Lecture 8 — Which motions are comparable to each other

Similarly, in the case of motion, two things are of the same velocity if they occupy an equal time in accomplishing a certain equal amount of motion.

Suppose that, in a certain time, an alteration is undergone by one half of a body’s length and the other is led by a locomotion. Can we say that, in this, the alteration is equal to the locomotion and of the same velocity?

That would be absurd, and the reason is that there are different species of motion.

And, if we must say in consequence of this that two things are of equal velocity if they accomplish locomotion over an equal distance in an equal time, we have to admit the equality of a straight line and a circumference.

What, then, is the reason of this? Is it that locomotion is a genus or that line is a genus? (We may leave the time out of account, since that is atomic.)

If the lines are specifically different, the locomotions also differ specifically from one another, since locomotion is specifically differentiated according to the specific differentiation of that over which it takes place.

It is also similarly differentiated accordingly as the instrument of the locomotion is different. Thus, if feet are the instrument, it is walking, but if wings, it is flying.

But perhaps this is not so, and, in this case, the differences in the locomotion are merely a diversity of figure in that which is in motion.

We may therefore say that things are of equal velocity if they traverse the same magnitude in an equal time;

when I call it “the same,” I mean that it contains no specific difference and thus no difference in the motion that takes place over it. So, we have now to consider how motion is differentiated.

And this discussion shows that the genus is not a unity, but that genera hide many joined things.

And, in the case of equivocal terms, sometimes the different senses are far removed from one another, while sometimes they have a certain likeness, and sometimes again they are nearly related either generically or analogically.

Hence, they seem not to be equivocal, though they really are.

When, then, is there a difference of species? Is an attribute specifically different if the same thing is found in things that are other, or if differing things are found in differing things? And what is a term?

What will enable us to decide that particular instances of whiteness or sweetness are the same or different? Is it enough that it appears different in one subject from what appears in another? Or must there be no sameness at all?

And further, where alteration is in question, how is one alteration to be of equal velocity with another? One person may be cured quickly and another slowly, and cures may also be simultaneous such that, recovery of health being an alteration, we have here alterations of equal velocity, since each alteration occupies an equal time.

But what alteration? We cannot here speak of an “equal” alteration: what corresponds in the category of quality to equality in the category of quantity is “likeness.”

However, let us say that there is equal velocity where the same change is accomplished in an equal time.

Are we, then, to find the commensurability in the subject of the passion or in the passion itself?

In the case that we have just been considering, it is the fact that health is one and the same that enables us to arrive at the conclusion that the one alteration is neither more nor less than the other, but that they are alike.

But if the passion is different in the two cases—for instance, when what is altered becomes white and what is healthy, respectively—here there is no sameness or equality or likeness, inasmuch as the difference in the passions at once makes the alterations specifically different, and there is no unity of alteration, as neither would there be unity of locomotion.

So, we must find out how many species there are of alteration and of locomotion respectively.

Now, if the things that are in motion—the things to which the motions belong essentially and not accidentally—differ specifically, then their respective motions will also differ specifically, but if they differ generically or numerically, the motions also will differ generically or numerically.

But there still remains the question whether, supposing that two alterations are of equal velocity, we ought to look for this equality in the sameness (or likeness) of the passions or in the things altered, to see, for instance, whether a certain quantity of each has become white.

Or ought we not rather to look for it in both? That is to say, the alterations are the same or different according as the passions are the same or different, while they are equal or unequal according as the things altered are equal or unequal.

And now we must consider the same question in the case of generation and corruption: how is one generation of equal velocity with another?

They are of equal velocity if, in an equal time, there are produced two things that are the same and specifically inseparable, such as two men (not generically inseparable, as two animals).

Similarly, one is quicker than the other if, in an equal time, the product is different in the two cases. I state it thus because we do not have two things in which there is an otherness called unlikeness.

If we adopt the theory that it is number that constitutes being, we may indeed speak of a “greater number” and a “lesser number” within the same species.

But there is no common term that will include both relations, nor are there terms to express each of them separately in the same way as we indicate a higher degree or preponderance of a passion by “more” and of a quantity by “greater.”

940. After pointing out in general what is required in order that things be able to be compared, the Philosopher now applies the truth found to the comparison of motions.

He does this first in general;

second, by comparing motions that belong to diverse genera, at suppose that, in a certain time (249a9; [941]);

third, by comparing one motion to another in the same genus, at and, if we must say (249a12; [942]).

He thus says first (249a8) that, just as in other matters the requirements for comparability are that the things compared be not equivocal, that there be an identical first receiver, and that they be of the same species, so also in regard to motion, “equally swift” is said of things that are moved in equal time, through such-and-such an equal length, and in this, that is, with respect to a change of the same kind.

