Lecture 3 — There is no motion per se in the categories other than quantity, quality, and place

If, then, the categories are severally distinguished as substance, quality, where, time, relation, quantity, and activity or passivity, then it necessarily follows that there are three kinds of motion—qualitative, quantitative, and local.

In respect of substance, there is no motion, because substance has no contrary among things that are.

Nor is there motion in respect of relation, for it may happen that, when one correlative changes, while the other does not itself change, it is no longer applicable, such that, in these cases the motion, is accidental.

Nor is there motion in respect of agent and patient—in fact, there can never be motion of mover and moved, because there cannot be motion of motion or generation of generation or in general change of change.

For in the first place, there are two senses in which motion of motion is conceivable.

The motion of which there is motion might be conceived as subject; for instance, a man is in motion because he changes from fair to dark. Can it be that, in this sense, motion grows hot or cold, or changes place, or increases or decreases? This is impossible, since change is not a subject.

Or can there be motion of motion in the sense that some other subject changes from a change as of a terminus, for instance, as a man changes from falling ill to getting well? Even this is possible only in an accidental sense.

For whatever the subject may be, motion is change from one form to another. (And the same holds good of generation and corruption, except that, in these processes, we have a change to a particular kind of opposite, while the other, motion, is a change to a different kind.)

So, if there is to be motion of motion, that which is changing from health to sickness must simultaneously be changing from this very change to another.

It is clear, then, that, by the time that it has become sick, it must also have changed to whatever may be the other change concerned (for that it should be at rest, though logically possible, is excluded by the theory).

Moreover, this other can never be any contingent change, but must be a change from something definite to some other definite thing.

So, in this case, it must be the opposite change, namely, convalescence.

It is only accidentally that there can be change of change: for instance, there is a change from remembering to forgetting only because the subject of this change changes at one time to knowledge, and at another to ignorance.

In the second place, if there is to be change of change and generation of generation, we shall have an infinite regress. Thus, if one of a series of changes is to be a change of change, the preceding change must also be so:

for instance, if simple generation was ever in process of generation, then that which was generating simple generation was also in process of generation,

such that we should not yet have arrived at what was in process of simple generation, but only at what was already in process of generation in process of generation.

And this again was sometime in process of generation, such that, even then, we should not have arrived at what was in process of simple generation. And, since in an infinite series there is no first term, here there will be no first stage, and therefore no following stage to be had either. On this hypothesis, then, nothing can become or be moved or change.

Third, if a thing is capable of motion, it is also capable of the contrary motion or coming to rest, and what is capable of generation is also capable of corruption.

Consequently, if there be generation of generation, when what comes to be comes to be, it is in process of corruption when it has reached the stage of generation,

for it cannot be in process of corruption when it is just beginning to become or after it has ceased to become, for that which is in process of corruption must be in existence.

Fourth, there must be a substrate underlying all processes of generation and changing. What can this be in the present case? It is either the body or the soul that undergoes alteration: what is it that correspondingly becomes motion or generation? And, again, what is the goal of their motion? It must be the motion or generation of something from something to something else.

But in what sense can this be so? For the generation of learning cannot be learning, and so neither can the generation of generation be generation, nor can the generation of any process be that process.

Finally, since there are three kinds of motion, the substratum and the goal of motion must be one or other of these—for instance, locomotion will have to be altered or to be locally moved.

To sum up, then, since everything that is moved is moved in one of three ways, either accidentally, or partially, or essentially, change can change only accidentally—as, for instance, when a man who is being restored to health runs or learns—and accidental change we have long ago decided to leave out of account.

660. After dividing change into generation, corruption, and motion, the Philosopher now subdivides motion into its parts.

And, because it is the same science that deals with a thing and with its opposite, he first gives the species of motion;

second, he explains the various senses of “immobile,” at the term “immobile” (226b10; [603]).

About the first, he does two things:

first, he posits a conditional proposition in the light of which he deduces the parts of motion;

second, he explains this conditional proposition, at in respect of substance (225b10; [662]).

