METAPHYSICS
BOOK X

LESSON 1

The Kinds of Unity and the Common Meaning of Unity

ARISTOTLE'S TEXT 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 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 place or to form or to thought, or to being a whole and something determinate.

COMMENTARY

Kinds of one

1920. Above in Book IV of this work the Philosopher showed (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 (1172) and about the kind of being which signifies the truth of a proposition, which he does in Book VI (1223), and about essential being as divided into the ten categories, which he does in Books VII (1245) and VIII (1681), and as divided into potency and actuality, which he does in Book IX (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 (1920) he establishes what is true of unity in itself; and in the second (1983) he considers unity in relation to plurality.

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 (1937) he establishes a property of unity or oneness.

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 (1932) he reduces all these to one common meaning. In the third (1933) he explains the different ways in which the term one is used of the things of which it is predicated.

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

1921. In treating the first member of this division he gives, first, the primary senses in which the term one is used. He says that he has explained in Book V (749) the different meanings of the terms which pertain to the study of this science; for it was pointed out there (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. (1) 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 (a) the continuous in general (i.e., anything continuous in any way at all) is called one; or only the continuous (b) 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).

(2) 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 be 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 (3) because the undivided, object apprehended is specifically one, or (4) 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, (1) of what is continuous by nature; (2) second, of a whole; (3) third, of a singular thing; and (4) 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. 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.

LESSON 2

Unity as a Measure

ARISTOTLE'S TEXT Chapter: 1: 1052b 19-1053b 8

820. But the essence of oneness or unity consists especially in being the first measure of each genus, and most properly of quantity; because it is from this genus that it is transferred to the others. For a measure is that by which quantity is first known; and quantity as quantity is known either by unity or by a number, and every number is known by unity. Hence all quantity as quantity is known by unity.

821. And that by which quantity is first known is unity itself; and for this reason unity is the principle of number as number.

822. And the measure of other things is also that by which each is first known. And the measure of each is a unit: in length, in breadth, in depth, and in heaviness and in rapidity. For the terms heavy and rapid are common to both contraries, since each of them has two meanings. Thus heavy is said both of what has any amount of inclination towards the center and of what has an excessive inclination; and rapid is said both of what has any amount of motion, and of what has an excessive motion. For even what is slow has a certain speed, and what is light a certain heaviness.

823. And in all these cases the measure and principle is something one and indivisible, since even in the case of lines we use the foot measure as something indivisible. For everywhere men seek as a measure something one and indivisible, and this is what is simple Either in quality or in quantity. Hence wherever it seems impossible to. add or to subtract anything, there the most certain measure is found. The measure of number, then, is the most certain; for men claim that the unit is indivisible in every respect. And in other cases they imitate such a measure; for any addition or subtraction might more easily escape our notice in the case of a furlong or of a talent or of anything which is always a larger measure than in that of something which is a smaller measure. Hence it is the first thing from which no perceptible subtraction can be made that all men make a measure, whether of liquids or of solids or of weight or of size; and they think they know the quantity of a thing when they know it by this measure.

824. And they also measure motion by that motion which is simple and most rapid; for this takes the least time. Hence in astronomy this kind of unit is the principle and measure; for astronomers suppose the motion of the heavens to be uniform and most rapid, and they judge the other motions by this motion. And in music the diesis is the measure, because it is the smallest interval; and in speech, the letter. And all of these are one, not in the sense that there is something common to all which is one, but in the sense that we have explained.

825. However, a measure is not always numerically one, but sometimes many; for example, there are two dieses not discernible by car but differing in their ratios. And the words by which we measure speech are many; and the diagonal of a square is measured by two quantities, and so also is a side; and so are all continuous quantities. Therefore all things have as their measure some unit, because we come to know the things of which substance is composed by dividing it either in regard to quantity or to species. Hence the unit is indivisible, because what is first in each class of things is indivisible. But not every unit is indivisible in the same way, for example, the foot and the unit; but the latter is indivisible in every respect, whereas the former belongs to that class of things which are indivisible from the viewpoint of the senses, as has already been stated (823); for perhaps every continuous thing is divisible.

826. And a measure is always of the same kind as the thing measured; for the measure of continuous quantities is a continuous quantity; and in particular the measure of length is a length; and of breath a breadth; and of width a width; and of vocal sounds a vocal sound; and of weight a weight; and of units a unit. For this is the view which must be taken, but not that the measure of numbers is a number. We should indeed have to speak in this way if we were to use parallel forms, but the meaning does not require such parallels: it would be as if the measure of units had to be designated as units and not as a unit. But number is a plurality of units.

827. And for the same reason we say that knowledge and perception are the measure of things, because we know something by them; yet they are measured rather than measure. But in our own case it is as though someone else were measuring us, and we learned how big we are by means of the cubit measure being applied to so much of us. But Protagoras says that man is the measure of all things, as if he were saying the man who knows or the man who perceives; and these because the one has intellectual knowledge and the other sensory perception, which we say are the measures of the things that are placed before them. Hence, while these men say nothing extraordinary, they seem to be saying something important.

828. It is evident, then, that unity in the strictest sense, according to the definition of the term, is a measure, and particularly of quantity and then of quality. And some things will be such if they are indivisible in quantity, and others if they are indivisible in quality. Therefore what is one is indivisible either in an unqualified sense or inasmuch as it is one.

COMMENTARY

One as a measure

1937. Having explained the various senses in which unity is predicated of things, and having stated what its essential note is, to which all its usages are reduced, i.e., being indivisible, here the Philosopher infers a property of unity from its essential note, namely, that it is a measure. This is divided into two parts. In the first he shows how the notion of a measure belongs to unity and to the various classes of accidents. In the second (1961) he shows how unity in the sense of a measure is found in substances (“It is necessary”).

In regard to the first part of this division he does two things. First, he indicates the class of things in which unity in the sense of a measure is primarily found, and how it is transferred from this class to the others with the proper notion of a measure. Second (1956), he explains how it is transferred figuratively to the other classes (“And for the same reason”).

In treating the first part he does two things. First, he indicates the class of things in which unity in the sense of a measure is first found, and how it is transferred from this class to the others. Second (1950), he makes a study of measures (“However, a measure”).

In regard to the first he does three things. First, he shows how unity as a measure is found in quantity, and how it is transferred from this category to the others. Second (1939), he indicates the species of quantity in which it is first found (“And that by which”). Third (1940), he shows how it is transferred to other species of quantity (“And the measure”).

1938. He accordingly says, first, that, since the essential note of unity consists in being indivisible, and what is indivisible in each genus is somehow the measure of that genus, unity must be said to be in the highest degree the first measure of each genus. This is said to apply most properly to quantity, and it is from this class that the notion of a measure is transferred to other classes of things. Now a measure is nothing else than that by which a thing’s quantity is known, and this is known by the unit or by a number: by a unit, as when we say one furlong or one foot; and by a number, as when we say three furlongs or three feet. Again, every number is known by the unit because the unit taken a certain number of times gives a number. It follows, then, that every quantity is known by unity. To “quantity” he adds “as quantity,” intending that this be referred to the measure of quantity; for the properties and other accidents of quantity are known in a different way.

1939. And that by which (821).

Then he indicates in what species of quantity unity or measure is primarily found. First, he makes it clear that the notion of a measure is primarily found in discrete quantity, which is number. He says that that by which quantity is first known is “unity itself,” i.e., the unit which is the principle of number. For in other species of quantity the unit is not unity itself but something of which unity is an attribute, as when we speak of one hand or of one continuous quantity. Hence it follows that unity itself, which is the first measure, is the principle of number as number.

1940. And the measure (822).

Second, he shows how unity is transferred to other species of quantity; and in regard to this he does two things. First, he indicates the species of quantity to which it is transferred. He says that it is from this class, i.e., from number and from the unit, which is the principle of number, that the notion of a measure is transferred to other quantities as that by which each of them is first known. And whatever is the measure in each class of things is the unit in that class.

1941. He gives examples of this in three classes of things, i.e., in dimensions—length, breadth and width; in weight, or in what he calls heaviness; and in speed, or in what he calls rapidity, which refers to the measure of time.

In the case of dimensions no one doubted that they were quantities and that they were properly susceptible to measurement, but in the case of weight and of speed there could be a difficulty because these seem to be qualities rather than quantities.

1942. He therefore explains how these pertain to the genus of quantity, and how they are susceptible to measurement. He says that heaviness and rapidity have something in common with their contraries because one contrary is found in the other; for what is heavy is in some sense light, and the reverse; and what is rapid is in some sense slow. For each of these terms is used in two senses. (1) In one sense the term heavy is used without qualification of anything that has an inclination to be borne towards the center of the earth, without taking into consideration how great its inclination is; and in this sense heavy does not refer to the category of quantity, and it is not susceptible to measurement. (2) In the other sense it is used of one thing in comparison with something else, namely, of what exceeds something else in terms of the abovementioned inclination; for example, we say that earth is heavy in comparison with water, and that lead is heavy in comparison with wood. Therefore it is by reason of this excess that some notion of quantity and measure is found.

The term rapid is similarly used in two senses. In one sense it is used without qualification of anything that has any motion; and in a second sense it is used of anything that has an excessive motion. And in one respect the notions of quantity and measure properly apply to it, and in another respect they do not.

1943. With a view to clarifying his statement about the condition of heaviness and rapidity in reference to contraries he adds that rapidity is found in something that is slow inasmuch as what is simply and unqualifiedly slow is more rapid in comparison with something that is slower than itself. And in a similar way heaviness is found in light things; for example, air is light in comparison with earth, and heavy in comparison with fire.

