BOOK VII

Lecture 1

It is necessary that whatever is moved, be moved by another.

884. After discussing motion in itself, and the concomitants of motion, and the division of motion into parts, in the preceding books, the Philosopher now begins to treat of motion in its relationship to movers and things moved, i.e., the mobiles. The treatment falls into two parts;

In the first he shows that there is a first motion and a first mover;

In the second he investigates the properties of the first motion and of the first mover, in Book VIII.

The first part is divided into two sections:

In the first he shows that there is a first motion and a first mover.

And because things that belong to one order are mutually related, therefore in the second part he compares the various types of motion (L-7).

About the first he does three things:

First he mentions the pre-notes needed for proving the proposition;

Secondly, he proves the proposition (L. 2).

            Thirdly, he proves something he took for granted (L. 3)

885. He proposes therefore first (676) that everything that is being moved is necessarily being moved by some other. In some cases this is indeed evident, for there are some things which do not possess in themselves the principle of their motion; rather the principle of their motion is from without, as in things which are being moved by compulsion. Therefore, if there is anything that does not have in itself the principle of its own motion but its principle of motion is from without, it is clear that it is being moved by some other. However, if there is a mobile which does have in itself the principle of its own motion, there could be doubt whether it too is being moved by some other. Accordingly, he devotes himself to showing that this type of mobile is being moved by some other. Therefore, if it is supposed that such a mobile is not being moved by some other, let AB be a mobile capable of being moved primarily and according to itself and not in the sense that some part of it is being moved; for then it would not be being moved according to itself, but according to a part. Now it is necessary that if something moves itself without having been moved by some other, that it be moved primarily and per se; for example, if something is hot not from some other source, it must be primarily and per se hot.

With this in mind, he proceeds to prove his proposition in two ways:

First by excluding the most evident case in which it would appear that something is not being moved by some other;

Secondly, by proving directly that nothing can be moved by itself, at 886.

The most evident reason why it seems that something is not being moved by some other is that it is not being moved by something outside itself but by an intrinsic principle.

He says therefore first (676 bis) that to believe that AB is being moved by itself because the whole is being moved, and this without being moved by anything outside of it, is like saying that, when one part of a whole is being moved and another part causes it to be moved, it is moving itself, because it is not evident which part is the mover and which is being moved. Such would be the case if a mobile DEZ is such that one part DE moves the part EZ and it is not seen which part moves the other, and which is being moved.

When he speaks of the first mobile AB as being moved as a whole by an intrinsic principle of motion, he means a living body which is, as a whole, being moved by the soul; but when he speaks of the mobile DEZ he means some body that is not being moved as a whole but one bodily part of it is the mover and another the moved. In this latter case, it is evident that what is being moved is being moved by some other. From this latter case he wants to prove of a living body that seems to move itself that it too is being moved by some other. For it seems to move itself inasmuch as one part moves another, i.e., as the soul moves the body, as will be more fully explained in Book VIII.

886. Then at (677) he proves directly that whatever is being moved is being moved by some other. This is his argument: Nothing that is being moved by itself rests from its motion on account of some other mobile’s resting. (He takes this as per se evident). From this he further concludes that if a mobile rests on account of the rest of another, then the mobile is moved by another. On this ground he concludes that. necessarily whatever is being moved is being moved by some other. And that this follows from the premisses, he now proves.

That mobile which we have supposed as being moved by itself, i.e., ABI must be divisible, for whatever is being moved is divisible, as was proved above. Hence, because it is divisible, nothing prevents it from being divided. Therefore, let it be divided at the point C so that one part of it is PC and the other part AC. Now, if PC is part, of AB, then when the part BC rests, the entire AB must rest. But if upon the part resting, the whole does not rest, let us grant that the whole is being moved and one part is at rest. But because we have assumed that one part is resting, the whole could not be granted as being moved except by reason of the other part. Therefore, when BC (which is one part) is at rest, the other part AC is being moved. But no whole of which one part only is being moved is being moved primarily and se. Therefore AB is not being moved primarily and per se, as we originally assumed. Therefore while BC is at rest, the entire AB must be at rest. Thus, what is being moved ceases to be moved upon the occasion of something else resting. But above we held that if something rests and ceases to be moved on the occasion of another’s resting, it is being moved by that other. Therefore, AB is being moved by some other.

The same argument applies to any other mobile, for whatever is being moved is divisible and, for the same reason, if the part rests the whole rests. Therefore, it is clear that whatever is moved is moved by some other.

887. Many objections are leveled against this argument of Aristotle. For Galen objects against the statement that if just one part of a mobile is being moved and the others are at rest, then the whole is not being moved per se. Galen says this is false, because things that are being moved according to a part are moved per se.