661. Therefore, he concludes (225b5) from the previous lecture that, since motion goes from subject to subject, and subjects are involved in certain genera of the predicaments, the species of motion must be distinguished according to the genera of predicaments, especially since motions derive their nature and name from the terminus, as was said above. (Lect. 1, n. 643.) Therefore, if the predicaments are divided into ten genera of things—substance, quality, and the rest (as is explained in the Categories (Aristotle, Categories, c. 2.) and in Metaphysics 5 (Aristotle, Metaphysics Δ.7; cf. St. Thomas, Commentary on Metaphysics, bk. 5, lect. 9.))—and motion is found in three of these genera, there must be three species of motion, that is, in the genus of quantity and in the genus of quality and in the genus of where, which is said in respect of place.

The way in which motion is present in these three genera, as well as how it is related to the predicaments of action and passion, has been explained in book 3. (Lect. 5, n. 324.) Hence it is enough to mention briefly that a motion is in the same genus as its terminus, not that the motion itself would be in the genus—for example, of quality—but it is placed there by reduction.

For just as potency is reduced to the same genus as its act, inasmuch as every genus is divided by potency and act, so it is necessary for motion, which is an imperfect act, to be reduced to the genus of its perfect act.

But, when motion is regarded as being in something, though originating from something else, or as originating from one thing and being in something else, then it belongs to the predicaments of action and passion.

662. Then, at in respect of substance (225b10), he explains the conditional proposition:

first, he shows that there is no motion in any but the three genera mentioned;

second, he shows how motion is present in those three genera, at since, then, motion can belong (226a23; [678]).

About the first, he does three things.

First, he shows that motion is not in the genus of substance;

second, that it is not in the genus of relation, at nor is there motion in respect of relation (225b11; [666]);

third, that it is not in the genera of action and passion, at nor is there motion in respect of agent and patient (225b13; [668]).

He passes over the three predicaments of when, position, and habit. For “when” expresses existence in time, which is the measure of motion. Hence, for the same reason that there is no motion in action and passion, which pertain to motion, there is no motion in when. Position denotes order of parts, and order is a relation; in like manner, habit bespeaks a relationship existing between a body and what is adjacent to it. Hence, there can be no motion in position and habit any more than in relation.

That motion (225b10) is not found in the genus of substance he proves by saying that every motion is between contraries, as we have said; (Lect. 2, n. 652.) but nothing is contrary to substance. Therefore, there is no motion in respect of substance.

663. Now, there seems to be a disagreement between this doctrine of the Philosopher and what he says in De generatione et corruptione, (Aristotle, De generatione 2.3; cf. St. Thomas, Commentary on De generatione, bk. 2, lect. 3.) that fire is contrary to water. And, again, in De caelo, (Aristotle, De caelo 1.3; cf. St. Thomas, Commentary on De caelo, bk. 1, lect. 4.) he says that the heaven is capable neither of coming to be nor of ceasing to be, because it does not have a contrary—which seems to imply that things that cease to be are either contrary or composed of contraries.

To reconcile this, some assert that one substance can be contrary to another, as fire to water, in respect to form but not in respect to their subject. But if that were so, Aristotle’s proof would be worthless, for then there would be motion in substance as long as the substantial forms were contrary. For motion is from form to form, because, even in alteration, subject is not contrary to subject, but form to form.

Consequently, another explanation must be given: fire is contrary to water in respect of their active and passive qualities—which are hot and cold, wet and dry—but not in respect of their substantial forms. It cannot be said that heat is the substantial form of fire, for in other bodies, it is an accident in the genus of quality, and substance cannot be an accident of something.