1944. And in all cases (823).

Then he shows how the notion of a measure is transferred from number to other kinds of quantity. He immediately makes this clear, first, in the case of dimensions and in that of weights; and second (1947), in that of the rapidity of motions (“And they also measure”).

He accordingly says, first, that the notion of a measure is transferred from number to the other kinds of quantity in this way that, just as the unit which is the measure of number is indivisible, so too all the other kinds of quantity have something that is one and indivisible as their measure and principle. For example, in measuring lines men use “the foot measure,” i.e., the measure of one foot, as something indivisible; for wherever something indivisible is sought as. a measure, there is something simple either in quality or in quantity; in quality, as whiteness in the case of colors, which is in a sense the measure of colors, as will be mentioned below (1968); and in quantity, as the unit in the case of numbers, and the foot measure in the case of lines.

1945. Further, he points out why a measure must be something indivisible. The reason is that an exact measure must be something which can be neither added to nor subtracted from. Thus the unit is the most exact or certain measure, because the unit which is the principle of number is altogether indivisible, and whatever unity is not susceptible either to addition or to subtraction remains one. The measures of the other classes of quantity resemble this unit which is indivisible inasmuch as men take some smallest thing as a measure to the extent that this is possible. For if anything large were taken, as the furlong among distances and the talent among weights, it would escape our notice if some small portion were subtracted from or added to it. And this would always be more true of a larger measure than of a smaller one.

1946. Hence all men take this as a measure both in the case of liquids, such as oil and wine, and in that of solids, such as grain and barley; and also in that of weights and dimensions, which are designated as heaviness and continuous quantity. And this is first found to be such that nothing perceptible can be subtracted from it or added to it that might escape our notice. And men think they know the quantity of a thing exactly when they know it by the smallest measure of this kind.

1947. And they also (824).

Then he makes the same thing clear with regard to the rapidity of motions. He says that men also measure motion “by that motion which is simple,” i.e., the motion which is uniform and quickest, because it takes the least time. Hence in astronomy they take such motion as the basis of measurement; for they take the motion of “the first heaven,” i.e., the daily motion, which is regular and quickest, and they judge and measure all other motions by this.

1948. And because the low and high pitch of sounds results from the quickness and slowness of motions, as is established in the science of music, he adds as an example the measurement of sounds. He says that in music the first measure is the “diesis,” i.e., the difference between two half tones; for a tone is divided into two unequal half tones, as is proved in the science of music. And similarly in speech the measure is the letter, because the shortness or length of a word is a natural consequence of the quickness or slowness of a motion.

1949. Now all these something one, not in measures are the sense that some measure is common to all, but in the sense that any measure in itself is something one, as has been pointed out.

1950. However, a measure (825).

After having shown in what class of things unity as a measure is primarily found, here the Philosopher clears up certain points that have to be investigated about measures.

The first of these is that, although a measure is understood to be one thing inasmuch as it comes close to being indivisible, it is not necessary that a measure be something numerically one; but sometimes many things are measures; for example, in the case of musical sounds “there are two dieses,” i.e., two half tones. However, because of their smallness they are not distinguished by the sense of hearing, for the senses do not perceive the difference between two things that are very small; but their difference is perceived “in their ratios,” i.e., in the different ratios which comprise their proportions, because they are caused by different numerical proportions.

1951. Similarly the things by which we measure words are also many; for the quantity of one meter or of one foot is measured by different syllables, some of which are short and some long.

The same thing is true of the diameter of a circle and of the diagonal of a square, and also of the side of a square.

And any continuous quantity is measured by two things, for an unknown quantity is found only by means of two known quantities.

1952. Having said this he brings this part of his discussion to a close by summarizing what has been said above, namely, that unity constitutes the measure of all things. The reason for this is that unity is the term of division. And those principles which constitute the substance of each thing are known by the division or dissolution of the whole into its component parts, whether they are quantitative parts or specific parts such as matter and form and the elements of compounds. Therefore what is one in itself must be indivisible since it is the measure by which a thing is known, because in the case of singular things whatever is first in the process of composition and last in the process of dissolution is indivisible, and it is by means of this that the thing is known, as has been explained.

1953. Yet indivisibility is not found in all things in the same way. (1) Some things are altogether indivisible, such as the unit which is the basis of number, whereas (2) others are not altogether indivisible but only to the senses, according as the authority of those who instituted such a measure wished to consider something as a measure; for example, the foot measure, which is indivisible in proportion [to the things measured] but not by nature. “For perhaps everything continuous is divisible”; and he says “perhaps” because of the difficulty facing those men who claimed that continuous quantity is composed of indivisible elements, or that natural continuous quantities are not infinitely divisible, but only mathematical quantities. For it is possible to find the smallest amount of flesh, as is mentioned in Book I of the Physics.

1954. And a measure (826).

Then he gives the second point that has to be investigated about a measure. He says that “the meter,” i.e., the measure, should always be of the same kind as the thing measured, i.e., of the same nature or measure as the thing measured; for example, a continuous quantity should be the measure of continuous quantities; and it is not enough that they have a common nature, as all continuous quantities do, but there must be some agreement between the measure and the thing measured in the line of their special nature. Thus a length is the measure of lengths, a width of widths, a vocal sound of vocal sounds, a weight of weights, and a unit of units.

1955. “For this is the view which must be taken” in order that we may speak without being criticized, “but not that number is the measure of numbers.” Now number does not have the notion of a first measure but unity does; and if unity is a measure, then in order to signify the agreement between the measure and the thing measured it will be necessary to say that unity is the measure of units and not of numbers. Yet if the truth of the matter be taken into consideration, it will be necessary to admit also that number is the measure of numbers or even that the unit may be taken in a similar way as the measure of numbers. But it does not seem equally fitting to say that the unit is the measure of units and number of number or unity of number, because of the difference which appears to exist between the unit and number. But to observe this difference is the same as if someone were to say that it is fitting for units to be the measure of units but not the unit, because the unit differs from units as things expressed in the singular differ from those expressed in the plural. And the same argument applies to number in relation to the unit, because a number is nothing else than a plurality of units. Hence to say that the unit is the measure of number is merely to say that the unit is the measure of units.

1956. And for the same reason (827).

Then he shows how the term measure is transferred in a figurative way to another class of things. He says that, since it has been stated that a measure is that by which the quantity of a thing is known, we may say that intellectual knowledge is the measure of that which is knowable intellectually, and that sensory perception is the measure of that which is perceptible; because we know something by means of them, namely, sensible objects by means of perception and intelligible objects by means of intellectual knowledge; but we do not know them in the same was as we do by a measure. For something is known by a measure as a principle of knowledge, whereas in sensation and knowledge we are measured by things that are outside ourselves.

1957. Therefore they are called measures figuratively, because in reality they are measured rather than measure. For it is not because we perceive or know a thing that it is so in reality; but it is because it is so in reality that we have a true knowledge or perception of it, as is said in Book IX (807:C 1896). Thus it follows that in perceiving and knowing something we measure our knowledge by means of the things which exist outside the mind.

1958. However, in knowing and measuring ourselves by some other measure we know how much bodily quantity we have by applying the cubit measure to ourselves. Hence, just as the external cubit is offered as a measure of our bodily quantity, in a similar way the things known or sensuously apprehended are the measures whereby we can know whether we truly apprehend something by our senses or by our intellect.

1959. And if there is a science which is the cause of the. thing known, it must be this science which measures that thing, just as the science of the master planner is the measure of things made by art, because anything made by art is complete insofar as it attains a likeness to the art. It is in this way that the science of God is related to all things. But Protagoras said that man is the measure of all things inasmuch as he knows or perceives them, because knowledge and perception are the measure of substances, i.e., of things which are intelligible and perceptible. For the followers of Protagoras, as has been stated in Book IV (344:C 637), said that things are such because we so perceive them or judge about them. Therefore, although they say nothing extraordinary or important, they nevertheless seem to be saying something of consequence, because they covertly insinuate their doctrine.

1960. It is evident (828).

Then he sums up the points discussed, namely, that the notion of unity involves being a measure; and this applies most properly to quantity, and then to quality and to the other genera, because anything that is a measure should be indivisible either in quantity or in quality. Thus it follows that unity is indivisible, “either in an unqualified sense” as the unit which is the basis of number, or “in a qualified sense,” i.e., to the extent that it is one, as was stated with regard to the other measures.

LESSON 3

The Nature of Unity

ARISTOTLE’S TEXT Chapter 2:1053b 9-1054a 19

829. It is necessary to inquire how unity is related to the substance and nature of things. In a sense this is a problem which we have examined (266) in the questions regarding the nature of unity, and how it must be taken: whether it must be taken to be a substance, as the Pythagoreans first claimed, and later Plato, or rather whether there is some nature that underlies it, and it is necessary to describe it more meaningfully and more in the terms of those who speak of nature; for one of them said that unity is friendship, another air, and another the indeterminate.

830. If, then, it is impossible for a universal to be a substance, as has been stated in our treatment of substance and being (651), and being itself cannot be a substance in the sense of one thing existing apart from the many (for it is common to all of them), but it is only a predicate, it is evident that unity cannot be a substance; for being and unity are the most universal of all predicates. Hence genera are not certain natures and substances which are separable from other things; and unity cannot be a genus, for the same reasons that being and substance cannot be such (229).