941. Then, at suppose that, in a certain time (249a9), he discusses the comparison of motions in diverse genera. And he asks, in keeping with what went before, (Lect. 7, nn. 928–29.) whether, if one mobile be altered and another led—that is, moved locally—the alteration can be said to be as swift as the local motion. To say this would be unacceptable, since the two motions are of different species and it has already been said that things not of the same species cannot be compared. (Lect. 7, n. 939.) Therefore, since local motion is not of the same species as alteration, the swiftness of the two cannot be compared.

942. Then, at and, if we must say (249a12), he discusses the comparison of the motions of one genus within that genus:

first, as to change of place;

second, as to alteration, at and further, where alteration (249a29; [949]);

third, as to generation and corruption, at and now we must consider (249b19; [954]).

He makes no mention of growth and decrease because they share with local motion the common characteristic of being according to some magnitude.

In regard to the first, he does three things:

first, he shows what is required in order that two local motions be able to be mutually compared;

second, he excludes one factor that seems to be required, at it is also similarly (249a17; [945]);

third, he comes to the conclusion he chiefly intended, at we may therefore say (249a19; [946]).

About the first, he does two things:

first, he argues that an impossibility would follow if all local motions could be compared;

second, he says why not all can be compared, at what, then, is the reason (249a13; [944]).

943. He says first (249a12) that, if the equally swift are things moved locally through an equal magnitude in equal time, and if it could happen that all local motions should be equally swift, it would follow that what is straight is equal to what is circular.

Now, this statement may be understood in two senses:

first, in respect to a rectilinear motion and a circular one;

second, in respect to a straight line and a circular one.

The latter is the better sense, because it follows from the foregoing. For if all rectilinear and circular motions are equally swift—and they are so when they traverse an equal magnitude in equal time—it follows that a straight line is equal to a circular one, a situation that must be rejected as unsuitable.

944. Then, at what, then, is the reason (249a13), he investigates the reason that rectilinear motions cannot be compared with circular ones. For since he had concluded that, if they are equal, then the magnitudes are equal—which seems to be unsuitable—someone might wonder whether this inability to be compared is due to the motion or to the magnitude. And this is his question: is the reason that a straight motion is not as swift as a circular one the fact that change of place is a genus containing diverse species under it (for it was said above that things of diverse species are not comparable), or is it that line is a genus containing under it straight and circular as species? Of course, time cannot be the reason, for all time is atomic—that is, indivisible—as to species.

To this question, therefore, he responds that both reasons hold, for in both cases is found a difference of species, but in such a way, nevertheless, that the diversity of species in local motion is due to the diversity of species of the magnitudes over which the motion takes place. And this is what he says: if that upon which the motion occurs has species, it follows that the local motion will have species.

945. Then, at it is also similarly (249a17), he rejects a factor that might seem to be required for identity of species and comparability in local motions. He says that changes of place are sometimes diversified by reason of the instrument—that is, by reason of that through which a local motion takes place as through an instrument; for example, if the feet are the instruments of local motion, it is walking, but if wings are, it is called flying. Yet this does not make for diversity of species in local motions, but for a diversity of figure in local motions; that is, such a diversity of motions is not according to species, but only according to a certain figure of motion, as the Commentator says.

However, it could possibly be better said that Aristotle here intends to say that changes of place are not diversified by reason of the instruments of motion, but by reason of the figure of the magnitude traversed. For it is in this way that straight and circular differ. The reason is that motions are not diversified on account of the mobiles, but on account of the things in respect to which the mobiles are moved. Now, instruments hold themselves on the part of the mobiles, while figures are on the part of that in which the motion occurs.

946. Then, at we may therefore say (249a19), he concludes his proposition.

Concerning this, he does three things:

first, he argues for the main proposition;

second, he draws from the conclusion a fact to be considered, at and this discussion serves (249a21; [947]);

third, he investigates the problem of diversity of species, at when, then, is there a difference (249a25; [948]).

He concludes first (249a19) that, since motions are not comparable unless they are of the same species, and local motions are not of one species unless they traverse magnitude of the same species, it follows that those are equally swift that traverse the same magnitude in equal time, where same refers to what is not different in species. For it is in this way that motions, too, do not differ in species. And, therefore, the main thing to be considered in the question of the comparison of motions is their differences. For if they differ either in genus or in species, they cannot be compared. But if they differ in accidents, they can be.

947. Then, at and this discussion serves (249a21), he draws from the foregoing a fact worthy of consideration: a genus is not something absolutely one, whereas a species is.

This is made known first of all from the preceding argument in which it was shown that things not of one genus are not comparable, whereas things of one species are;

second, from what was said above, in which it was stated that the nature of comparable things is one. (Lect. 7, n. 939.)