But, even this answer presents a difficulty. It is clear that properties originate from the principles of the subject, that is, from matter and form. Now, if the properties of fire and water are contrary, then, since the causes of contraries are themselves contrary, it seems that the substantial forms are contrary. Moreover, it is proved in Metaphysics 10 (Aristotle, Metaphysics I.8; cf. St. Thomas, Commentary on Metaphysics, bk. 10, lect. 10.) that every genus is divided by differences that are contrary, and differences are traced to the forms, as Metaphysics 8 explains. (Aristotle, Metaphysics H.2; cf. St. Thomas, Commentary on Metaphysics, bk. 8, lect. 2.) Therefore, it seems that there is contrariety between substantial forms.

664. Consequently, it must be asserted that contrariety of differences in all the genera is based on the common root of contrariety, which is excellence and defect, to which set of contraries all others are reduced, as was explained in book 1. (Lect. 8, n. 54.) For all differences that divide a genus are so related that one is like abundance and the other is like defect in relation to the first. For which reason, Aristotle says in Metaphysics 8 (Aristotle, Metaphysics H.3; cf. St. Thomas, Commentary on Metaphysics, bk. 8, lect. 3.) that the definitions of things are like numbers in which the addition or subtraction of unity makes a different number. But nevertheless there does not need to be contrariety in every genus according to the proper account of this and that species, but only according to the common account of excellence and defect. For since contraries are things most distant, then, in order to have contrariety in a genus, there must be found two extremes that are most distant, such that between them fall all the things in that genus.

Yet that is not enough for positing motion in a genus, unless it is possible to pass without a break from one extreme to the other. Now, these two conditions are lacking in some genera, such as in numbers. For although all numbers differ according to excellence or defect, yet there cannot be found in that genus two extremes that are most distant; for it is possible to find a lowest number—that is, two—but not a greatest. In like manner, there are breaks between the species of number, since each number is formally constituted by unity, which is indivisible and not continuous with another unity.

The genus of substance is the same, since the forms of diverse species differ in respect to excellence and defect, inasmuch as one form is more noble than another, for which reason diverse qualities can be caused by diverse forms, as the objection mentions. Yet one form of a species is not contrary to another if you consider it in regard to its own specific account.

This is first of all because, when you are speaking of substantial forms, there is no maximum distance between any two forms such that you must pass through an orderly array of intermediate forms to go from the one extreme to the other.

Rather, when matter doffs one form, it can indiscriminately receive any other form without a specific order. For this reason, Aristotle says in De generatione et corruptione 2.4 (Cf. St. Thomas, Commentary on De generatione, bk. 2, lect. 4.) that, when fire comes to be from earth, it is not necessary that the intermediate elements be involved at all.

A second reason is that, since the substantial essence of anything consists in an indivisible, no continuity can be found in substantial forms such as to make a continuous motion from one form to another by one form growing weak and the other growing strong.

Hence, the proof by which Aristotle shows that there is no motion in substance—because contrariety is absent—is a demonstration, and not merely a probability, as the Commentator seems to suggest. However, besides the reason given above, (Lect. 2, n. 656.) there is another that proves that, in substance, there is no motion: the subject of substantial form is merely a being in potency.

665. In qualities of the third species, the two above-mentioned characteristics of contraries (namely, continuity and maximum distance between the extremes) are clearly manifest:

first, because qualities can be weakened and strengthened so as to make for a continuous motion from quality to quality;

second, because there exists a maximum distance between two definite extremes of one genus, as black and white in the genus of color and sweet and bitter in the genus of taste.

However, in quantity and place, one of these two characteristics is evident, namely, continuity; but the other, which is maximum distance between definite extremes, is not found in them if you seize upon the general account of quantity and place. But it is found if you look for it in a definite thing. For example, in a definite species of animal or plant, there is a minimum quantity at which the motion of growing begins and a maximum at which it is terminated. Likewise, in place, there are involved two termini that are most distant in respect to some particular motion—from one of them motion begins and at the other it is terminated—and this happens whether the motion be natural or by force.