831. Further, the same thing must be true of unity in all categories of things. Now unity and being are used in an equal number of ways. Hence, since in the category of qualities there is something which is one and a certain nature, and since the same thing is true of quantities, it is evident that we must investigate in a general way what unity is, just as we must investigate what being is, inasmuch as it is not sufficient to say that its nature is just itself. But in the sphere of colors unity is a color, for example, white; and then the other colors seem to be produced from this and from black; and black is the privation of white as darkness is of light; for it is the absence of light. If, then, all beings were colors, they would be a number. But of what? Evidently, of colors. And unity itself would be some one color, for example, white. Similarly if beings were tunes, they would be a number of minor half tones; but their substance would not be a number; and unity would be something whose substance is not unity but a minor half tone. Similarly if beings were sounds, they would be a number of elements, and unity would be a vowel. And if beings were rectilinear figures, there would be a number of figures, and unity would be a triangle. The same reasoning applies to the other genera. Therefore if in all affections, qualities, quantities and motions there are numbers and unity, and if the number is a number of particular things, and the unity is a particular unity, but unity is not its substance, then the same thing must be true of substances, because the same is true of all things. It is evident, then, that in every genus unity is a determinate nature, and that in no case is the nature of its unity merely unity. But just as in the case of colors the unity for which we must look is one color, in a similar fashion in the case of substances the unity must be one substance.

832. That unity and being somehow signify the same thing is evident from the fact that they have meanings corresponding to each of the categories and are contained in none of them: neither in quiddity nor in quality, but unity is related to each in the same way that being is; and from the fact that “one man” does not express something different from “man,” just as being does not exist apart from quiddity or from quality or from quantity; and because to be one is just the same as to be a particular thing.

COMMENTARY

1961. After having shown how unity in the sense of a measure is found first in quantity and then is transferred to the other categories, here the Philosopher deals with the relationship of unity to substance, i.e., whether unity constitutes the very substance of a thing. This is divided into three parts. In the first (829:C ig6i) he raises the question and gives the different opinions regarding it. In the second (830:C 1963) he answers the question by showing that unity and being are not the substance of the things of which they are predicated (“If, then”). In the third (832:C 1974) he compares unity with being (“That unity and being”).

He accordingly says, first (829), that, since it has already been shown how unity in the sense of a measure belongs to quantity and to the other classes of things, it is now necessary to ask how unity relates to the substances and natures of things. This question was asked above in Book III (266:C 488), in which different problems were raised.

1962. The question is whether the very thing which is called unity is a substance, i.e., something which subsists of itself, as the Pythagoreans first claimed, and as the Platonists, who followed them, later held; or rather whether there is some subsistent nature which underlies unity, in terms of which the quiddity of the thing designated as one should be more meaningfully and adequately expressed. The philosophers of nature presupposed this entity, one of them saying that unity is love, namely, Empedocles, who claimed that there are four material principles, the four elements, to which the active principles posited by him, love and hate, are said to be prior. And of these the most important is love, inasmuch as it is perfect and the principle of good things. Therefore, if the first principle is called unity, it follows according to him that unity is love. And this fits the case inasmuch as it indicates a certain union of the lover and the thing loved. Another philosopher, Diogenes, who claimed that air is the principle of all things (41:C 86), said that unity is air. And still another philosopher said that unity is the indeterminate, namely, Melissus, who claimed that there was one infinite and unchangeable being, as is clear in Book I of the Physics.

1963. If, then (830).

Here he answers the question which was raised. He says that unity is not a subsisting substance, of which one may predicate the term one. He proves this in two ways. First (830:C 1963), by an argument; and second (831:C 1967), by a comparison (“Further, the same”).

He says, then, that it was proved above in Book VII (651:C 1572), where he treats of being, and especially of substance, that no universal can be a substance which subsists of itself because every universal is common to many. A universal also cannot be a subsisting substance because otherwise it would have to be one thing apart from the many, and then it could not be common but would be in itself a singular thing.

1964. Unity might, it is true, be said to be common as a cause is. But the common aspect of a universal differs from that of a cause; for a cause is not predicated of its effects, since the same thing is not the cause of itself. But a universal is common in the sense of something predicated of many things; and thus it must be in some way a one-in-many, and not something subsisting apart from them.

1965. But being and unity must be predicated of all things in the most universal and common way. Hence those things which are called being and unity are not themselves subsisting substances, as Plato maintained.

1966. From this argument he concludes that no genera are natures and substances which subsist of themselves as though separable from the things of which they are predicated. This too was one of the questions debated above (229:C 432). Yet this is not said in the sense that unity is a genus; for unity cannot be a genus for the very same reason that being cannot, since it is not predicated univocally. This is also true in the light of the other reasons given in Book III (269-74:C 493-501). And for the same reason unity and being cannot be subsisting substances.

1967. Further, the same thing (831).

Here he proves the same point by a comparison. He says that unity must be found in the same way in all categories of things, because being and unity are predicated in an equal number of ways of all genera. But in each genus of things we look for something that is one (implying that unity is not the very nature of what is said to be one), as is evident in the case of qualities and in that of quantities. It is clear, then, that in no genus is it sufficient to say that the nature of what is said to be one is just unity itself, but we must inquire what unity and being are.

1968. That it is necessary to investigate what unity is in the category of qualities and in that of quantities he makes clear by examples. He does this first in the case of colors; for we look for something which is one, such as whiteness, which is the primary color. Hence, if what is primary in each class of things is its unity, whiteness must constitute the unity in the class of color; and it must be in a sense the measure of the other colors, because the more perfect a thing’s color the closer it comes to whiteness. He shows that whiteness is the primary color by reason of the fact that intermediate colors are produced from white and from black, and are therefore subsequent. Black is subsequent to white because it is the privation of white as darkness is of light. But this must not be understood to mean that black is pure privation in the same way that darkness is (for black is a species of color, and thus possesses the nature of color), but that blackness contains the least amount of light, which causes colors; and thus it is compared to white as the absence of light is compared to light.

1969. And because in colors we look for something that is first and one, namely white, it is clear that if all beings were colors, they would have some number, not in the sense, however, that number would constitute subsisting things themselves, but in the sense that there would be a number of subsisting things of a particular sort, i.e., colors. And then there would be something that is the subject of unity, namely, that which is white.

1970. The same thing would be true if all things were tunes; because beings would be of a certain number, that is, a number of minor half tones or tones. Yet number is not the very substance of beings, and consequently it would be necessary to look for something which is one, namely, the minor half tone; but not in such a way that unity itself would be a substance.

1971, In a similar way too if all beings were sounds, they would be a number of beings, because there are a number of particular subjects of number, namely, “of elements,” or letters. Hence the vowel, which is the primary letter (since consonants cannot be pronounced without vowels) would constitute their unity.

And in a similar way if all figures were rectilinear figures, there would be a number of subjects, namely, figures; and the triangle, which is the primary rectilinear figure, would constitute their unity; for all such figures are reducible to the triangle. The same reasoning applies to every category.

1972. If it is in this way, then, that number and unity are found in all other categories: in affections, qualities, and quantities, and in motion; and if number and unity are not the substance of the things of which they are predicated, but number is predicated of certain substances, and if unity similarly requires some subject which is said to be one, the same thing must be true of substances, because being and unity are predicated in the same way of all things. It is evident, then, that in any category of things there is some nature of which the term one is predicated, not because unity itself is the nature of a thing, but because it is predicated of it.

1973. And just as when we speak of unity in the case of colors we are looking for some color which is said to be one, so too when we speak of unity in the case of substances we are looking for some substance of which unity may be predicated. And this is predicated primarily and chiefly of what is first among substances (which he investigates below, 2553-66), and subsequently of the other classes of things.

1974. That unity and being (832).

Since he had given the same argument for being and for unity, he now shows that unity and being somehow signify the same thing. He says “somehow” because unity and being are the same in their subject and differ only in meaning. For unity adds to being the note of undividedness, because what is one is said to be an indivisible or undivided being. He gives three reasons why unity signifies the same thing as being.

1975. (1) The first is that unity naturally belongs to all of the different categories and not just to one of them; that is, it does not pertain just to substance or to quantity or to any other category. The same thing is also true of being.

1976. (2) The second reason is that, when a man is said to be one, the term one does not express a different nature from man, just as being does not express a different nature from the ten categories; for, if it did express a different nature, an infinite regress would necessarily result, since that nature too would be said to be one and a being. And if being were to express a nature different from these things, an infinite regress would also follow; but if not, then the conclusion of this argument must be the same as that of the first one.

1977. (3) The third reason is that everything is said to be one inasmuch as it is a being. Hence when a thing is dissolved it is reduced to non-being.

1978. [Objection] Now in this solution of the question the Philosopher seems to contradict himself; for he first said that unity and being are not the substance of the things of which they are predicated, but here he says that unity and being do not express a nature different from the things of which they are predicated.

1979. Hence it must be noted that the term substance is used in two senses. (1) In one sense it means a supposit in the genus of substance, which is called first substance and hypostasis, to which it properly belongs to subsist. (2) In a second sense it means a thing’s quiddity, which is also referred to as a thing’s nature. Therefore, since universals are subsistent things according to the opinion of Plato, they signify substance not only in the second sense but also in the first. But Aristotle proves in Book VII (1572) that universals are not subsistent things, and therefore it follows that universals are not substances in the first sense but only in the second. And for this reason it is said in the Categories that second substances, which are genera and species, do not signify particular things, which are subsisting substances, but “they signify the quiddity of a thing,” i.e., a nature in the genus of substance.