But Galen was deceived by playing on the phrase “per se”. For sometimes it is taken in opposition to per accidens, and then it is true that what is being moved according to a part is being moved per se, as Galen said. But sometimes per se is taken in opposition both to per accidens and to what is according to a part: and in this sense something is said to be not only per se, but also primarily so. And this is the sense in which it was being used by Aristotle in his proof. That he does so is clear, because after concluding, “therefore AB is not being moved per se,” he adds, “whereas it had been assumed that it was being moved primarily and per se.”

888. But a more serious objection is that of Avicenna who says against the argument that it proceeds from an impossible assumption, from which the impossible follows, and not from the assumption that something is being moved by itself. For if we assume that a mobile is being moved first and per se, it is natural that it be moved both according to the whole and according to the parts. Therefore, if it is then assumed that a part is at rest, that is the same as assuming what is impossible. And it is from this added assumption that there follows the impossibility which Aristotle deduces, namely, that the whole is not being moved first and per se, as was assumed.

One might obviate this objection by countering that although it is impossible for a part to rest if you confine yourself to a body of a definite kind, for example, the heaven or fire, yet it is not impossible, if you consider the general definition of body, for body as body is not prevented from being at rest or in motion.

However, Avicenna forestalled such a response. First, because for the same reason it could be said of a whole body that it is not being prevented from resting just because it is a body, just as it is said of the part. Thus it was superfluous to assume, in order to prove the proposition, the division of the mobile and the rest of a part. Secondly, because some propositions are rendered impossible absolutely, if the predicate is repugnant to the subject by reason of its specific difference even though it be not repugnant to it by reason of its genus. For it is impossible for man to be non-rational, although he is not prevented from being non-rational from the fact of his being animal. Thus, therefore, it is impossible absolutely that a part of a body moving itself be at rest, for this is against the nature of any particular body, even though it be not against the common notion of body.

889. With this possible answer rejected, Avicenna solves it in another way. He says that a conditional whose antecedent is impossible and whose consequent is impossible can be true; for example, “If man is a horse, he is a non-rational animal.” It should be conceded, therefore, that it is an impossible assumption that mobile be moving itself and yet have the whole or a part of itself at rest, just as it is impossible for fire not to be hot, for fire is its own cause of its heat. Hence this conditional is true: “If a part of a mobile moving itself is at rest, the whole is at rest.” But Aristotle, if his words are carefully studied, does not speak of the rest of the part, except in a statement that has the force of a conditional. For he does not say, “Let BC be at rest,” but “If BC is at rest, AB must rest,” and “If the part rests, the whole rests”: and from this true conditional Aristotle proves his proposition.

But, says Averroes, that demonstration is not an absolute demonstration but one of the type called “demonstrating by a sign” or a demonstration “quia”, in which such conditionals are used.

However, this solution is agreeable in regard to what he says about the truth of a conditional but not in regard to the statement that it is a “quia” demonstration, for it seems to be a “propter quid’, because it contains the cause why it is impossible for a mobile to move itself.

To see this, recall that to move oneself is nothing more than to be the cause of one’s own motion. Whatever is its own cause of something must possess it primarily, i.e., first, because what is first in any group is the cause of what comes after it. Hence fire, the cause of heat for itself and for other things, is the first hot thing. But, in Book VII Aristotle showed that there is no first in motion, whether on the side of time or the magnitude or the mobile—for they are all divisible. Therefore, it is impossible to find a first whose motion does not depend on a prior, for the motion of the whole depends on the motions of the parts and is divided into those motions, as was proved in Book VI. Aristotle, therefore, thus shows the cause why no mobile moves itself: it is because there cannot be a first mobile whose motion does not depend on its parts any more than the first being can be a divisible, for the existence of any divisible depends on the parts. Hence this conditional is true “If the part is not being moved, neither is the whole,” just as this one is true “If the part does not exist, the whole does not.”

890. Hence even the Platonists, who assumed that some things move themselves, said that no body or divisible thing moves itself; rather to move itself is a prerogative of a spiritual substance which understands and loves itself (here all operations are being called “motions,” just as Aristotle in Book III of On the Soul calls sensing and understanding by the name of “motions” in the sense that motion is the act of a perfect thing). However, in this Book VII he takes motion as the act of an imperfect thing, i.e., of a thing existing in potency. It is in this sense of motion that no indivisible is moved, as was proved in Book VI and is here taken for granted. And so it is clear that Aristotle, in stating that whatever is moved is moved by some other, and Plato, in stating that some things move themselves, are here not apart in their opinions but solely in their words.

Lecture 2

No process to infinity in movers and moved.

One must arrive at a first mover unmoved.

891. After showing that whatever is moved is moved by some other, the Philosopher now turns to the proof of his main proposition, namelyq that there exists a first motion and a first mover. About this he does two things:

First he proposes what he intends;

Secondly, he proves his proposition, at 892.

He says therefore first (678) that since it has been proved for all cases that whatever is moved is moved by some other, it must be true even in regard to local motion that whatever is being moved with respect to place is being moved by something else. Now he applies to local motion in particular the very proposition which he proved universally true, because local motion is the first of the motions, as will be proved in Book VIII. Therefore, it is according to this motion that he now proceeds to demonstrate a first mover.