666. Then, at nor is there motion in respect of relation (225b11), he shows that there is no motion in the genus of relation. For in any genus in which per se motion exists, nothing can newly arise in that genus without its being changed, just as new color is never found in a colored object without that object’s being changed. But it does happen that something can be newly said truly of one thing relative to another, where the latter is changed but the former not. Therefore, in relation, motion is not found per se, but only per accidens, inasmuch as a new relation follows upon some change, such as when equality or inequality accompany a quantitative change or when resemblance or dissimilarity accompany qualitative change.

667. What has just been said seems to offer difficulty in respect of some types of relation and not of others. There are some relations that do posit no reality at all in the thing of which they are predicated. This happens sometimes on the side of both extremes, as when it is said that the same thing is the same thing to the same thing, for this relation of identity would be multiplied to infinity if each thing were the same as itself through an added relation, since it is evident that each thing is the same as itself. Consequently, this relation exists only in the reasoning power, inasmuch as the reason takes one and the same thing as the two extremes of the relation. The same thing is true in many other relations.

But there are some relations in which one relation is really in one of the extremes, but only according to reason in the other, such as knowledge and the knowable. For “knowable” is a relative term that is applied to an object not because it is related to something else by reason of a relationship existing in the object, but because that something else is related to it, as is clear in Metaphysics 5. (Aristotle, Metaphysics Δ.15; cf. St. Thomas, Commentary on Metaphysics, bk. 5, lect. 17.) Another example is when a pillar is said to be on the right of an animal, for right and left are real relations in the animal (because animals possess definite energies on which these relations are based), but in the pillar they are not present in reality, but only according to reason, for the pillar lacks the energies that are the basis of these relations.

Again, there are relationships in which both extremes possess a real relation, such as equality and resemblance, for both extremes possess the quantity or the quality that serves as the root of the relationship. The same is apparent in many other relationships.

Now, in those relations that put something real in only one of the extremes, it is not hard to see that, if the extreme in which the relation really exists undergoes a change, something new will be said correlatively of the other extreme, even though it remains unchanged, since nothing really happened to it. However, in those cases in which the relation is really found in both extremes, it is hard to see how something relative can be said of A if B changes but A does not, for nothing can be newly acquired by A without A being changed.

Hence, it must be said that, if some change in someone makes him equal to me (even though I do not change at all), that equality was in a sense in me in advance as in its root, from which that equality has real existence: since I have such and such a quantity, it belongs to me to be equal to anything having the same quantity. Hence, when someone newly acquires that quantity, that common basis of equality reaches to him, which is why nothing new happens to me, when I begin to be equal to someone, since he changes.

668. Then, at nor is there motion in respect of agent and patient (225b13), he proves that motion is not in the genera of action and passion. For action and passion do not differ really from motion, but they add to it something of reason, as we said in book 3. (Lect. 5, nn. 317–18.) Hence, it is the same thing to say that motion is present in acting and being acted upon as to say that motion is present in motion.

Therefore, in regard to this, he does three things:

first, he proposes what he intends;

second, he proves his proposition, at for in the first place (225b16; [669]);

third, he posits a distinction that will explain the proposition, at to sum up, then (226a19; [677]).

Accordingly, he says (225b16) that, just as motion is not found in something relative, so also there is no motion of an agent or a patient and, strictly speaking, not even of the mover and moved, for there cannot be motion of motion or a coming to be of coming to be, which are types of change, nor even a change of change (which is the genus) or a ceasing to be of a ceasing to be.

669. Then, at for in the first place (225b16), he proves that there cannot be change of changes. And he does this with six arguments.

The first is that there are two ways of interpreting change of change. In one sense, it means that there is a change of a change, that is, of the subject that is being changed, as there is change of a man because the man is being changed from white to black (for example). In this interpretation, there would be a motion or change of a change or motion as of a subject in such a way that the motion or change is changed—for example, that the change gets hot or cold or changes place or grows or decreases. This, however, is impossible, because change is not listed among the subjects of change, for it is not a substance existing by itself. So there cannot be change of change in this sense.