1980. The Philosopher accordingly proved above that unity and being do not signify substance in the sense of this particular thing, but it is necessary to look for something that is one and a being, just as we look for something that is a man or an animal, as Socrates or Plato.

Later he shows that these terms signify the natures of the things of which they are predicated and not something added, like accidents. For common attributes differ from accidents in this respect (although they agree in not being particular things), that common attributes signify the very nature of supposits, whereas accidents do not, but they signify some added nature.

1981. And Avicenna, who did not take this into account, claimed that unity and being are accidental predicates, and that they signify a nature added to the things of which they are predicated. For he was deceived by the equivocal use of the term one, because the unity which is the principle of number and has the role of a measure in the genus of quantity signifies a nature added to the things of which it is predicated, since it belongs to a class of accident. But the unity which is interchangeable with being extends to everything that is, and therefore it does not signify a nature which is limited to one category.

1982. He was also deceived by the equivocal use of the term being; for being as signifying the composition of a proposition is predicated accidentally, since composition is made by the intellect with regard to a definite time. Now to exist at this or at that particular time is to be an accidental predicate. But being as divided by the ten categories signifies the very nature of the ten categories insofar as they are actual or potential.

LESSON 4

Ways in Which One and Many Are Opposed

ARISTOTLE’S TEXT Chapter 3: 1054a 20-1055a 2

833. One and many are opposed in many ways, and one of these is the opposition between one and many as between something indivisible and something divisible; for many means either what is divided or what is divisible, and one means either what is undivided or what is indivisible.

834. Hence, since we speak of four modes of opposition, and one of these two opposites is expressed privatively, they will be contraries and not contradictories or relative terms (313).

835. And what is one is described and made known in reference to its contrary, and what is indivisible in reference to what is divisible; for what is many and is divisible is better known to the senses than what is indivisible. Hence what is many is prior in intelligibility to what is indivisible, because of sensory perception.

836. And as we have already indicated in our division of contraries, same, like and equal relate to what is one; but diverse, unlike and unequal relate to what is many.

837. Now things are said to be the same in several ways; for in one way we say that a thing is numerically the same; and in another way we say that it is the same if it is one both in its intelligible structure and numerically; for example, you are the same as yourself in both form and matter. Again, things are the same if the intelligible structure of their primary substance is one, as equal straight lines are the same, and equal quadrangles which are equiangular, and also many other things; but in these cases equality is unity.

838. Things are like if, while being the same in an unqualified sense or without a difference as regards their substance, they are the same in species; for example, a larger square is like a smaller one. And this likewise holds true of unequal straight lines, for these are like but not the same in an unqualified sense. And some things are said to be like if, while having the same form and admitting of difference in degree, they do not differ in degree. And other things are like if the same affection belongs to both and is one that is the same in species; for example, both what is whiter and what is less white are said to be like because they have one species. And other things are said to be such if they have more of sameness than diversity, either absolutely, or in regard to those attributes which are more important; for example, tin is like silver in being white, and gold is like fire in being red or yellowish.

839. It is evident, then, that the terms diverse and unlike are used in many senses; and that other or diverse is used in a way opposite to the same. Hence everything in relation to everything else is either the same or diverse. And things are diverse in another sense if their matter and intelligible structure are not one; thus you and your neighbor are diverse. A third meaning of this term is that found in mathematics. Hence for this reason everything is either diverse or the same as everything else, i.e., everything of which men predicate unity and being. For other is not the contradictory of the same, and this is why it is not predicated of non-beings (but they are said to be “not the same”), but it is predicated of all beings; for whatever is by nature a being and one is either one or not one. Hence diverse and same are opposed in this way.

840. But different and diverse are not the same. For that which is diverse and that from which it is diverse need not be diverse in some particular respect, because every being is either diverse or the same. But that which is different differs from something in some particular respect. Hence there must be some same thing by which they differ. Now this same thing is either a genus or a species; for everything that differs, differs either generically or specifically: generically, if they have no common matter and are not generated from each other, like those things which belong to a different figure of predication (60), and specifically, if they have the same genus. Genus means that by which both of the things that differ are said to be without difference in substance. But contraries are different, and contrariety is a kind of difference.

841. That this assumption is correct becomes clear by an induction; for all these contraries seem to be different, and they are not merely diverse, but some are generically diverse and others belong to the same category, so that they are contained in the same genus and in the same species. The kinds of things which are generically the same and those which are generically diverse have been established elsewhere (445).

COMMENTARY

Ways one and many are opposed

1983. After having treated of one considered in itself, here the Philosopher deals with one in comparison with many; and this is divided into two parts. In the first (1983) he treats one and many and their concomitant attributes. In the second (2023) he establishes what is true about the contrary character of one and many; for the investigation of this involves a special difficulty.

The first member of this division is divided into two parts. In the first part he shows how one and many are opposed. In the second (1999) he considers their concomitant attributes.

In regard to the first he does three things. First, he indicates how we should understand the opposition between one and many. He says that, although one and many are opposed in many ways, as will be made clear below, none the less one of these ways, and the most important one, concerns one and many insofar as they are opposed as something indivisible is opposed to something divisible, because this mode of opposition pertains to the proper notion of each.

1984. For the essential note of plurality consists in things being divided from each other or in being divisible. He says “divided” because of the things which are actually separated from each other and which are for this reason said to be many. He says “divisible” because of the things which are not actually separated from each other but come close to being separated, for example, moist things such as air and water and the like, of which we use the term much because they are easily divided; thus we speak of much water and much air.

1985. But the formal constituent of unity or oneness consists in being indivisible or in being undivided; for the continuous is said to be one because it is not actually divided, although it is divisible.

1986. Hence, since (834).

Second, he makes clear to what kind of opposition the aforesaid manner of being opposed is ultimately reduced. He says that, since there are four kinds of opposition, one of which is based on privation, it is evident that one and many are not opposed as contradictories or as relative terms, which are two kinds of opposition, but as contraries.

1987. That they are not opposed as (~) contradictories is evident because neither of them applies to non-being, for non-being is neither one nor many. But the second member of the contradiction would have to apply to being as well as to non-being. That they are not opposed as relative terms is likewise evident, for the terms one and many are used in an absolute sense.

1988. And although he had said that one and many are opposed as what is indivisible and what is divisible, and these appear to be opposed as privation and possession, none the less he concludes that one and many are opposed as contraries; for the opposition between privation and possession is the basis of the opposition between contraries, as will be made clear below (2036). For one of the two contraries is always a privation, but not a pure privation; otherwise it would not share in the nature of the genus, since contraries belong to the same genus. Each of the two contraries, then, must be a positive reality, even though one of them shares in the nature of the genus with a certain deficiency, as black in relation to white, as has been stated above (1967). Therefore, since unity does not signify a pure privation, for it does not designate the mere lack of division but the very being which is undivided, it is evident that one and many are opposed not as pure privation and possession but as contraries.

1989. And what is one (835).

[Objection] Third, he answers an implied question. Because he had said that one is related to many as what is indivisible to what is divisible, and what is indivisible seems to be the privation of what is divisible since privation is subsequent to possession or form, it seems to follow that one is subsequent to many, although he had said above (1939) that one is the principle of many, from which it becomes known.

1990. In order to see the solution of this difficulty, then, it must be borne in mind that things which are prior and better known by nature are subsequent and less well known to us, because we derive our knowledge of things from the senses. Now the first things to be perceived by us are composite and confused things, as is said in Book I of the Physics; and this is why the first things to be known by us are composite things. But simpler things, which are prior and more intelligible by nature, are known by us only derivatively; and this is why we define the first principles of things only by the negations of subsequent things; for example, we say that the point is what has no parts; and we know God by way of negations inasmuch as we say that God is incorporeal, unchangeable and infinite.

1991. Accordingly, even though what is one is prior by nature to what is many, yet in our knowledge it is defined and gets its name from the privation of division. This is why the Philosopher says that “what is one is described,” i.e., named, “and made known,” i.e., understood, “in reference to its contrary,” just as the indivisible is known from the divisible. And for this reason many things are able to be perceived more easily than one thing; and what is divisible is able to be perceived more easily than what is indivisible, not in the order of nature but because of sensory perception, which is the foundation of our knowledge.

1992. [Objection] But a twofold difficulty arises with regard to those things which the Philosopher is expounding. The first concerns his statement that one and many are opposed as contraries. For this appears to be impossible, because unity is the basis of plurality, whereas one of two contraries does not ground the other but rather destroys it.

1993. Hence it must be noted that, since contraries differ formally, as is said below (2120), when we say that things are contraries, each of them is to be taken (+) insofar as it has a form, but not (~) insofar as it is a part of something having a form.

(+) For insofar as body is taken without the soul, as something having a form, it is opposed to animal as the non-living is opposed to the living. (~) But insofar as it is not taken as something complete and informed, it is not opposed to animal but is a material part of it.

We see that this is likewise true of numbers; for insofar as the number two is a kind of whole having a determinate species and form, it differs specifically from the number three; but if it is taken insofar as it is not made complete by a form, it is a part of the number three.

1994. Therefore insofar as unity itself is considered to be complete in itself and to have a certain species, it is opposed to plurality; because what is one is not many, nor is the reverse true. But insofar as it is considered to be incomplete as regards form and species, it is not opposed to plurality but is a part of it.