From this, it can be gathered that a genus is not one nature, while a species is.

The reason for this is that the species is taken from the last form, which is absolutely one in the nature of things, whereas the genus is not taken from a form that is one in the universe of things, but from one that is so in account only. For the form by which man is animal is not other than that by which man is man. Therefore, all men who are of one species agree in the form that constitutes their species, because each has a rational soul. But there is not some common soul that makes man, horse, and ass all to be animal over and above the soul that makes one a man, a horse, or an ass. (If there were, then the genus would be one and comparable, just as the species.) But it is only in our mental consideration that a generic form is extracted, namely, it is brought about by the intellect’s abstracting from the differences.

Consequently, a species is one quiddity deriving from a unity of form existing in the universe of things. The genus, however, is not one, for according to the diverse forms existing in the nature of things, diverse species are capable of receiving a same genus as a predicate. Consequently, a genus is one thing logically but not physically.

In a certain sense, a genus is one, but not purely. Rather, genera hide many joined things; that is, the equivocation of many things is often masked on account of their likeness and their closeness to a unity of genus.

Now, certain equivocal things are very unlike and possess in common only a name, as when the dog star and the animal that barks are called “dogs.” Other things, however, have a certain likeness, as when the word “man” is applied to a real man and to one that is in a painting on account of the latter’s likeness to a real man.

Yet other equivocations are very close. This may be on account of agreement in genus. For example, when “body” is said of a heavenly body and of a corruptible body, it is equivocation, because, naturally speaking, the matter is not one. They agree, however, in logical genus, for which reason they appear not to be equivocal. Or it may be on account of some likeness. For example, one who teaches in the schools is called “master” and so is the head of a house, equivocally; this is by a close equivocation, however, on account of the likeness, for each is a ruler—one in the school and the other in the house. Hence, on account of their close resemblance in genus or likeness, some things do not appear to be equivocal that nevertheless are.

948. Then, at when, then, is there a difference (249a25), he now inquires how specific differences may be taken in motions and in other things as well, because he had said that we must consider the question of the differences of motion—that is, whether motions differ specifically.

And, because the definition designates the essence of the species, he poses two questions:

one about the species;

and one about the definition.

He first of all asks about species. When is something to be reckoned of a different species from another? Is it only because the same nature is found in different receivers, as Plato held? According to the foregoing, this cannot be the case. For it has been said that a genus is not absolutely one; therefore, a difference of species is not reckoned on the basis that something is the same in two different things, except by the Platonists, who posited that a genus is absolutely one. On this account, as though answering the question, Aristotle adds specifically different not because the same thing is in a different receiver, but because a different nature is in a different receiver.

The second question is about definition. What is a term—that is, what is the definition that declares a species? And because things that have the same definition are absolutely the same, he then, as if answering the question, adds that the proper definition of a thing is that by which we can discern whether something is the same or other, for instance, white or sweet.

And “other” may be taken in two ways, as before:

in one way, as meaning that the white is said to be something other than the sweet, for in the white thing is found a subject-nature other than the one in the sweet;

in another way, as meaning that they differ not only in subject-nature, but that they are wholly not the same.

These two are the same as the two he mentioned above, when he said if the same thing is found in things that are other, or if differing things are found in differing things. For it is clear that there is a same reason of identity and diversity in species and in definition.

949. Then, at and further, where alteration (249a29), he discusses the comparison of alterations.

About this, he does two things:

first, he shows that one alteration is as fast as another;

second, he investigates from what aspect equality of quickness in alteration is considered, at but what alteration (249b2; [950]).

He first asks, therefore, about alteration, how one alteration is as fast as another. And he proves that two alterations are equally fast. For being healed is to be altered. But one can be healed swiftly and another slowly, and likewise, some come to be healed at the same time. Therefore, one alteration is as swift as another, for what is moved in an equal time is said to be moved with equal speed.

950. Then, at but what alteration (249b2), because equality of speed in local motion requires equality not only of time but also of magnitude traversed, and assuming that, in alteration, equality of time is required for equality of speed, he asks what else is required: but what alteration? What is it that must be reached in equal time in order that an alteration be called equally swift?

And the reason for this question is that, in quality, with which alteration is concerned, the equal is not found such as to enable us to say that, when an equal quantity is reached in equal time there is an equally fast alteration, as indeed happens in local motion as well as in growth and decrease. But, just as equality is found in quantity, so likeness is found in quality.

To this question he responds at however, let us say (249b4). And first he answers the question, saying that alterations should be called equally swift if, in an equal time, it is the same change that has been changed—that is, altered.

