LESSON 7

The Kinds of Accidental Unity and of Essential Unity

Chapter 6: 1015b 16-1016b 3

             423. The term one is used both of what is accidentally one and of what is essentially one. A thing is said to be accidentally one, for example, when we say "Coriscus" and "musical" and "musical Coriscus." For to say "Coriscus" and "musical" and "musical Coriscus" amounts to the same thing; and this is also true when we say "just" and "musical" and "just musical Coriscus." For all of these are said to be accidentally one; just and musical because they are accidents of one substance, and musical and Coriscus because the one is an accident of the other. And similarly in a sense musical Coriscus is one with Coriscus, because one of the parts of this expression is an accident of the other. Thus musical is an accident of Coriscus and musical Coriscus is an accident of just Coriscus, because one part of each expression is an accident of one and the same subject. For it makes no difference whether musical is an accident of Coriscus [or whether just Coriscus is an accident of musical Coriscus]. The same thing also holds true if an accident is predicated of a genus or of any universal term, for example, when one says that man and musical man are the same; for this occurs either because musical is an accident of man, which is one substance, or because both are accidents of some singular thing, for example, Coriscus. Yet both do not belong to it in the same way, but one perhaps as the genus and substance, and the other as a habit or modification of the substance. Therefore whatever things are said to be accidentally one are said to be such in this way.

             424. But in the case of things which are said to be essentially one, some are said to be such by nature of their continuity; for example, a bundle becomes one by means of a binding, and pieces of wood become one by means of glue. And a continuous line, even if it is bent, is said to be one, just as each part [of the human body] is, for example, a leg or an arm. And of these things themselves those which are continuous by nature are one to a greater degree than those which are continuous by art. And that is said to be continuous whose motion is essentially one and cannot be otherwise. And motion is one when it is indivisible, i.e., indivisible in time.

             425. Again, all those things are essentially continuous which are one not merely by contact; for if you place pieces of wood so that they touch each other, you will not say that they are one, either one board or one body or any other continuous thing. Hence those things which are continuous throughout are said to be one even though they are bent. And those which are not bent are one to an even greater degree; for example, the lower leg or the thigh is one to a greater degree than the leg, because the motion of the leg may not be one. And a straight line is one to a greater degree than a bent line. But what is bent and angular we refer to as either one or not one, because its motion may be either simultaneous or not. But the motion of a straight line is always simultaneous, and no part of it which has extension is at rest when another moves, as in a bent line.

             426. Again, a thing is said to be one in another sense because its underlying subject is uniform in species; and it is uniform in species as those things whose form is indivisible from the viewpoint of sensory perception. And the underlying subject is either one that is primary or one that is last in relation to the end. For wine is said to be one and water is said to be one inasmuch as they are indivisible in species. And all liquids are said to be one, as oil, wine and fluids, because the ultimate subject of all is the same; for all of these are made up of water or of air.

             427. And those things are said to be one whose genus is one and differs by opposite differences. And all these things are said to be one because the genus, which is the subject of the differences, is one; for example, man, dog and horse are one because all are animals; and it is such in a way closest to that in which matter is one. And sometimes these things are said to be one in this way, and sometimes in their higher genus, which is said to be the same if those which are higher than these are the last species of the genus; for example, the isosceles and the equilateral triangle are one and the same figure because both are triangles; but they are not the same triangles.

             428. Further, any two things are said to be one when the definition expressing the essence of one is indistinguishable from that signifying the essence of the other. For in itself every definition is divisible. And what has increased and what has decreased are one in this way, because their definition is one. An example of this is found in plane figures, which are one in species.

             429. And those things are altogether one and in the highest degree whose concept, which grasps their essence, is indivisible and cannot be separated either in time or in place or in its intelligible structure; and of these, all those which are substances are especially such.

COMMENTARY

             842. Having given the various senses of the terms which signify causes, the Philosopher now proceeds to do the same thing with those terms which signify in some way the subject of this science. This is divided into two parts. In the first (423:C 843) he gives or distinguishes the different senses of the terms which signify the subject of this science; and in the second (445:C 908) he distinguishes the different senses of the terms which signify the parts of this subject ("Things are said to be the same").

             Now the subject of this science can be taken either as that which has to be considered generally in the whole science, and as such it is unity and being, or as that with which this science is chiefly concerned, and this is substance. Therefore, first (423), he gives the different senses of the term one; second (435:C 885) of the term being ("The term being"); and third (440:C 898), of the term substance ("The term substance").

             In regard to the first part of this division he does two things. First, he makes a distinction between what is essentially one and what is accidentally one, and he also indicates the various senses in which things are said to be accidentally one. Second (424:C 848), he notes the various senses in which things are said to be essentially one ("But in the case").