1995. [Objection] The second difficulty has to do with the statement that plurality is prior in intelligibility to unity; for, since the concept of plurality or multitude involves unity, because a plurality is nothing else than an aggregate of units, if unity is subsequent in intelligibility to plurality, it follows that the notions of unity and plurality involve circularity, i.e., in the sense that unity is intelligible in terms of plurality and vice versa. But circularity of definition is not admissible in designating the intelligible structures of things, because the same thing would then be known both to a greater and to a lesser degree. This is impossible.

1996. The answer to this difficulty, then, must be that nothing prevents one and the same thing from being prior and subsequent in intelligibility according to different traits which are considered in it. For in multitude it is possible to consider both multitude as such and division itself.

Thus from the viewpoint of division multitude is prior in intelligibility to unity; for that is one which is undivided. But multitude as multitude is subsequent in intelligibility to unity, since a multitude means an aggregate of units or ones.

1997. Now the division which is implied in the notion of that kind of unity which is interchangeable with being is not (~) the division of continuous quantity, which is understood prior to that kind of unity which is the basis of number, but is (+) the division which is caused by contradiction, inasmuch as two particular beings are said to be divided by reason of the fact that this being is not that being.

1998. Therefore what we first understand is being, and then division, and next unity, which is the privation of division, and lastly multitude, which is a composite of units.

For even though things which are divided are many, they do not have the formal note of a many until the fact of being one is attributed to each of the particular things concerned. Yet nothing prevents us from also saying that the notion of multitude depends on that of unity insofar as multitude is measured by one; and this already involves the notion of number.

1999. And as we have (836).

Here he indicates the attributes which stem from unity and plurality; and in regard to this he does two things. First, he gives the attributes which naturally stem from unity and plurality. He says that sameness, likeness and equality flow from unity, as has been pointed out above in Book V (911), where he divided or distinguished the various senses in which things are said to be contrary; for those things are the same which are one in substance; those are like which are one in quality; and those are equal which are one in quantity.

2000. And the contraries of these, diverse, unlike and unequal, pertain to plurality. For those things are diverse whose substance is not one; those are unlike whose quality is not one; and those are unequal whose quantity is not one.

2001. Now things (837).

He now explains the various senses in which these terms are used; and in regard to this he does two things. First, he shows how the modes of those attributes which accompany unity differ from each other. Second (2013) he does the same thing for those attributes which accompany plurality (“It is evident”).

In regard to the first part he does two things. First, he explains the various ways in which things are said to be the same; and second (2006), those in which they are said to be like (“Things are like”). He does not make any distinctions as regards equality, however, because there are not many ways in which things are said to be equal, unless perhaps in reference to the various kinds of quantity.

2002. He accordingly gives three ways in which the term same is used. For since same means one in substance, and substance is used of two things, namely, of the supposit itself and of the nature or species of a thing, the term same is used of three things: either (1) of the supposit alone, as this white thing or this musical man, assuming that Socrates is white or musical; or (2) of the nature of the supposit alone, that is, its intelligible expression or species, as Socrates and Plato are the same in terms of humanity; or (3) of both together, as Socrates is the same as Socrates.

2003. Hence, the Philosopher, in giving these three ways in which the term is used, says that the term same is used in many senses. (1) In one sense it means what is numerically the same, which we sometimes express by the term itself, as when we say that Socrates is a man and that he himself is white. For since the pronoun itself is reflexive, and a reflexive term brings back the same supposit, wherever the term itself is used it signifies that the supposit is numerically one and the same.

2004. (2) A thing is said to be the same in another sense if it is one not only by the oneness of the supposit, as this wood and this white thing, but if it is the same both in its intelligible structure and in number, as you are the same as yourself both specifically and materially, inasmuch as matter, which is the principle of individuation is taken for the supposit, and species is taken for the nature of the supposit.

2005. (3) Things are said to be the same in a third sense when “the intelligible structure of the primary substance,” i.e., of the supposit, is one, even though there is not one supposit. And these things are the same specifically or generically but not numerically. He gives an example of this in the case of quantity, according to the opinion of those who claimed that quantities are the substances of things; and according to this opinion many straight lines are regarded as many supposits in the genus of substance, and the measure of a line is considered to be its species. This opinion maintains, then, that many straight lines are one, just as distinct supposits are one which have one specific nature in common. And since mathematicians speak of lines in the abstract, for them many equal straight lines are considered as one. And in a similar fashion many “equal quadrangles,” i.e., figures which have four angles and are equal in size and “equiangular,” i.e., having equal angles, are considered to be the same. And in such things as these equality provides the unity of their specific nature.

2006. Things are “like” (838).

Here he reveals the different ways in which things are said to be like, and there are four of these.

(1) The first corresponds to the third way in which things are the same; for since that is the same which is one in substance, and that is like which is one in quality, the basis of likeness must be related to the basis of sameness as quality to substance. And since he has used equality to designate oneness of substance, he uses figure and proportion to designate quality.

2007. It should also be noted that, since quality and quantity are rooted in substance, it follows that wherever there is oneness of substance there is oneness of quantity and quality, although this oneness or unity does not derive its name from quantity and quality but from something more basic, namely, substance. Hence, wherever there is oneness of substance we do not speak of likeness or of equality but only of identity.

2008. Diversity of substance, then, is required for likeness or equality. This is why he says that some things are said to be like even though they are not absolutely the same as to the species of their substance (provided that they are also not without difference in their underlying subject, which is called the supposit) but are specifically the same in some way. Thus a larger quadrangle is said to be like a smaller one when the angles of one are equal to those of the other and the sides containing the angles are proportional. It is evident, then, that this likeness is viewed from the standpoint of oneness of figure and proportion. And in a similar way many unequal straight lines are not the same in an absolute sense even though they are like.

2009. It can also be noted here that, when there is unity in regard to the complete concept of the species, we speak of identity. But when there is no unity in regard to the whole concept of the species, we speak of likeness; so that if someone says that things which are generically one are like, then those which are specifically one are the same, as the examples given above would seem to indicate. For he said that equal straight lines and equal quadrangles are identical with each other, whereas unequal quadrangles and unequal straight lines are said to be like.

2010. (2) Things are said to be like in a second sense when they have in common one form which admits of difference in degree although they participate in that form without difference in degree; for example, whiteness admits of greater and lesser intensity, so that, if some things are equally white without any difference in degree, they are said to be like.

2011. (3) Things are said to be like in a third sense when they have in common one form or affection but to a greater or lesser degree; for example, a thing which is whiter and one which is less white are said to be like because they have “one form,” i.e., one quality.

2012. (4) Things are said to be like in a fourth sense when they have in common not merely one quality but many, as those things which are said to be like because they agree in more respects than they differ, either in an absolute sense, or in regard to certain particular attributes; for example, tin is said to be like silver because it resembles it in many respects. And similarly fire is like gold, and saffron like red.

2013. It is evident (839).

Here he treats the attributes which naturally accompany plurality. First, he considers unlikeness and diversity; and second (2017), he treats difference (“But different”).

He accordingly says, first, that, since the terms same and diverse and like and unlike are opposed to each other, and since the terms same and like are used in many senses, it is evident that the terms diverse and unlike are used in many senses; for when, one of two opposites is used in many senses, the other is also used in many senses, as is said in the Topics, Book I.

2014. But omitting the many senses in which the term unlike is used, since it is quite apparent how the senses of this term are taken in contrast to those of the term like, he gives three senses in which the term diverse, or other, is employed. (1) First, the term diverse refers to everything that is other in contrast to the same; for just as everything that is itself is said to be the same, and this is the relation of identity, in a similar fashion everything that is diverse is said to be other, and this is the relation of diversity. Hence everything is either the same as or other than everything else. (2) Second, the term diverse, or other, is used in another sense when the matter and intelligible structure of things are not one; and in this sense you and your neighbor are diverse. (3) The term is used in a third sense in mathematics, as when unequal straight lines are said to be diverse.

2015. [Objection] And since he had said that everything is either the same as or other than everything else, lest someone think that this is true not only of beings but also of non-beings, he rejects this by saying that everything is either the same as or other than everything else in the case of those things of which the terms being and unity are predicated, but not in the case of those things which are non-beings. For same and diverse are not opposed as contradictory terms, of which one or the other must be true of any being or non-being; but they are opposed as contraries, which are only verified of beings. Hence diversity is not predicated of non-beings. But the phrase not the same, which is the opposite of the same in a contradictory sense, is also used of non-beings. However, same or diverse is used of all beings; for everything that is a being and is one in itself, when compared with something else, is either one with it, and then it is the same, or it is capable of being one with it but is not, and then it is diverse. Diverse and same, then, are opposites.

2016. But if someone were to raise the objection that diversity and sameness do not apply to all beings, since sameness is a natural consequence of oneness of substance, and diversity is a natural consequence of plurality of substance, we should have to answer that, since substance is the root of the other genera, whatever belongs to substance is transferred to all the other genera, as the Philosopher pointed out above regarding quiddity in Book VII (1334).

2017. But “different” (840).

Then he shows how difference and diversity differ. He says that diverse and different mean different things; for any two things which are diverse need not be diverse in some particular respect, since they can be diverse in themselves. This is evident from what has been said above, because every being is either the same as or other than every other being.

2018. But that which differs from something else must differ from it in some particular respect. Hence that by which different things differ must be something that is the same in things which do not differ in this way. Now that which is the same in many things is either a genus or a species. Therefore all things that differ must differ either generically or specifically.