Therefore, let us take something that is being moved in regard to place. This thing is being moved by something else. Now that something else is in turn being moved by something else or it is riot. If it, is not, we have the proposition clinched; namely, that there exists a mover that is immovable, which is a property of the first mover. But if that something else is also being moved by something other, this other is being moved by still another which is itself being moved by yet another mover. This, however, cannot go on ad infinitum, but a halt must be made at some mover. Therefore, there will be a first mover which will be the first cause of the motion, and of such a nature that it is itself not being moved but moves the others.

892. Then at (679) he proves a statement not yet proved. About this he does three things:

First he gives the proof;

Secondly, he shows that the proof he gives is insufficient, at 893;

Thirdly, he supplies what was lacking in the insufficient proof, at 894.

He says therefore first (680) that if it is not granted that there is a first cause of the motion, then, since whatever is being moved is moved by some other, it follows that an infinite series of movers and moved is involved. And he shows that such a situation is impossible.

Let A, then, be something that is being moved in respect of place and let it be moved by B; let B be moved by C, and C by D, and so on ad infinitum in ascending order. Now it is evident that, when something moves by virtue of the fact that it is itself being moved by another, then both the mover and the mobile are being moved simultaneously, just as, when the hand by its motion moves a stick, the hand and the stick are moved at one and the same time. Therefore, B is being moved simultaneously with A, and C with B, and D with C. Therefore, the motion of A and that of all the others exist together and at the same time. And we could have considered one by one each of these infinite motions. Likewise, although each one of these mobiles is being moved by some mover—not in the sense that one is being moved by all, but one by another—nevertheless, even though there be an infinitude of movers and mobiles, yet the motion of each of the mobiles is numerically one motion. And although all the motions are infinite in number, they are not infinite in a privative sense, i.e., as though lacking a boundary, but the motion of each mobile is finite and has its own definite boundaries.

That the motion of each one of the infinite mobiles is numerically one and finite, he proves by the fact that since whatever is moved is moved between two termini, i.e., from something to something, then necessarily according to the diverse ways in which the termini are identical, the motion itself will be one in diverse ways, i.e., numerically, or specifically, or generically.

Motions are numerically the same when they are from the same terminus a quo into the same numerical terminus ad quem, provided that it takes place in the same numerical time and that the numerically same mobile is involved. To explain what he means, he adds that a motion that is numerically one is “from the same into the same”, for example, from this white, i.e., from the same numerical white, into this black, i.e., the same numerical black, and in this same numerical time— because if all the conditions but time were numerically the same, the motion would be not numerically, but specifically one.

But a motion is generically one, when it is in the same predicament, i.e., of substance or some other genus; for example, all generations of substance are generically the same, and all alterations likewise.

But a motion is specifically one, when it is from the same specific terminus to the same specific terminus; for example, every case of blackening, which is from white to black, is specifically the same, and every case of becoming depraved, i.e,, from good to bad, is specifically the same. All this was explained in Book V.

Keeping in mind, therefore, these two facts, namely, that the mover and the moved are being moved together, and that the motion of each of the mobiles can be taken as one and finite, let us take the motion of mobile A and call it motion E, and the motion of B and call it Z, and let the motion of C, D and of all the others following be called IT. Also let the time in which A is being moved be K. Now, since the motion of A is finite, then the time K of that motion is definite and not infinite, because we showed in Book VI that the finite in time corresponds to a finite in motion and an infinite in time corresponds to an infinite in motion. From what we have said, however, it is clear that in the very same time that A is being moved, B is being moved, and so for all the others; hence the motion of all, i.e., the motion EZIT, occurs in finite time. But this motion is infinite, since it is the motion of an infinite number. Therefore it will follow that an infinite motion occurs in finite time, which is impossible. Now why does our conclusion follow? Because in the very same time that A is being moved all the others are being moved and they are infinite in number.

It makes no difference, so far as our proposition is concerned, whether the motion of all the mobiles had equal velocity or not, or whether the lower mobiles move more slowly and in a greater time, because in any case it will follow that an infinite motion occurs in finite time—since each of the mobiles must have a finite rapidity and a finite slowness. However, it is impossible for an infinite motion to occur in finite time. Therefore, it is also impossible that we go to infinity in the series of mobiles and movers.

893. Then at (680) he shows that the foregoing argument is not conclusive. And he says that in the above way we seemed to have demonstrated the main proposition, namely, that one does not go to infinity in the series of movers and mobiles. Yet it is not an efficacious proof, because no impossibility flows from these premisses. For it is possible that there be an infinite motion in finite time, so long as the motion is not one and the same but other and other, insofar, namely, as an infinite number of things are being moved. For there is nothing to prevent an infinite number of things from being moved at once in finite time. And it was this that our argument concluded. For the infinite mobiles were diverse and so their motions were diverse, because for a motion to be one it is required not only that the time be one and that the termini be identical but also that the mobile be one, as was proved in Book V.