670. In another way, it can be interpreted that there be change of change as of a terminus, such that a subject is moved from one type of change to another, such as from getting hot to getting cold or healthy, such that two changes are understood to be the termini of one change, as sickness and health are taken as the two termini of a change when a man is changed from health to sickness. But it is not possible for a subject to be moved per se from one change to another, but only per accidens.

And that it is impossible per se he proves in two ways.

The first is this. Every motion is a change from one definite form to another definite form; even generation and ceasing to be, which are codivided with motion, have their definite termini. But there is this difference: generation and corruption are to opposite termini of a particular kind, that is, according to contradiction, whereas motion tends to an opposite terminus of a different kind, that is, according to contrariety.

Therefore, if a subject should be passing from one change to another—for example, from getting sick to getting white—while it is at the same time changing from health to sickness, it will be passing from one change into another change. For while the subject is still partially in the terminus from which, it is being moved to the terminus to which, just as, while it still has some health, it is being moved to sickness.

Now, if the very motion from health to sickness is the terminus from which of some motion, then, while that change (from health to sickness) is still going on, the subject is at the same time passing from this change into another change, which succeeds in the subject to the first change. But it is evident that, when the first change shall have ended—that is, when someone has now already changed from health to sickness—some other change could succeed it. And this is not strange, for after the first change is over, the subject might remain at rest or it might be affected by another change. Therefore, if there is a passing from the first to the second change, it will follow that the motion goes from the first change to an indeterminate goal. And this is against the true account of per se motion, because every motion is from a definite terminus to a determinate goal, for a body does not change per se from white to just anything, but to black or to something intermediate. It is evident, therefore, that two changes cannot be the per se termini of a change.

671. He proves this same point again with another argument: if the passing from a previous changing to a subsequent change were motion per se, then it would not be necessary that the passing be always to a contingent change—that is, one that could co-exist with the previous change, as becoming white can co-exist with becoming sick, but getting well cannot co-exist with getting sick because these are contrary changes.

But it is possible that, just as becoming white can follow becoming sick in the same subject, so also could becoming well. And this is what he says: that the passing from one change to another will not always be to a contingent change, since it is sometimes to a non-contingent, and that non-contingent change proceeds from something definite to some other definite thing; that is, it is between two other termini. Hence, that non-contingent change into which something passes from the change called getting sick will be getting well, which is the opposite of getting sick.

Now, that this is strange is evident from what we have said above: while the first change is still going on, it is being changed to the second change, and thus, while something is being moved to sickness, it will be changing to another change called getting well. But the goal of getting well is health (for it is from something to something, as was said).

Hence, it remains that, while something is being moved to sickness, it is at the same time being moved to health, which means it is being moved toward two contraries at the same time and intends them at the same time—which is impossible. Consequently, it is clear that no change from one change to another is per se.

However, that such a thing can take place per accidens, as he had said before, he makes clear when he says that this can happen per accidens, as when a subject is now affected by one change and later by another—for example, if someone is changed per accidens from remembering to forgetting or to any other change—because the subject of the change is sometimes changed to knowledge and sometimes to something else, such as to health.

672. At in the second place (225b33), he presents two conditional propositions before giving the second of the six reasons he promised. The first of these is that, if there is change of change and generation of generation, it would be necessary in either case to go on to infinity, because, for the same reason, the second generation will have another generation, and so on to infinity.

The second conditional is that, if generations and changes are so arranged that there is change of change and generation of generation, then, if there is a last change or generation, there necessarily had to be a first.

This second conditional he now proves. Let fire be the thing that is unqualifiedly generated; if, then, there is a generation of generation, it is necessary to say that that unqualified generation was itself generated and that its coming to be came to be.

When, however, that generation was being generated, the fire was not existing (for it is being assumed that the fire is being unqualifiedly generated), because a thing does not exist while it is coming to be, but it exists for the first time after it has come to be.

Therefore, as long as the generation of fire was in the state of coming to be, the fire had not yet come to be; therefore, it was not yet existing. And, again, the very generation of its generation was itself coming to be, for the same reason.