2019. Those things differ generically which have no common matter; for it has been said above, in Book VIII (1697), that although matter is not a genus, still the essential note of a genus is taken from a thing’s material constituent; for example, sensory nature is material in relation to the intellectual nature of man. Hence anything that does not possess sensory nature in common with man belongs to a different genus.

2020. And since those things which do not have a common matter are not generated from each other, it follows that those things are generically diverse which are not generated from each other. It was also necessary to add this because of the things which do not have matter, such as accidents, so that those things which belong to different categories are generically diverse, for example, a line and whiteness, neither one of which is produced from the other.

2021. Now those things are said to be specifically diverse which are the same generically and differ in form. And by genus we mean that attribute which is predicated of two things which differ specifically, as man and horse. Moreover, contraries differ, and contrariety is a type of difference.

2022. That this assumption (841).

Then he proves by an induction what he had said above about the formal note whereby things differ, because all things that are different seem to be such that they are not merely diverse but diverse in some particular respect. Some things, for instance, are diverse in genus; some belong to the same category and the same genus but differ in species, and some are the same in species. What things are the same or diverse in genus has been established elsewhere, namely, in Book V of this work (931).

LESSON 5

Contrariety Is the Greatest and Perfect Difference

ARISTOTLE’S TEXT Chapter 4: 1055a 3-1055a 33

842. But since it is possible for things which differ from each other to differ to a greater or lesser degree, there is a greatest difference.

843. And I call this difference contrariety. That this is the greatest difference becomes clear by induction; for things which differ generically cannot pass into each other, but they are too far apart and cannot be compared; and those things which differ specifically arise from contraries as their extremes. But the distance between extremes is the greatest; therefore the distance between contraries is the greatest.

844. Now what is greatest in each class is perfect (or complete); for that is greatest which nothing exceeds, and that is perfect beyond which it is impossible to find anything else; for the perfect difference is an end, just as other things are said to be perfect because they have attained their end. For there is nothing beyond the end, since in every case it is what is ultimate and contains everything else. There is nothing beyond the end, then, and what is perfect needs nothing else. It is therefore clear from these remarks that contrariety is the perfect or complete difference. And since things are said to be contrary in many ways, it follows that difference will belong to contraries perfectly in proportion to the different types of contrariety.

845. Since this is so, it is evident that one thing cannot have many contraries; for there can be nothing more extreme than the extreme (since, if there were, it would be the extreme); nor can there be more than two extremes for one distance.

846. And in general this is evident if contrariety is difference, and difference must be between two things. Hence this will also be true of the perfect difference.

847. And the other formulations of contraries must also be true. For the perfect difference is the greatest, since in the case of things which differ generically it is impossible to find any difference greater than in those which differ specifically; for it has been shown (843) that there is no difference between things in a genus and those outside it, and for those specifically different the perfect difference is the greatest. And contraries are things which belong to the same genus and have the greatest difference; for the perfect difference is the greatest difference between them. And contraries are things which have the greatest difference in the same subject; for contraries have the same matter. And contraries are things which come under the same potency and have the greatest difference; for there is one science of one class of things, and in these the perfect difference is the greatest.

COMMENTARY

2023. Having settled the issue about the one and the many, and about the attributes which naturally accompany them, of which one is contrariety, which is a kind of difference, as has been pointed out (840:C 2021), here the Philosopher explains contrariety, because the investigation of it involves a special difficulty. This is divided into two parts. In the first (842:C 2023) he shows that contrariety is the greatest difference. In the second (887:C 2112) he inquires whether contraries differ generically or specifically (“That which is “ ).

The first part is divided into two. In the first he settles the issue about contraries. In the second (878:C 2097) he deals with their intermediates (“And since”).

The first part is divided into two. In the first he settles the issue about the nature of contraries. In the second (857:C 2059) he raises certain difficulties about the points which have been established (“But since one thing”).

The first part is divided into two. In the first he shows what contrariety is. In the second (848:C 2036) he establishes what is true of contrariety as compared with the other kinds of opposition (“The primary contrariety”).

In treating the first part he does two things. First, he gives a definition of contrariety. Second (847:C 2032), he reduces all the other definitions which have been assigned to contraries to the one given (“And the other”).

In regard to the first he does two things. First, he gives the definition of contrariety. Second (844:C 2027), he draws a corollary from this definition (“Now what is”).

In regard to the first he does two things. First (842), he shows that there is a greatest difference, as follows: there is some maximum in all things which admit of difference in degree, since an infinite regress is impossible. But it is possible for one thing to differ from something else to a greater or lesser degree. Hence it is also possible for two things to differ from each other to the greatest degree; and therefore there is a greatest difference.

Contrary

2024. And I call (843).

Second, he shows by an induction that contrariety is the greatest difference; for all things which differ must differ either generically or specifically.

Now those things which differ generically cannot be compared with each other, being too far apart to admit of any difference of degree between them. This is understood to apply to those things which are changed into each other, because a certain process or way of change of one thing into another is understood from the fact that at first they differ more and afterwards less, and so on until one is changed into the other. But in the case of things which differ generically we do not find any such passage of one thing into another. Hence such things cannot be considered to differ in degree, and so cannot differ in the highest degree. Thus in things which differ generically there is no greatest difference.

2025. However, in the case of things which differ specifically there must be a greatest difference between contraries, because:’reciprocal processes of generation arise from contraries as their extremes. And an intermediate arises from an extreme or vice versa, or an intermediate also arises from an intermediate, as gray is produced from black or from red. Yet generations of this kind do not arise from two things as extremes; for when something passes from black to gray in the process of generation, it can still pass farther to some color which differs to a greater degree. But when it has already become white, it cannot continue farther to any color which differs to a greater degree from black, and there it must stop as in its extreme state. This is why he says that processes of generation arise from contraries as extremes. But it is evident that the distance between extremes is always the greatest. Hence it follows that contraries have the greatest difference among things which differ specifically.

2026. And since we have shown that things which differ generically are not said to have a greatest difference, although there is a greatest difference, it follows that contrariety is nothing else than the greatest difference.

2027. Now what is greatest (844).

He draws two corollaries from what has been said. The first is that contrariety is the perfect difference. This is proved as follows. What is greatest in any class is the same as what is perfect. This is clear from the fact that that is greatest which nothing exceeds; and that is perfect to which nothing can be added. Hence the difference of the greatest and that of the perfect [from a common referent] are seen to be the same.

2028. That that is perfect to which nothing external can be added is evident, because all things are said to be perfect when they go up to the end. Now there is nothing beyond the end, because the end is what is ultimate in every case and contains the thing. Hence nothing lies beyond the end, nor does what is perfect need anything external, but the whole is contained under its own perfection. Thus it is evident that the perfect difference is one which goes up to the end.

2029. Therefore, since contrariety is the greatest difference, as has already been proved (843:C 2024), it follows that it is the perfect difference. But since things are said to be contrary in many ways, as will be stated later (849:C 2039), not all contraries are said to differ perfectly; but it follows that all contraries differ perfectly in the way in which contrariety belongs to them, i.e., to some primarily and to others secondarily.

2030. Since this is so (845).

Here he gives the second corollary. He says that, since the foregoing remarks are true, it is evident that one thing cannot have many contraries. He proves this in two ways. He does this, first, on the grounds that contrariety is the greatest and perfect difference between extremes. But there can be no more than two extremes of one distance; for we see that one straight line has two end points. Further, there is nothing beyond the extreme. If, then, contrariety is one distance, it is impossible for two things to be equally opposed as extremes to one contrary, or for one to be more contrary and another less so, because whatever is less contrary will not be an extreme but will have something beyond it.

2031. And in general (846).

He now proves the same thing in another way. He says that since contrariety is a kind of difference, and every difference is a difference between two things, then the perfect difference must also be a difference between two things. Thus one thing has only one contrary.

2032. And the other (847).

Next he shows that all the definitions of contraries which have been given are seen to be true on the basis of the definition of contrariety posited above (842:C 2023). He gives “four formulations,” i.e., definitions, of contraries assigned by other thinkers. The first is that contraries are things which have the greatest difference. Now this is seen to be true on the basis of the foregoing definition, since contrariety is the perfect difference, and this causes things to differ most. For it is evident from what has been said that in the case of things which differ generically nothing can be found which differs more than things which differ specifically, because there is no difference as regards those things which lie outside the genus, as has been stated. And of things which differ specifically the greatest difference is between contraries. Hence it follows that contraries are things which differ most.

2033. The second definition is that contraries are attributes which differ to the greatest degree in the same genus. This is also seen to be true on the basis of the foregoing definition, because contrariety is the perfect difference. But the greatest difference between things which belong to the same genus is the perfect difference. Hence it follows that contraries are attributes which have the greatest difference in the same genus.

2034. The third definition is that contraries are attributes which have the greatest difference in the same subject. This is also seen to be true on the basis of the foregoing definition; for contraries have the same matter since they are generated from each other.

2035. The fourth definition is that contraries are attributes which have the greatest difference “under the same potency,” i.e., the same art or science; for science is a rational potency, as has been stated in Book IX (746:C 1789). This definition is also seen to be true on the basis of the foregoing definition, because there is one science of one class of things. Therefore, since contraries belong to the same genus, they must come under the same potency or science. And since contrariety is the perfect difference in the same genus, contraries must have the greatest difference among those things which come under the same science.

LESSON 6

Contrariety Based on Privation and Possession

ARISTOTLE’S TEXT Chapter 4: 1055a 33-1055b 29

848. The primary contrariety is between possession and privation, not every privation (for privation has several meanings), but any which is perfect.