894. Then at (681) he shows how to make the argument efficacious.

First, how it can be made efficacious by making another assumption;

Secondly, how it is efficacious all by itself, at 895.

He says therefore first that what is locally and corporeally being moved first and immediately by a mobile mover must be touched by it, as a stick is touched by the hand, or must be continuous with it, as one part of the air is continuous with the next part, or as one part of an animal is continuous with another. And this seems to occur in all, i.e., that the mover is always in contact with the mobile in one of these ways.

Let us therefore take one of these ways, namely, that from all the infinite mobiles and movers there is formed one thing—namely, the whole universe—through some kind of continuity. Since this is something contingent, let us take it for granted and let that whole unit—which is a continuous magnitude—be called ABCD and its motion EZIT. And because someone could say that EZIT was the motion of finite mobiles and so not the motion of an infinite whole, he adds that, so far as our proposition is concerned, it makes no difference whether the magnitude is finite or infinite. For just as when A was being moved in a finite time K, each of the finite mobiles which are infinite in number were being moved at the same time, so also in the same time the entire infinite magnitude will be moved all at once. Therefore, an impossibility follows whichever one is taken, i.e., either a finite magnitude composed of magnitudes infinite in number, or an infinite magnitude whose motion occurs in finite time; for it has been proved above that an infinite mobile cannot be moved in finite time. Therefore the premiss from which this impossibility followed is itself impossible, i.e., that we go to infinity in the series of movers and things moved. It is clear, therefore, that the process of one thing being moved by another does not go on ad infinitum, but a halt must be made and there will exist a first mobile which is being moved by a mover that is immovable.

895. Since our proof depended on an assumption, namely, that all the infinite movers and moved form a continuum and constitute one magnitude, it might seem to someone that the conclusion is not absolute, Consequently, he adds that it makes no difference to the validity of this conclusion that it should have proceeded from this assumption. For an impossibility cannot follow from an assumption that is contingent, even if the assumption be false. Therefore, since the proof led to an impossibility, that impossibility did not follow from our contingent premiss but from some other cause which must be impossible, since an impossibility followed from it. So it is clear that in demonstrations that lead to an impossibility it makes no difference whether a false contingent assumption or something true be joined to what is impossible. For that is shown to be impossible which, by the addition of some false contingent statement, gives rise to an impossibility, just as if something impossible should follow from it by the addition of a true proposition. For just as an impossibility cannot follow from a true premiss, so neither can it from a contingent one.

896. But someone could say that for all mobiles to form one continuum is not contingent but impossible, for the elements cannot form a continuum with one another and with the heavenly bodies.

But it must be answered that “contingent” and “impossible” are taken in one sense when something is demonstrated about a genus and in another sense when something is demonstrated about a species. When a discussion is about the species, whatever is repugnant either to the genus or the specific difference, which forms the nature of the species, must be regarded as impossible. But when the discussion is about the genus, we can take as contingent anything to which the genus is not repugnant, even though the difference which constitutes a species of that genus is repugnant to it. For example, if I am speaking of animal, I can suppose as a contingent proposition that all animals are winged; but if I go a step further and consider man, it is impossible for this animal to have wings. Now since Aristotle is here speaking about mobiles and movers in a general way without making applications to particular mobiles, and to be in contact or to be continuous is a matter of indifference if you consider the general nature of mover and mobile, therefore he takes it as contingent that all mobiles mutually form a continuum, even though this is impossible if you consider the mobiles in their specific natures.

Lecture 3

In local motion mover and moved must be together

897. In the previous demonstration the Philosopher had assumed that a mover is continuous, or at least contiguous, with the mobile. This he now intends to prove.

First he proves his proposition;

Secondly, he proves something he had assumed in his proof, (L. 4)

About the first he does two things:

First he states his intention;

Secondly, he proves his proposition, at 898.

He says therefore first (682) that mover and moved are together. But something is said to be “moved” in two senses. In one sense as the end moves the agent, and such a mover is sometimes distant from the agent it moves; in another sense as that moves which is the actual beginner of the motion. It is of this latter that Aristotle speaks, and that is why he adds “not as that for the sake of which, but as that from which the source of motion is.”

Again, a mover as principle of motion can be immediate or remote. Aristotle speaks of what causes motion immediately and calls it the “first mover” which refers not to what is first in the series of movers but to a mover that is immediate to the mobile.

And because in Book V he had said that things in the same place are together, one might, conclude from that and from the statement that mover and moved are together, that when one body is moved by another they must both be in the same place. Therefore, to prevent this misunderstanding, he adds that “together” is not taken here in the sense of being in the same place, but in the sense that nothing is intermediate between the mover and the moved. It is in this sense that things in contact, or things that are continuous are together, because their extremities are together or are one and the same.