Consequently, just as, when the generation of the fire was coming to be, the fire did not exist, so also, as long as the generation of the generation was taking place, the generation of the fire was not existing.

From this it is clear that generation of fire cannot exist till that generation is completed, and for the same reason, the previous generation of the generation of the fire, and so on to the first. Consequently, if there was no first generation, there will be no last—that is, no generation of the fire. But, if an infinite process be posited in cases of generation, there will be no first change and no first generation, because there is no first in the realm of the infinite. Hence, it follows that there is no following stage to be had among generations and among changes. But, if there is no generation or change, nothing comes to be and nothing changes. Consequently, if there were generation of generation or change of change, nothing would ever come to be or change.

Note, however, that this argument does not exclude the possibility of one change following another to infinity per accidens, which has to be admitted according to the opinion of Aristotle, who posited eternal motion. But the argument intends to show that there is no per se change to infinity, for in that case, a present change would depend on an infinitude of preceding changes and would never end.

673. He gives the third reason at third, if a thing (226a6), and it is this. One and the same motion has as its contraries both motion and rest; (Cf. lect. 8ff.) for example, both descending and rest in the lower place are contrary to ascending. In the same way are generation and ceasing to be contrary. But contraries are apt to affect the same thing. Therefore, whatever comes to be can cease to be.

But, if there is coming to be of coming to be, then coming to be must come to be. Therefore, coming to be ceases to be. But what ceases to be must be, for just as only what is not comes to be, so only what is ceases to be. Therefore, it is necessary that when what comes to be comes to be—that is, when something comes to be and the coming to be exists—then the very coming to be ceases to be, not indeed as soon as the coming to be is finished or some time after it is finished, but during the coming to be—which seems absurd.

But it should be observed that coming to be is as a terminus of what comes to be as a substance does, because coming to be is a change tending to substance. But the subject of coming to be is not what comes to be, but its matter. Hence, Aristotle is not departing from his proposition that there is no change of change as of a terminus.

674. He gives the fourth reason at fourth, there must be (226a10). In every coming to be, there must be matter from which that which comes to be is generated, just as every change requires some matter or subject. For example, in alteration, the subject is the body, if you are dealing with bodily qualities, or the soul, if you are dealing with qualities of soul. If, therefore, generation comes to be, there must be some matter of the generation itself (namely, which passes into the form), as the matter of generated fire passed into the form fire. However, such matter is not discoverable.

In the same vein, he makes use of another middle term: in every coming to be or change, there must be involved a goal toward which something is moved. And this goal must be something definite and capable of being pointed out. But neither change nor coming to be is such a goal. Therefore, it is not possible that there be either change of change or coming to be of coming to be.

675. He gives the fifth reason at but in what sense (226a14), which is this: genus is to genus as species is to species. If, therefore, there is coming to be of coming to be, then the coming to be of teaching is itself teaching. But this is evidently false, since teaching is the generation of science and not of teaching. Therefore, neither can there be a coming to be of coming to be.

676. He gives the sixth reason at finally, since there are (226a16), and it is this: if there is change of change, whether as of a subject or as of a terminus, then, since there are three species of motion, as was said above (motion to where and quantity and quality), it will follow that one of these species could be the subject and terminus of some other species, or even of its own species. Therefore, it will follow that local motion can be altered or even be moved locally. Such a thing is more plainly absurd when you get down to cases than when you speak in general. Therefore, it cannot be admitted that there is change of change or coming to be of coming to be.

677. Then, at to sum up, then (226a19), he shows in what sense there can be change of change. He says that, since there are three ways in which something can be moved, as was said above (Lect. 1, n. 639.)—namely, in respect to an accident or in respect to a part or per se—it is only per accidens that there could be change of change, that is, only inasmuch as the subject of the change changes. For example, if someone, while he is becoming healthy, would run or learn, then the healing process would be running or learning per accidens, just as a musician builds per accidens. But it is not our intention to treat of per accidens motion, for we have already decided to pass it by. (Lect. 1, n. 647.)