849. And the other contraries are referred to these: some because they possess them, others because they produce or can produce them, and others because they are the acquisitions or losses of them or of other contraries.

850. If, then, the modes of opposition are contradiction, privation, contrariety and relation, and the first of these is contradiction, and there is no intermediate between contradictories whereas there is between contraries, then it is evident that contradiction is not the same as contrariety.

851. And privation is a kind of contradiction; for that which suffers privation, either totally or in some determinate way, is either that which is totally incapable of having some attribute, or that which does not possess it even though it is naturally fitted to do so; for we have already used this term in many senses, which have been distinguished elsewhere (511). Hence privation is a kind of contradiction which is found either in a determinate potency or is conceived along with something that is susceptible of it. And for this reason there is no intermediate in contradiction, although there is an intermediate in one kind of privation; for everything is either equal or not equal, but not everything is equal or unequal; but this is so only in the ca§e of something susceptible of equality.

852. If, then, the processes of generation in matter start from contraries, and these are produced -either from the form and the possession of the form, or from the privation of some form or specifying principle, it is evident that every contrariet~ will be a kind of privation.

853. But perhaps not every privation is contrariety. And the reason is that whatever suffers privation does so in many ways; for it is the things from which change proceeds as extremes that are contraries.

854. This also becomes evident by induction; for every contrariety has privation as one of its contrary terms, but not all in the same way; for inequality is the privation of equality, unlikeness the privation of likeness, and vice the privation of virtue.

855. And privation differs in the ways we have stated (850); for it has one meaning if a thing is merely deprived of some attribute, and another if it is deprived at a certain time or in a certain part (for example, if this happens at a certain age or in the most important part) or entirely. Hence in some cases there is an intermediate (there is a man who is neither good nor evil) and in others there is not (a number must be either even or odd). Again, some have a definite subject, and others do not. Hence it is evident that one of two contraries is always used in a privative sense.

856. But it is enough if this is true of the primary or generic contraries-one and many; for the others may be reduced to them.

COMMENTARY

2036. Having defined contrariety the Philosopher now compares it with the other kinds of opposition. In regard to this he does two things. First (848:C 2036), he states his thesis, namely, that the basis of contrariety is the opposition between privation and possession. Second (850:C 2040), he proves it (“If, then”).

In regard to the first he does two he states that the basis of contrariety is privation and possession. He says that the primary contrariety is privation and possession because privation and possession are included in every contrariety.

2037. But lest someone should think that the opposition between privation and possession and that between contraries are the same, he adds that not every privation is a contrary; for, as has been pointed out above, the term privation is used in several ways. Sometimes a thing is said to be deprived of something when it does not have in any way what it is naturally fitted to have. However, such privation is not a contrary, because it does not presuppose a positive reality which is opposed to possession, though it does presuppose a definite subject. But it is only that privation which is perfect that is said to be a contrary.

2038. And since privation by its very nature does not admit of difference in degree, a privation can be said to be perfect only by reason of some positive reality which is farther removed from possession. For example, not every privation of white is its contrary, but only that which is farthest removed from white, which must be rooted in some nature of the same genus and farthest removed from white. And according to this we say that black is the contrary of white.

2039. And the other contraries (849).

Second, he explains how the other contraries are derived from this first contrariety. He says that other contraries “are referred to these,” namely, to privation and possession, in different ways. For some things are called contraries because they have in themselves privation and possession, for example, such things as white and black, hot and cold; others because they actually cause privation and possession, as things which cause heat and cold, or because they are virtually the active causes of privation and possession, as things capable of heating and cooling. And others are called contraries because they are acquisitions of the attributes mentioned, as the processes of becoming hot and becoming cold, or because they are the losses of these, as the destruction of heat and cold. And others again are called contraries not only because they express the aforesaid relationships to the primary contraries but also because they have the same relationships to subsequent contraries; for example, if we were to say that fire and water are contraries because they have heat and cold, which are called contraries themselves, as we have seen, because they include privation and possession.

Other kinds of opposition

2040. If, then, the modes (850).

Then he proves his thesis, namely, that the primary contrariety is privation and possession; and he does this in two ways: first, by a syllogism; second (2054), by an induction (“This also”).

In regard to the first he does two things. First, he shows that contrariety is not contradiction. He says that among the four kinds of opposition between two things—(1) contradiction, as sitting is opposed to not-sitting; (2) privation, as blindness is opposed to sight; (3) contrariety, as black is opposed to white; and (4) relation, as a son is opposed to his father—the first is contradiction.

2041. The reason is that contradiction is included in all the other kinds of opposition as something prior and simpler; for in any kind of opposition it is impossible that opposites should exist simultaneously. This follows from the fact that one of two opposites contains the negation of the other in its notion; for example, the notion of blind contains the fact of its not seeing, and the notion of black, of its not being white. And similarly the notion of son contains his not being the father of him of whom he is the son.

2042. Moreover, it is evident that there is no intermediate in contradiction; for one must either affirm or deny, as has been shown in Book IV (725). However, it belongs to contraries to have an intermediate; and thus it is clear that contrariety and contradiction are not the same.

2043. And privation (851).

Then he shows how privation is related to contradiction by indicating the way in which they are alike and that in which they differ. He says that privation is a kind of contradiction; for the term privation is used in one sense when a thing does not have in any way some attribute which it is capable of having, for example, when an animal does not have sight. And this occurs in two ways: (a) first, if it does not have it in any way at all; and (b) second, if it does not have it in some definite respect, for example, at some definite time or in some definite manner, because privation is used in many senses, as has been stated in Books V (1070) and IX (1784).

2044. It is evident from what has been said, then, that privation is a kind of contradiction; and this is shown from the fact that a thing is said to be deprived of something because it does not have it.

2045. That it is not a simple contradiction but one of a sort is evident from the fact that according to its meaning a contradiction requires neither (~) the aptitude nor the existence of any subject; for it may be truly affirmed of any being or non-being whatsoever. Thus we say that an animal does not see, and that wood does not see, and that a non-being does not see.

A privation, however, necessarily (+) requires some subject, and sometimes it also requires aptitude in a subject; for that which is a non-being in every respect is not said to be deprived of anything.

2046. He says, then, that privation “is found either in a determinate potency,” i.e., one with a capacity for possessing something, or at least “is conceived along with something that is susceptible of it,” i.e., along with a subject, even though it has no capacity for possessing something. This would be the case, for example, if we were to say that a word is invisible, or that a stone is dead.

2047. (~) Contradiction, then, cannot have an intermediate, whereas in a sense (+) privation has an intermediate; for everything must be either equal or not equal, whether it is a being or a non-being. However, it is not necessary to say that everything is either equal or unequal, but this is necessary only in the case of something that is susceptible of equality.

2048. Hence the opposition of contradiction has no intermediate whatsoever, whereas the opposition of privation has no intermediate in a determinate subject; but it is not without an intermediate in an absolute sense. And from this it is evident that contrariety, which is such as to have an intermediate, is closer to privation than to contradiction. Yet it still does not follow that privation is the same as contrariety.

2049. If, then, the processes (852).

Third, it remains to be shown that contrariety is privation, and in regard to this he does two things. First, he shows by a syllogism that contrariety is privation. He argues as follows: everything from which a process of generation arises is either a form (i.e., the possession of some form) or the privation of some specifying principle (i.e., some form). He says “everything” because generation is twofold. For things are generated absolutely in the genus of substance, but in a qualified sense in the genus of accidents; for generations arise from contraries in matter. Hence it is evident that every contrariety is a privation; for if in any process of generation one of the two extremes is a privation, and each of the contraries is an extreme in the process of generation (because contraries are generated from each other, as white from black and black from white), then one of the two contraries must be a privation.

2050. But perhaps (853).

Here he proves another assertion made above, that not every privation is a contrariety. He says that the reason for this is that there are many ways of being deprived; for a thing that is capable of having a form and does not have it in any way can be said to be deprived of it, and it makes no difference whether it is proximately or remotely disposed for that form.

Now a contrary is always remotely disposed; for contraries are the sources, in the sense of extremes from which changes arise. Hence it was said above (2038) that they are farthest removed from each other. For whether a thing is yellowish or of some other color, it is said to be deprived of whiteness if it is not white. But it is not on that account called a contrary except when it is farthest removed from whiteness, namely, when it is black. Thus it is clear that not every privation is a contrariety.

2051. And since privation requires nothing else than the absence of form (merely presupposing a disposition in a subject without conferring upon that subject any definite disposition through which the subject is close to a form or distant from it), it is evident that privation does not designate any positive reality in a subject, but presupposes a subject with an aptitude. But a contrary requires a definite disposition in a subject, by which it is farthest removed from a form. Therefore it necessarily designates in a subject some positive reality which belongs to the same class as the absent form, as black belongs to the same class as white.

2052. It should also be noted that privation is of two kinds. (1) There is one which has an immediate relationship to the subject of the form (as darkness has an immediate relationship to the transparent medium), and between a privation of this kind and its opposite form there is (+) reciprocal change; for the atmosphere passes from a state of illumination to one of darkness, and from a state of darkness to one of illumination. (2) And there is another kind of privation which is related to the subject of the form only by means of the form, since it has the nature of a corruption of form; for example, blindness is the corruption of sight, and death the corruption of life. In such cases there is no (~) reciprocal change, as has been pointed out in Book IX (1785).