And because in the previous demonstration he proceeded solely along the line of local motion, this does not mean that his proposition is true only in cases of local motion. Therefore, to exclude this possible misunderstanding, he adds that the statement “mover and moved are together” must be taken in a sense common to all motions, for it is found in every kind of motion that mover and moved are together, in the sense explained.

898. Then at (683) he proves his proposition. About this he does two things:

First he enumerates the species of motion;

Secondly, he proves his proposition for each kind, at 899.

He says therefore first (683) that there are three kinds of motion: one is in respect to place and is called “local motion”; one is in respect of quantity and is called “growth and decrease; the third is in respect of quality and is called “alteration.” He makes no mention of generation and ceasing to-be, because they are not motions, as was explained in Book V. However, since generation and ceasing-to-be are the termini of a motion, i.e., of alteration, as was proved in Book VI, then if he proves his proposition inbregard to alteration, it will also be proved in regard to generation and ceasing-to-be.

Now just as there are three kinds of motion, so there are three kinds of mobile and also three kinds of mover. And in all it is true that the mover and the moved are together, as will be shown for each case. But first it must be proved for local motion: which is the first of motions, as will be shown in Book VIII.

899. Then at (684) he proves his proposition for each kind of motion:

First in local motion;

Secondly, in the motion of alteration, in L. 4;

Thirdly, in the motion of growth and decrease, also in L. 4.

About the first he does two things:

First he shows the proposition in cases that are evident;

Secondly, in less evident cases, at 900.

He says therefore first (684) that we must say that whatever is being moved in respect of place is moved either by itself or by something else. To say that something is “moved by itself” can be taken in two senses: first, by reason of the parts, as when we shall prove in Book VIII that in things that move themselves one part moves and another part is moved; secondly, first and per se, i.e., so that the whole moves itself according to itself and as a whole, as when he proved earlier that in this way nothing moves itself. But if it be granted that something is moved by itself in both ways, it is clear that the mover will be in what is being moved, either in the way that a same thing is in itself, or as a part is in a whole, as a soul is in an animal. Thus it will follow that the mover and the moved are together in such a way that nothing exists between them.

900. Then at (685) he proves the same, in regard to things that are moved according to place by something else, in those cases where it is less evident. About this he does three things:

First he distinguishes the ways in which something happens to be moved by something else;

Secondly, he reduces these ways to two ways, at 906 bis;

Thirdly, he proves his proposition for these two ways, at 907.

About the first he does two things:

First he divides the ways in which something is moved by something else into four: pushing, pulling, carrying and twirling. For all motions that are caused by something distinct from the moved are reduced to these four.

901. Secondly, he explains these four ways. First he explains pushing as that which occurs when the mover makes a mobile be distant from him by moving it. Pushing is of two kinds: pushing on and pushing off. Pushing on occurs when the mover pushes a mobile but does not desert it but rather accompanies it to the place it is going. Pushing off (expulsion) occurs when the mover moves a mobile in such a way that it deserts and does not accompany it to the very end of the motion.

902. Then at (687) he explains carrying as a motion based on three other motions; namely, pushing, pulling and twirling, in the same way that what is per accidens is based on what is per se. For that which is carried is not moved per se but per accidens, inasmuch as something in which it exists is being moved; as, for example, when someone is carried by a ship on which he is, or carried by a horse upon which he is. That which carries is moved per se, since one does not proceed ad infinitum in things that are moved per accidens. And thus the first vehicle is moved per se on account of some motion which is either a push or a pull or a twirls. From this it is clear that carrying is contained in the other three motions.

903. Then at (688) he explains the third way, i.e., pulling. And note that pulling differs from pushing, because in the latter the mover is related to the mobile as terminus a quo of its motion, whereas in pulling he is related as the terminus ad quem. Therefore only what moves something to itself is said to “pull.” However, the act of moving something to oneself in respect of place occurs in three ways: first in the way that an end moves, i.e., in the sense in which the poets declare that the end is said to pull, when they say that one’s own desire pulls him. It is in this sense that a place may be said to pull what is naturally moved to a place.

In a second way something is said to pull something else, when it moves it to itself by altering it somehow, so that as a result the altered object is moved in respect of place. It is in this way that a magnet is said to pull iron. For just as the generator of a thing moves heavy and light things inasmuch as it gives them the form through which they are moved to their place, so the magnet confers some quality on the iron by which it is moved toward itself. That this is true he makes clear by three facts:

First, because a magnet does not draw iron from just any distance but within a certain limit of nearness. But if the iron were moved to the magnet only as to an end in the way that a heavy body is moved to its place, it should do so no matter how great the distance they are separated by.

Secondly, because if the magnet be covered with oil, it cannot draw the iron, because the oil impedes the altering quality or modifies it.

Thirdly, because in order that a magnet attract iron, the iron must first be rubbed by the magnet, especially if the magnet is weak. It is as though the iron receives from the magnet some power by which it is moved toward it. Thus a magnet pulls the iron not only as an end but as a moving cause and as an altering cause.