             843. He says (423), then, that the term one signifies both what is essentially one and what is accidentally one. And he tells us that what is accidentally one we should consider first in the case of singular terms. Now singular terms can be accidentally one in two ways: in one way according as an accident is related to a subject; and in another way according as one accident is related to another. And in both cases three things have to be considered--one composite thing and two simple ones. For if what is accidentally one is considered to be such according as an accident is related to a subject, then there are, for example, these three things: first, Coriscus; second, musical; and third, musical Coriscus. And these three are accidentally one; for Coriscus and what is musical are the same in subject. Similarly when an accident is related to an accident, three terms must be considered: first, musical; second, just; and third, just musical Coriscus. And all these are said to be accidentally one, but for different reasons.

             844. For just and musical, which are two simple terms in the second way, are said to be accidentally one because both are accidents of one and the same subject. But musical and Coriscus, which are two simple terms in the first way, are said to be accidentally one because "the one," namely, musical, "is an accident of the other," namely, of Coriscus. And similarly in regard to the relationship of musical Coriscus to Coriscus (which is the relationship of a composite term to one of two simple terms), these are said to be accidentally one in the first way, because in this expression, i.e., in the complex term, musical Coriscus, one of the parts, namely, musical, is an accident of the other, which is designated as a substance, namely, Coriscus. And for the same reason it can be said that musical Coriscus is one with just Coriscus, which are two composites in the second way, because two of the parts of each composite are accidents of one subject, Coriscus. For if musical and musical Coriscus, and just and just Coriscus, are the same, then whatever is an accident of musical is also an accident of musical Coriscus; and whatever is an accident of Coriscus is also an accident of just Coriscus. Hence, if musical is an accident of Coriscus, it follows that musical Coriscus is an accident of just Coriscus. Therefore it makes no difference whether we say that musical Coriscus is an accident of just Coriscus, or that musical is an accident of Coriscus.

             845. But because accidental predicates of this kind are first applied to singular things and then to universals (although the reverse is true of essential predicates), he therefore makes clear that what he showed in the case of singular terms also applies in that of universal terms. He says that, if an accident is used along with the name of a genus or of any universal term, accidental unity is taken in the same way as it is in the above cases when an accident is joined to a singular term; for example, when it is said that man and musical man are accidentally one, although they differ in some respect.

             846. For singular substances are neither present in a subject nor predicated of a subject, so that while they are the subject of other things, they themselves do not have a subject. Now universal substances are predicated of a subject but are not present in a subject, so that while they are not the subjects of accidents, they have something as their subject. Hence, when an accident is joined to a singular substance, the expression stating this can only mean that an accident belongs to a singular substance, as musical belongs to Coriscus when Coriscus is said to be musical.

             847. But when we say musical man, the expression can mean one of two things: either that musical is an accident of man, by which substance is designated, and from this it derives its ability to be the subject of an accident; or it means that both of these, man and musical, belong to some singular thing, for example, Coriscus, in the way that musical was predicated of just, because these two belong to the same singular thing and in the same way, i.e., accidentally. But perhaps the one term does not belong to the other in the same way, but in the way that universal substance belongs to the singular as a genus, as the term animal; or if it is not a genus, it at least belongs to the substance of the subject, i.e., as an essential predicate, as the term man. But the other term, namely, musical, does not have the character of a genus or essential predicate, but that of a habit or modification of the subject, or whatever sort of accident it may be. He gives these two, habit and modification, because there are some accidents which remain in their subject, such as habits, which are moved with difficulty, and others which are not permanent but transient, such as modifications. It is clear, then, that these are the ways in which things are said to be accidentally one.

             848. But in the case (424).

             Then he gives the ways in which things are essentially one, and in regard to this he does two things. First (424), he indicates the different senses in which the term one is used; and second (434:C 880), the different senses in which the term many is used ("Moreover, it is evident").

             In regard to the first he does two things. First, he gives the different senses in which things are one from the viewpoint of nature, i.e., according to the conditions found in reality; and second (433:C 876), from the viewpoint of logic, i.e., according to the considerations of logic ("Further, some things").

             In regard to the first he does two things. First, he distinguishes the different senses in which things are said to be one. Second (432:C 872), he indicates a property which accompanies unity ("But the essence of oneness").

             In regard to the first he does two things. First, he sets down the different senses in which things are said to be one. Second (430:C 866), he reduces all of them to a single sense ("For in general").

             In the first part (424) he gives five senses in which the term one is used.

             849. The first is this: some of the things which are said to be essentially one are such "by nature of their continuity," i.e., by being continuous, or "because they are continuous," as another translation says. But things are said to be continuous in two ways; for, as another text says, some things are continuous by reason of something other than themselves, and some in themselves.