2053. Therefore, since it has been shown here that contrariety is the privation arising from reciprocal change which involves contraries and privation and form, it is clear that contrariety is not the type of privation which is the corruption of a form, but that which has an immediate relation to the subject of the form. Hence the objection raised in the Categories, that it is impossible to revert from privation to possession, does not apply here. But contraries are changed into each other.

2054. This also becomes (854).

Then he shows by induction that contrariety is privation, and he does this in two ways. First, by making an induction from each type of contrary; and second (856:C 2058), by reducing them to a primary kind of contrary (“But it is”).

In regard to the first (854) he does two things. First, he shows by an induction that contrariety is privation. He says that the point proved above by a syllogistic argument is also made clear by an induction; for every contrariety is found to include the privation of one of the two contraries, since one of the two is always lacking in the other. Yet one contrary is not found to be the privation of the other in the same way in all types of contraries, as will be stated below (855:C 2055). That one of two contraries is the privation of the other is evident from the fact that inequality is the privation of equality, and unlikeness the privation of likeness, and evil the privation of virtue.

2055. And privation differs (855).

Then he shows that one contrary is the privation of the other in various ways; for this is relative to different types of privation. Now this difference may be considered from two points of view. First, privation can mean either that a thing has been deprived of something in any way at all; or, that it is deprived at some definite time or in some definite way. For example, it is deprived at some definite time if this occurs at some definite age; and it is deprived in some definite part if the privation is found in some important part. Or it may also be “entirely,” i.e., in the whole. For a man is said to be senseless if he lacks discretion at a mature age but not as a child. And similarly a person is said to be naked, not if any part of him is uncovered, but if many of his parts or the principal ones are left uncovered.

2056. And because of the various kinds of privation which are included under contrariety it is possible for some contraries to have an intermediate and for some not. For there is an intermediate between good and evil, since a man may be neither good nor evil. For a man is said to be good by reason of virtue, because virtue is what causes its possessor to be good. However, not everyone who lacks virtue is evil; for a boy lacks virtue, yet he is not said to be evil. But if one does not have virtue at an age when he ought to have it, he is then said to be evil. Or if someone also lacks virtue as regards certain insignificant actions and those which, so to speak, make no difference to life, he is not said to be evil, but only if he lacks virtue as to the important and necessary acts of life. But the even and the odd in numbers do not have an intermediate; for a number is said to be odd in the sense that it lacks evenness in any way at all.

2057. The second way in which privations differ is this: one kind of privation has a definite subject of its own, and another kind has not. For it was said above that everything which lacks an attribute, even though it is not naturally such as to have it, is sometimes said to be deprived of it. And according to this difference between privations it is possible for some contraries to have an intermediate or not. For example, we might say that, since man is said to be good with respect to political virtue, if evil, which includes the privation of good, requires a determinate subject, then a rustic who does not participate in civic affairs is neither good nor evil with respect to civic goodness or evil. Hence it is evident from what has been said that one of two contraries is used in a privative sense.

2058. But it is enough (856).

He proves the same point by reducing the other contraries to the primary ones. He says that in order to show that one of two contraries is a privation it is enough if this is found to be true in the case of the primary contraries, which are the genera of the others, for example, one and many.

That these are the primary contraries is evident from the fact that all other contraries are reduced to them; for equal and unequal, like and unlike, same and other, are reduced to one and many. Moreover, difference is a kind of diversity, and contrariety is a kind of difference, as has been said above (2017; 2023). Hence, it is evident that every contrariety is reducible to one and many. But one and many are opposed as the indivisible and the divisible, as has been pointed out above (1983). Therefore it follows that all contraries include privation.

LESSON 7

Opposition of the Equal to the Large and the Small

ARISTOTLE’S TEXT Chapter 5: 1055b 30-1056b 2

857. But since one thing has one contrary, someone might raise the question how the one is opposed to the many, and how the equal is opposed to the large and the small.

858. For we always use the term whether antithetically, for example, whether it is white or black, or whether it is white or not white. But we do not ask whether it is white or man, unless we are basing our inquiry on an assumption, asking, for example, whether it was Cleon or Socrates that came; but this is not a necessary antithesis in any one class of things. Yet even this manner of speaking came from that used in the case of opposites; for opposites alone cannot exist at the same time. And this manner of speaking is used even in asking the question which of the two came. For if it were possible that both might have come at the same time, the question would be absurd; but even if it were possible, the question would still fall in some way into an antithesis, namely, of the one or the many, for example, whether both came, or one of the two.

859. If, then, the question whether something is such and such always has to do with opposites, and one can ask whether it is larger or smaller or equal, there is some opposition between these and the equal. For it is not contrary to one alone or to both; for why should it be contrary to the larger rather than to the smaller?

860. Again, the equal is contrary to the unequal. Hence it will be contrary to more things than one. But if unequal signifies the same thing as both of these together, it will be opposed to both.

861. And this difficulty supports those who say that the unequal is a duality.

862. But it follows that one thing is contrary to two; yet this is impossible.

863. Further, the equal seems to be an intermediate between the large and the small; but no contrariety seems to be intermediate, nor is this possible from its definition; for it would not be complete if it were intermediate between any two things, but rather it always has something intermediate between itself and the other term.

864. It follows, then, that it is opposed either as a negation or as a privation. Now it cannot be opposed as a negation or a privation of one of the two; for why should it be opposed to the large rather than to the small? Therefore it is the privative negation of both. And for this reason whether is used of both, but not of one of the two; for example, whether it is larger or equal, or whether it is equal or smaller; but there are always three things.

865. But it is not necessarily a privation; for not everything that is not larger or smaller is equal, but this is true of those things which are naturally capable of having these attributes. Hence the equal is what is neither large nor small but is naturally capable of being large or small; and it is opposed to both as a privative negation.

866. And for this reason it is also an intermediate. And what is neither good nor evil is opposed to both but is unnamed; for each of these terms is used in many senses, and their subject is not one; but more so what is neither white nor black. And neither is this said to be one thing, although the colors of which this privative negation is predicated are limited; for it must be either gray or red or some other such color.

867. Hence the criticism of those people is not right who think that all terms are used in a similar way, so that if there is something which is neither a shoe nor a hand, it will be intermediate between the two, since what is neither good nor evil is intermediate between what is good and what is evil, as though there were an intermediate in all cases. But this does not necessarily follow. For one term of opposition is the joint negation of things that are opposed, between which there is some intermediate and there is naturally some distance. But between other things there is no difference, for those things of which there are joint negations belong to a different genus. Hence their subject is not one.

COMMENTARY

2059. After having shown what contrariety is, here the Philosopher settles certain difficulties concerning the points established above. In regard to this he does two things. First (857:C 2059), he raises the difficulties; and second (858:C 2060), he solves them (“For we always”).

Now the difficulties (857) stem from the statement that one thing has one contrary; and this appears to be wrong in the case of a twofold opposition. For while the many are opposed to the one the few are opposed to the many. And similarly the equal also seems to be opposed to two things, namely, to the large and to the small. Hence the difficulty arises as to how these things are opposed. For if they are opposed according to contrariety, then the statement which was made seems to be false, namely, that one thing has one contrary.

2060. For we always (858).

Then he deals with the foregoing difficulties; and, first, he examines the difficulty about the opposition between the equal and the large and the small. Second (868:C 2075), he discusses the difficulty about the opposition between the one and the many (“And one might”).

In regard to the first he does two things. First, he argues the question dialectically. Second (864:C 2o66), he establishes the truth about this question (“It follows”).

In regard to the first he does two things. First, he argues on one side of the question in order to show that the equal is contrary to the large and to the small. Second (862:C 2o64), he argues on the opposite side of the question (“But it follows”).

In regard to the first he gives three arguments. In the first of these he does two things. First, he clarifies a presupposition of the argument by stating that we always use the term whether in reference to opposites; for example, when we ask whether a thing is white or black, which are opposed as contraries; and whether it is white or not white, which are opposed as contradictories. But we do not ask whether a thing is a man or white, unless we assume that something cannot be both a man and white. We then ask whether it is a man or white, just as we ask whether that is Cleon or Socrates coming, on the assumption that both are not coming at the same time. But this manner of asking about things which are not opposites does not pertain to any class of things by necessity but only by supposition. This is so because we use the term whether only of opposites by necessity, but of other things only by supposition; for only things which are opposed by nature are incapable of coexisting. And this is undoubtedly true if each part of the disjunction “whether Socrates or Cleon is coming” is not true at the same time, because, if it were possible that both of them might be coming at the same time, the above question would be absurd. And if it is true that both cannot be coming at the same time, then the above question involves the opposition between the one and the many. For it is necessary to ask whether Socrates and Cleon are both coming or only one of them. And this question involves the opposition between the one and the many. And if it is assumed that one of them is coming, then the question takes the form, whether Socrates or Cleon is coming.

2061. If, then, the question (859).

From the proposition which has now been made clear the argument proceeds as follows: those who ask questions concerning opposites use the term whether, as has been mentioned above. But we use this term in the case of the equal, the large and the small; for we ask whether one thing is more or less than or equal to another. Hence there is some kind of opposition between the equal and the large and the small. But it cannot. be said that the equal is contrary to either the large or the small, because there is no reason why it should be contrary to the large rather than to the small. And again, according to what has been said before, it does not seem that it is contrary to both, because one thing has one contrary.

2062. Again, the equal (860).

He now gives the second argument, which runs thus: the equal is contrary to the unequal. But the unequal signifies something belonging to both the large and the small. Therefore the equal is contrary to both.

2063. And this difficulty (861).</