In a third way something is said to pull something else, because it moves it to itself in respect of local motion only. And it is in this sense that Aristotle here defines “pulling,” i.e., in the sense that one body pulls another in such a way that the puller accompanies what it pulls.

904. This, therefore, is what he says, namely, that pulling occurs “when the motion of what pulls something toward itself or toward something else is swifter but not separated from what is pulled.” And he says “toward itself or toward something else,” because a voluntary mover can use something else just as itself; hence such a mover can both push something from something else as from itself, and pull something toward something else as toward itself. However, this does not happen in natural motions, where a natural push is always away from the pusher and a natural pull is toward the puller.

He said, “when the motion is swifter,” because sometimes what is pulled is being moved toward its objective by its own motion, but is compelled by the puller to move with a swifter motion. And since the puller acts by its own motion, the motion of the puller must be swifter than the natural motion of what is being pulled.

The reason for saying, “not separated from what is being pulled,” is to distinguish it from a push. For in some pushes the pusher separates itself from the object pushed and in some not, whereas the puller is never separated from what is pulled; indeed, both the puller and the pulled are moved at once.

Finally he said, “to itself or to something else” because a pull can be toward the puller or toward something else, as was explained for voluntary motions.

905. Since there are motions in which the presence of a pull is not clearly evident, he shows that even those are reduced to the types mentioned, i.e., that they are directed toward the puller or toward something else. And this is what he says, namely, that all other types of pulling which are not called “pull” are reduced to these two types, because they are specifically the same as one or the other of these two, insofar as a motion derives its species from its terminus—for the motions he has in mind are either toward the puller or toward something else, as is evident in inhaling and exhaling. For “inhaling” is pulling air in, and “exhaling” is pushing it out; likewise, spitting is the pushing out of spittle. The same is to be said of all those other motions by which bodies are expelled or drawn inwards, because emitting is reduced to pushing out and receiving to pulling.

In like manner, spathesis is a type of pushing and kerkisis is a type of pulling. The former comes from the Greek word for sword; hence spathesis is to cut with a sword, which is done by pushing. Kerkisis, however, is from the Greek word “kerkis”—which refers to a weaver’s tool which he pulls toward himself as he weaves, called in Latin “radius” (hence another text has “radiatio”).

These two motions, and indeed all cases of emitting or receiving are either a gathering, which pertains to drawing toward, the gatherer being one who moves something to something else, or a scattering, a scatterer being one who pushes, for a push is a motion of one thing from another. In this way it is clear that all local motion is either a gathering or a scattering, because every local motion is either from something or toward something. Consequently, all local motion is either a pushing or a pulling.

906. Then at (689) he explains twirling as a motion composed of a pull and a push, for when something is twirled, it is on the one hand pushed, and on the other being pulled.

906 bis. Then at (690) he shows that the four general ways are reduced to pushing or pulling, and that whatever can be said of all four is contained in these two. For, since carrying consists of the other three, and twirling is composed of a push and a pull, what remains is that every local motion caused by a mover is reduced either to a push or a pull. Hence it is evident that if the mover and moved are together in the motions of pulling and of pushing, so that the pusher is together with what is being pushed, and the puller with what is being pulled, then it is universally true that there is nothing between the mover, in respect of place, and what is moved.

907. Then at (691) he proves his proposition for these two motions;

First he presents two arguments that prove the proposition;

Secondly, he answers an objection, at 908.

The first argument is based on the definition of the two motions: for a “push” is a motion from the mover or from something else into something else; consequently, at the beginning of the motion the pusher must be together with what is being pushed, at least when the pusher removes from himself or from something else the object that is being pushed. A “pull,” however, is a motion toward the puller or toward something else, as we have said; a motion, I say, in which the puller is not separated from what is being pulled. Hence it is clear that in these two motions the mover and the moved are together.

The second argument is based on gathering and scattering. For it was said above that pushing is scattering and pulling is gathering. Now, no one gathers (synosis) or scatters (diosis) without being present to the things he is gathering or scattering. Therefore, it is clear that in pulling and in pushing the mover and the moved are together.

908. Then at (692) he answers an objection that could be lodged against the push. For it was said of pulling that the motion of the puller is not separated from what is being pulled. But in pushing it was said that the pusher is in certain cases removed from the object pushed. Such a case of pushing is called “projection,” which occurs when something is pushed with some force into the distance. Hence it seems that in this case the mover and the moved are not together.

To answer this he says that projecting occurs when the motion of what is thrown becomes faster than its natural motion on account of a strong impulse. For when something is projected by a strong push, the air is moved with a motion swifter than its natural motion, and with air’s motion the projected body is carried along. And so long as the air stays pushed, so long does the projectile remain in motion. This is what Aristotle says, namely, that when such a push is made, so long as there remains in the air a motion stronger than its natural motion, so long does the projectile remain in motion.