951. Second, at are we, then, to find (249b5), he raises a question about this answer. Since it has been said that there is an equally swift alteration if it is the same thing that has been altered in an equal time, and since, in that which has been altered, there are two things to consider—namely, the quality with respect to which alteration occurred and the subject in which the quality exists—this question arises. Should a comparison of this sort be regarded from the viewpoint of the identity of the quality or from that of the identity of the subject in which the quality exists?

952. Then, at in the case that we have (249b5), he answers one part of the question and says that, with respect to the quality received in alteration, two types of identity must be considered in order that alterations be equally swift.

First, the same specific quality must be involved, for example, the same health of the eye or of something similar;

second, the quality that is taken must be present in the same way, and neither more nor less.

But, if the passions—that is, the passible qualities in question—differ specifically, such as if one alteration involves becoming white and another healthy, then in these two cases nothing is the same; they are neither equal nor alike. Hence, a diversity of these qualities causes a diversity in species of alteration, such that the alterations are not one, just as it was said above that a straight motion and a circular one are not one local motion. Consequently, whenever you wish to compare either local motions or alterations, you have to consider the species of alterations or of local motion to see whether they are the same or many. And this may be considered from the things in which motions occur, for if the things that are in motion—that is, in which motion occurs per se, and not per accidens—differ specifically, then the motions differ specifically; if they differ generically, so do the motions differ generically; if they differ numerically, then also the motions differ numerically, as was pointed out in book 5. (Lect. 6.)

953. Third, at but there still remains (249b14), having determined one part of the question he raised, he now attacks the other: in order that alterations be adjudged similar or equally swift, should regard be paid only to the quality to see if it is the same, or also to the subject that is altered? That is, if a certain portion of this body becomes white in a certain time and an equal part of another becomes white in the same or in equal time, should the alterations be judged equally swift?

And he answers that attention must be paid to both the quality involved and the subject, but in different ways. For from the viewpoint of the quality, we judge an alteration to be the same or different according to whether the quality is the same or not; but we judge an alteration to be equal or unequal if the part of the subject altered is equal or unequal. For if a large part of this body becomes white and a small part of another becomes white, the alterations will be specifically the same, but they will not be equal.

954. Then, at and now we must consider (249b19), he shows how comparison should be made with respect to generation and ceasing to be:

first, according to his own opinion;

second, according to the opinion of Plato, at if we adopt the theory (249b23; [955]).

He says first (249b19) that, in generation and ceasing to be, in order that a generation be called equally swift, we must consider whether, in an equal time, the same thing is generated and is something indivisible as to species—for example, if a man is begotten in equal time in both generations, they are equally swift. But generations are not equally swift just because an animal is generated in equal time, for some animals, on account of their perfection, require more time for being generated. But generation is said to be swifter if something else is generated in an equal time—for instance, if in the same time in one part of which a dog is generated, and in another part of which a horse is generated, the horse is generated more quickly.

And, since he had said that, in alteration, two things must be considered from the viewpoint of the quality involved—namely, whether it is the same health and whether it exists in the same way and not more or less—while here he says that, in generation, only one thing has to be considered, namely, whether it is the same that is being generated, he now gives the reason for this difference, saying, because we do not have two things in which there is an otherness called unlikeness.

It is as if he said that the reason that the only thing to be considered in generation is whether it is the same thing that is being generated is that, in generation, we do not have something that could vary with regard to two things, according to which a difference could be discerned in the way that unlikeness occurs in alteration through the fact that one and the same quality can vary according to more and less. For a substance, which is the proper terminus of generation, is not capable of more and less.

955. Then, at if we adopt the theory (249b23), he discusses the comparison of generations according to the opinion of Plato, who supposed that number is the substance of a thing. For he thought that the one that is the principle of number is the substance of a thing. Now, what is one is entirely of one nature and species. Therefore, if number, which is nothing more than an aggregate of units, is, according to Plato, the substance of things, it follows that a number will be called larger or smaller according to the species of quantity, but as to substance, it will be of like species. And hence it is that Plato declared that one is the species, but that the contraries through which things differ are the large and the small, which are considered from the side of the matter. Accordingly, it will follow that, just as one and the same health has two aspects, inasmuch as it receives more and less, so also substance, which is number (since it is of the same species on account of unity), will have two aspects according as the number is larger or smaller. But, in substance, no general word exists to signify both, that is, the diversity which arises from the largeness and smallness of number. In qualities, when more of one is in a subject or when it is in any way outstanding, the quality is said to be more—for example, “more white” or “more healthy.” And, in quantity, excellence is described as greater, as a greater body or a greater surface. But, in this sense, there is no common word to signify excellence in substance—which is due to the largeness of number, according to the Platonists.