             850. First, he proceeds to deal with those things which are continuous by reason of something other than themselves. He says that there are things which are continuous as a result of something else; for example, a bundle of sticks is continuous by means of a cord or binding; and in this way too pieces of wood which have been glued together are said to be one by means of the glue. Now there are also two ways in which this occurs, because the continuity of things which are fastened together sometimes takes the form of a straight line, and sometimes that of a line which is not straight. This is the case, for example, with a bent line having an angle, which results from the contact of two lines in one surface in such a way that they are not joined in a straight line. And it is in this way that the parts of an animal are said to be one and continuous; for example, the leg, which is bent, and contains an angle at the knee, is said to be one and continuous; and it is the same with the arm.

             851. But since this kind of continuity which comes about by reason of something else can exist or come to be both by nature and by art, those things which are continuous by nature are one to a greater degree than those which are continuous by art; for the unity that accounts for the continuity of things which are continuous by nature is not extrinsic to the nature of the thing which is made continuous by it, as happens in the case of things which are one by art, in which the binding or glue or something of the sort is entirely extrinsic to the nature of the things which are joined together. Hence those things which are joined by nature hold the first place among those which are essentially continuous, which are one in the highest degree.

             852. In order to make this clear he defines the continuous. He says that that is said to be continuous which has only one motion essentially and cannot be otherwise. For the different parts of any continuous thing cannot be moved by different motions, but the whole continuous thing is moved by one motion. He says "essentially" because a continuous thing can be moved in one way essentially and in another or others accidentally. For example, if a man in a ship moves against the motion of the ship essentially, he is still moved accidentally by the motion of the ship.

             853. Now in order for motion to be one it must be indivisible; and by this I mean from the viewpoint of time, in the sense that at the same time that one part of a continuous thing is moved another is also moved. For it is impossible that one part of a continuous thing should be in motion and another at rest, or that one part should be at rest and another in motion, so that the motion of the different parts should take place in different parts of time.

             854. Therefore the Philosopher defines the continuous here by means of motion, and not by means of the oneness of the boundary at which the parts of the continuous things are joined, as is stated in the Categories, and in the Physics; because from this definition he can consider different grades of unity in different continuous things (as will be made clear later on [425:C 856]), but he cannot do this from the definition given there.

             855. Moreover, it should be noted that what is said here about the motion of a continuous thing being indivisible from the viewpoint of time is not opposed to the point proved in Book VI of the Physics, that the time of a motion is divided according to the parts of the thing moved. For here the Philosopher is speaking of motion in an unqualified sense, because one part of a continuous thing does not begin to be moved before another part does; but there he is speaking of some designation which is made in the continuous quantity over which motion passes. For that designation, which is the first part of a continuous quantity, is traversed in a prior time, although in that prior time other parts of the continuous thing that is in motion are also moved.

             856. Again, all those (425).

             Then he proceeds to deal with things which are essentially continuous. He says that those things are essentially continuous which are said to be one not by contact. He proves this as follows: things which touch each other, as two pieces of wood, are not said to be one piece of wood or one body or any other kind of one which belongs to the class of the continuous. Hence it is evident that the oneness of things which are continuous differs from that of things which touch each other. For those things which touch each other do not have any unity of continuity of themselves but by reason of some bond which unites them; but those things which are continuous are said to be essentially one even though they are bent. For two bent lines are continuous in relation to one common boundary, which is the point at which the angle is formed.

             857. Yet those things are one to a greater degree which are essentially continuous and without a bend. The reason is that a straight line can have only one motion in all of its parts, whereas a bent line can have one or two motions. For the whole of a bent line can be understood to be moved in one part; and it can also be understood that when one part is at rest, the other part, which makes an angle with the part at rest, can come closer by its motion to the unmoved part; for example, when the lower leg or shin is bent in the direction of the upper leg, which here is called the thigh. Hence each of these--the shin and thigh--is one to a greater degree "than the scelos," as the Greek text says, i.e., the whole composed of the shin and thigh.

             858. Further, it must be noted that the text which reads "curved" instead of "bent" is false. For, since the parts of a curved line do not contain an angle, it is evident that they must be in motion together or at rest together, just as the parts of a straight line are; but this does not happen in the case of a bent line, as has been stated (425:C 857).

             859. Again, a thing (426).

             Here he gives the second way in which things are one. He says that a thing is said to be one in a second way not merely by reason of continuous quantity but because of the fact that the whole subject is uniform in species. For some things can be continuous even though they differ in species; for example, when gold is continuous with silver or something of this kind. And then two such things will be one if quantity alone is considered but not if the nature of the subject is considered. But if the whole continuous subject is uniform in species, it will be one both from the viewpoint of quantity and from that of nature.