Thus, with this objection answered, he concludes that the mover and the moved are together, and that nothing intervenes between the two.

Lecture 4

It is shown in alteration, and growth and decrease, that mover and moved are together

909. After showing that the mover and moved are together in local motion, he shows the same for alteration, i.e., that there is nothing between the thing altered and the cause of the alteration. This he proves first by induction at (693). For in all things that are altered, it is clear that the last thing altering, and the first thing altered, are together. However this seems to suggest a difficulty in certain alterations, e.g. when the sun heats the air without heating the intermediate orbs of the planets, or when a certain kind of fish held in a net shocks the hand of the one holding the net without shocking the net.

To this it must be said that things which are passive undergo the action of things that are active in their own special way, and therefore the intermediate between the first cause of an alteration and the last thing altered undergo something from the first cause, but perhaps not in the same way as the last thing affected. For the net undergoes something from the fish that causes the shock, but not a shock, because it is not capable of being shocked. And the intermediate orbs of the planets receive something from the sun, namely, its light, but not its heat.

910. Secondly, at (694) he proves the same thing by an argument, which is this: Every alteration is similar to an alteration which affects a sense. But in an alteration which affects a sense the cause of the alteration and the thing altered are together. Therefore, the same is true in every alteration.

To prove the major premiss, he says that every alteration takes place according to a sensible quality, which is the third species of quality. For bodies are apt to be altered in respect of those qualities by which bodies are primarily distinguished one from the other, i.e. in sensible qualities, such as heaviness, light-ness, hardness and softness, which are perceived by touch, sound and non-sound, which are perceived by hearing. (However, if sound is considered in act, it is a quality of the air, resulting from a local motion; consequently, it does not seem that there can be a primary and per se alteration according to a quality of this sort. But if sound is taken in an aptitudinal sense, then it is through some alteration that something becomes soundable or non-soundable.) There are also blackness and whiteness, which pertain to sight; sweetness and bitterness, which pertain to taste; dryness and wetness, density and rarity, which pertain to touch. The same goes for the contraries of these and for the intermediates. Likewise, there are others which are perceptible by sense, such as cold and heat, smoothness and roughness, which are apprehended by touch.

All these are passions contained within the genus of quality. And they are called “passions” because they produce a passion in the sense (i.e., the senses come to be in the state of being acted upon) or because they are caused by certain passions, as is explained in the Predicaments. But they are called “passions of sensible bodies” because it is in respect of these that sensible bodies differ, inasmuch as one is hot and another cold, one is heavy and another light, and so on, or inasmuch as someone of them is present in two things, more so in one thing and less so in another. Fire, for example, differs from water by reason of the difference of hot and cold, and from air according to more and. less hot. Again, the difference of sensible bodies is based on the ability of some of them to receive one or the other of these qualities, although it not be in them naturally; for example, we say that heated objects differ from cooled objects and sweetened things from things made bitter, not because they are so by nature, but because they have been acted upon by these qualities.

The capacity to be altered in respect of qualities of these kinds is common to all sensible bodies both living and non-living. And some parts of living bodies are animate, i.e., capable of sensing, as the eye and the hand, and some parts inanimate, i.e., incapable of sensing, as the hair and bones, yet in either case all these parts are altered by qualities of this sort, because even the senses in sensing are acted upon. For the acts of the senses, such as hearing and seeing, are motions through the body and involve the sense being acted upon. For the senses have no action independent of a bodily organ, which is a body that is apt to be moved and altered. Hence passion and alteration are more properly spoken of in regard to the senses than to the intellect, whose operation does not take place through a bodily organ.

Thus it is evident that according to whatever qualities and according to whatever ways inanimate bodies are altered, animate bodies are altered according to the same qualities and in the same ways. But not vice versa: for an alteration is found in animate bodies that is not found in inanimate bodies, i.e., the one according to sense. For inanimate bodies do not perceive the alterations they undergo—something that would not be, if they were altered in respect of sense.

Lest anyone believe that it is impossible for something to be altered with respect to a sensible quality without a sensation of the alteration, he adds that this is true not only in inanimate things but also in the animate. For there is nothing to prevent living bodies from not perceiving that they are being affected by a quality, as when something happens in them without the sense being affected; for example, when they are altered in regard to non-sensitive parts.

From this, therefore, it is evident that if the passions of the senses are such that there is nothing intermediate between the agent and the patient, and if it is true that every alteration takes place through passions by which senses are apt to be altered, it follows that the cause of an alteration (when it is producing a passion) and the object acted upon are together, and there is nothing intermediate between them.

