the different senses in which the term one is used. In the second (820:C 1937) he establishes a property of unity or oneness ("But the essence").

             The first part is divided into three members. In the first he establishes the different senses in which the term one is used. In the second (818:C 1932) he reduces all these to one common meaning ("The term one"). In the third (819:C 1933) he explains the different ways in which the term one is used of the things of which it is predicated ("Now it must").

             In regard to the first he does three things. First, he gives two senses in which the term one is used. Second (816:C 1927), he exposes the notion of unity contained in these two senses ("And a thing"). Third (817:C 1929), he gives two other senses of the term one ("And other things").

             1921. In treating the first member of this division (814) he gives, first, the primary senses in which the term one is used. He says that he has explained in Book V (403:C 749) the different meanings of the terms which pertain to the study of this science; for it was pointed out there (423:C 842) that the term one is used in many senses. And while this is true, there are four principal senses in which it is employed. But let us speak of those senses in which the term one is used primarily and essentially and not accidentally; for what is accidentally one has different modes of its own.

             1922. Now one of the senses in which things are said to be essentially one is that in which the continuous is said to be one; and this can be taken in two ways: either the continuous in general (i.e., anything continuous in any way at all) is called one; or only the continuous by nature is called one by continuity. And this latter is what is continuous in the fullest sense of the term, and not that which is continuous by force or by art or by any kind of contact (as is evident in the case of pieces of wood), or by any kind of continuity (as is evident in the case of things which are continuous or held together by a nail or by any other bond).

             1923. And the phrase continuous by nature designates two things: what is a uniform whole, as a straight line or even a circular one, and what is not a uniform whole, as two lines which constitute the angle in which they are connected. And of these, lines which are said to be straight and those which are said to be circular are one to a greater degree than those which form an angle, and they are one anteriorly. For a straight line must have one motion, since one part cannot be moved and another at rest, or one be moved in this way and another in that; but the whole must be moved simultaneously and by one motion. The same holds true of a circular line.

             1924. But this does not apply to two continuous quantities which form an angle; for we can imagine either that one line is at rest and the other is moved closer to it so as to form a smaller angle, or that it is moved away from it so as to form a larger angle, or even that both lines are moved in opposite directions. Hence he says that a continuous quantity whose motion is more indivisible and simpler is one to a greater degree.

             1925. And not only (815).

             Then he gives a second sense in which things are said to be essentially one; and here we must consider that what "is such," i.e., continuous, is not only said to be one but also has something more; i.e., it is a whole having some form or specifying principle, just as an animal is one, and a triangular surface is one. Hence this sense of one adds to the oneness of continuity the kind of unity which comes from the form by which a thing is a whole and has a species.

             1926. And since one thing is a whole by nature and another by art, he added that "a thing is one to the greatest degree" if it is such by nature and not by force. For example, all those things which are united by glue or by some such bond so as to become a whole are joined by force. But whatever is joined by nature is one to the greatest degree, because it is clearly the cause of its own continuity; for it is such by its very nature.

             1927. And a thing is such (816).

             Then he clarifies the meaning of unity contained in these two senses of the term one. He says that a thing is such, i.e., continuous and one, because its motion is one and indivisible both as to place and to time; as to place, because whithersoever one part of a continuous thing is moved another part is also moved; and as to time, because when one part is moved another is also moved.

             1928. Hence, if a thing that is continuous and whole by nature is said to be one because its motion is one, then it is evident that, if anything continuous and whole has within itself a principle of the primary kind of motion, this will be the primary kind of one in the realm of continuous quantity; for example, of all motions the primary kind is local motion, and of local motions the primary kind is circular motion, as is proved in Book VIII of the Physics. And of bodies which are moved by circular motion there is one which contains the principle of such motion, i.e., the body which is moved circularly and causes the circular motion of other bodies by a daily motion. It is evident, then, that this is the one primary continuous quantity which contains the first principle of the primary kind of motion. Hence two senses of the term one are evident, namely, that in which the continuous is called one, and that in which a whole is called one.

             1929. And other things (817).

             Then he gives the other ways in which things are said to be one. He says that certain other things are said to be one, not because their motion is one, but because their intelligible structure is one. And things of this kind whose concept is one are those which are apprehended by a single intellectual act. And such things as are said to be apprehended by a single intellectual act are those of which there is a single apprehension of an undivided object.

             1930. This can be so for two reasons: either because the undivided object apprehended is specifically one, or because it is numerically one. Now what is numerically undivided is the singular thing itself, which cannot be predicated of many things; and what is specifically one is undivided because it is a single object of knowledge and acquaintance. For in distinct singular things there is no nature numerically one which can be called a species, but the intellect apprehends as one that attribute in which all singulars agree. Hence the species, which is distinct in distinct individuals in reality, becomes undivided when apprehended by the intellect.

             1931. And since substance is prior in intelligibility to all the other genera, and the term one is used in these senses because it has one meaning, then it follows that the primary sort of one in these senses is what is one in substance, i.e., what causes substance to be one, just as in the first two senses the primary sort of one was the continuous quantity which is moved circularly.

             1932. The term one (818).

             Here he reduces the senses of one given above to a single meaning by summarizing what he had said above. He says that the term one is used of four things: first, of what is continuous by nature; second, of a whole; third, of a singular thing; and fourth, of the universal, for example, a species. And all of these are said to be one because of one common aspect, namely, being indivisible; for properly speaking, a one is an undivided being. But the term one is used in the first two senses because a motion is undivided, and in the latter two senses because an intelligible structure or concept is undivided, inasmuch as the apprehension of a particular thing is also included under this.

             1933. Now it must (819).

             Here he shows how the term one is predicated of things which are said to be one. He says that it must be borne in mind that the term one should not be taken to mean the same thing when a thing is said to be one and when someone expresses the essence of oneness, which is its intelligible structure; just as wood too is not said to be white in the sense that whiteness is the essence of wood, but in the sense that it is an accident of it.

             1934. Then he gives the following explanation of a statement which he had made, saying that, since the term one is used in many senses (as has been stated), a thing is said to be one because some one of these senses applies to it, i.e., continuous, whole, species, or singular thing. But the essence of oneness sometimes applies to something that is one in some one of the foregoing senses, as when I say that what is one in continuity is one (and the same holds true of the others); and sometimes it is attributed to something which is nearer to the nature of one, for example, what is undivided but contains within itself potentially the senses of one given above; because what is undivided as regards motion is continuous and whole, and what is undivided in meaning is singular or universal.

             1935. He adds to this the example of elements and causes, viewed in the problem of identifying them in things, as when we say that such and such a thing is an element or cause by defining the term; for example, we say that that is a cause which has the essence of a cause. And in this way we say that fire is an element or "the indeterminate itself," i.e., what is unlimited in itself (which the Pythagoreans posited as a separate entity and the element of all things), or anything else of this sort for whatever reason it can be called an element. But in a sense fire is not an element, and neither is the indeterminate; for fire does not constitute the essence of an element, because the notion of fire is not the same as that of an element. It is an element, however, as existing in reality or in the natural world. But when the term element is predicated of fire, it signifies that something "has become accidental to fire," i.e., that fire is that of which something is composed as a primary constituent, and this is the formal note of an element. He says "constituent" in order to exclude privations.

             1936. What has been said about an element also applies to cause and to one and to all such terms; because the things of which they are predicated are not the very things which the terms signify; for example, white man is not the very thing which the term white signifies, for white signifies a quality. Hence the essence of oneness consists in being undivided, i.e., in being an individual thing; and this is proper to a thing which is inseparable as to place or to form or in whatever other way it is inseparable.