             860. Now a subject is said to be uniform in species when the same sensible form is not divided in such a way that there are different sensible forms in different parts of the subject, as it sometimes happens, for example, that one part of a sensible body is white and another black. And this subject, which does not differ in species, can be taken in two ways: in one way as the first subject, and in another as the last or ultimate subject which is reached at the end of a division. It is evident, for example, that a whole amount of wine is said to be one because its parts are parts of one common subject which is undifferentiated specifically. The same is true of water. For all liquids or moist things are said to be one insofar as they have a single ultimate subject. For oil and wine and the like are ultimately dissolved into water or air, which is the root of moistness in all things.

             861. And those things (427).

             Then he indicates the third way in which things are said to be one. He says that those things are said to be one whose genus is one, even though it is divided by opposite differences. And this way resembles the preceding one; for some things were said to be one in the preceding way because their subject-genus is one, and now some things are said to be one because their genus, which is the subject of differences, is one; for example, a man and a horse and a dog are said to be one because they have animality in common as one genus, which is the subject of differences. Yet this way differs from the preceding, because in the preceding way the subject was one thing which was not differentiated by forms; but here the subject-genus is one thing which is differentiated by various differences, as though by various forms.

             862. Thus it is evident that some things are said to be one in genus in a most proximate sense, and in a way similar to that in which some things are said to be one in matter. For those things which are said to be one in matter are also differentiated by forms. For even though a genus is not matter, because it would then not be predicated of a species since matter is part of a thing, still the notion of a genus is taken from what is material in a thing, just as the notion of a difference is taken from what is formal. For the rational soul is not the difference of man (since it is not predicated of man), but something having a rational soul (for this is what the term rational signifies). Similarly, sensory nature is not the genus of man but a part. But something having a sensory nature, which the term animal signifies, is the genus of man. In a similar fashion, then, the way in which things are one in matter is closely related to that in which they are one in genus.

             863. But it must be borne in mind that to be one in generic character has two meanings. For sometimes some things are said to be one in genus, as has been stated, because they belong to one genus, whatever it may be. But sometimes some things are said to be one in genus only in reference to a higher genus, which, along with the designation "one" or "the same," is predicated of the last species of a lower genus when there are other higher species in one of which the lower species agree. For example, figure is one supreme genus which has many species under it, namely, circle, triangle, square, and the like. And triangle also has different species, namely, the equilateral, which is called isopleural, and the triangle with two equal sides, which is called equi-legged or isosceles. Hence these two triangles are said to be one figure, which is their remote genus, but not one triangle, which is their proximate genus. The reason for this is that these two triangles do not differ by any differences which divide figure, but by differences which divide triangle. And the term same means that from which something does not differ by a difference.

             864. Further, any two (428).

             He now describes the fourth way in which things are said to be one. He says that things such that the definition of one (which is the concept signifying its quiddity) is not distinguished from the definition of the other (which also signifies its quiddity) are also said to be one. For while every definition must be divisible or distinguishable in itself, or essentially, since it is composed of genus and difference, it is possible for the definition of one thing to be indistinguishable from that of another when the two have one definition. And this applies whether those definitions signify the total [intelligible structure] of the thing defined, as tunic and clothing (and then things whose definition is one are one in an absolute sense), or whether that common definition does not totally comprehend the intelligible structure of the two things which have it in common, as an ox and a horse have in common the one definition of animal. Hence they are never one in an absolute sense, but only in a relative sense inasmuch as each is an animal. The same applies in the case of increase and decrease; for there is one common definition of the genus, because each is a motion relating to quantity. And the same thing is true of plane figures, for there is one definition of the species, plane figure.

             865. And those things (429).

             He gives the fifth way in which things are one. He says that those things are "altogether" one, i.e., perfectly, and in the highest degree, whose concept, which grasps their quiddity, is altogether indivisible, like simple things, which are not composed of material and formal principles. Hence the concept which embraces their quiddity does not comprehend them in such a way as to form a definition of them from different principles, but rather grasps them negatively, as happens in the case of a point, which has no parts; or it even comprehends them by relating them to composite things, as happens, for example, when someone defines the unit as the principle of number. And because such things have in themselves an indivisible concept, and things which are divided in any way at all can be understood separately, it therefore follows that such things are indivisible both in time and in place and in their intelligible structure. Hence these things are one in the highest degree, and especially those which are indivisible in the genus of substance. For even though what is indivisible in the genus of accident is not composite in itself, none the less it does form a composite with something else, namely, the subject in which it inheres. But an indivisible substance is neither composite in itself nor does it form a composite with something else. Or the term substance can be taken in the ablative case, and then the sense is that, even though some things are said to be one because they are indivisible in time and in place and in definition, still those things in this class which are indivisible in substance are said to be one in the highest degree. This sense is reduced to the preceding one.