911. Then at (695) he proves a second point, namely, that in alterations of the senses, the altering cause and the sense affected are together, because the air is continuous with the sense, for example, of sight, i.e., they are in immediate contacts just as the visible body is in contact with the air. Indeed, the visible body’s surface, which is the subject of color, is terminated at the light, i.e., at air which is illumined, which is terminated at the sense. And so it is evident that the altered air and what alters it are together, as are the altered sight and the air which alters sight. The same is true in hearing and in smelling, if you relate them to the first mover, namely, the sensible body, for these two senses are affected by an extrinsic medium. Taste, however, and its object are together, for they are not joined by means of an extrinsic medium, and the same goes for touch. Consequently, it remains that inanimate and insensible things are related in the same way, i.e., the cause of alteration and the thing altered are together.

912, Then at (696) he proves the same thing for the motion of growth and decrease. First of all in the motion of growth. For the cause of increase and the very thing that is increased must be together, because growing is a kind of “adding to,” a quantity being increased by adding to it another quantity. The same is true of decrease, because the cause of decrease is the taking away of some quantity.

Now this proof can be understood in two ways. In one way, that the very quantity added or taken away is the immediate mover in these motions, for Aristotle says in On the Soul II that flesh increases because it is quantified. Thus it is clear that the mover and the moved are together, for nothing can be added or taken away from something unless it be together with it.

In another way, this argument can be understood in terms of the principal agent. For adding is a type of gathering and subtracting a type of scattering. But it was proved above that in the motions of gathering and scattering, the mover and the moved are together. Hence, what remains is that even in the motion of growth and decrease, they are together.

In this way, then, he concludes universally that between the last mover and the first moved there is nothing in between.

Lecture 5

Alteration is not found in the fourth species of quality (form and figure),

nor in the first (habit and disposition)

913. Because the Philosopher had assumed in the preceding argument that every alteration takes place in respect of what is sensible, he now undertakes to prove this.

First he proposes what he intends;

Secondly, he proves the proposition, at 914.

He says therefore first (697) that from what will follow it must be considered that all things that are altered, are altered according to sensible qualities, and that, consequently, to be altered belongs only to those things which are per se affected by such qualities.

914. Then at (698) he proves his proposition a majori.

First he posits the proposition;

Secondly, he proves certain things he assumed, at 915-

He says therefore first (698) that in addition to the sensible qualities (the third species of quality), alteration seems to occur especially in respect to the fourth species of quality, a quality concerned with quantity, namely, form and figure, and to the first species, which contains habits and dispositions. For when such qualities are freshly removed or newly acquired, alteration seems to be involved—for these things seem unable to occur without some changes and a change in respect of quality is alteration, as was said above.

But in the above-mentioned qualities of the first and fourth species, there is no alteration primarily and principally but only in a secondary sense, for such qualities follow upon alterations of the primary qualities, as is clear from the fact that when the underlying matter becomes dense or rare, a consequent change of figure results, In like manner, when it becomes hot or cold, there follows a change in regard to health and sickness, which pertain to the first species of quality. Rare and dense, hot and cold are sensible qualities, and so it is clear that there is not alteration in the first and fourth species of quality primarily and per se; rather the receiving or removing of them are a consequence of some alteration affecting sensible qualities.

From this is also plain why he makes no mention of the second species of quality, i.e., natural potency and impotency. For it is clear that these latter are not received or lost without a change in the nature, which takes place through alteration. That is why he did not mention them.

915. Then at (699) he proves what he had assumed:

First, that alteration does not occur in the fourth species of quality;

Secondly, that it does not occur in the first species, at 918.

In regard to the first he gives two reasons, the first of which (699) is based on the way people speak. Here it must be considered that form and figure mutually differ in this, that figure implies termination of quantity, for the figure is that which is confined by the terminus or termini; but form is something which gives artifacts a kind of species, for the forms of artifacts are accidents.

He says therefore that that from which the form of a statue comes to be is not called a form, i.e., the matter of the statue is not predicated of the statue in principali et recto, and the same for the figure of a pyramid or of a couch; rather in all such cases the matter is predicated denominatively. For we say that a triangle is wooden or golden or waxen. But in things that are altered, we predicate of the subject the quality received by the alteration, for we say that brass is wet and strong and hot, and conversely we say that the wet thing or the hot thing is brass, i.e., we predicate the matter of the quality and the quality of the matter, In fine, we say that a man is a white thing and that some white thing is a man. Therefore, because in forms and figures the matter is not predicated conversely with the figure, so that either could be said of the other in principali et recto, but rather the matter is predicated of the figure only in a denominative way, whereas in things that are altered the subject and the quality are mutually predicated, it follows that in forms and figures there is not alteration but only in sensible qualities.

916. He gives a second reason at (700) and it is based on a property of a thing. For it is foolish to say that a man or a house or anything else is altered just because it receives the end of its perfection. For example, if a house is made perfect when it gets a roof or when it is decorated or enclosed with walls, it is ridiculous to say that the house is being altered when it becomes roofed. It is also clear that alteration does not affect things that come to be, precisely as coming to be; rather a thing becomes perfect and comes to be inasmuch as it receives its own form and figure. Consequently, alteration is not involved in the receiving of figure and form.

917. In order to make these reasons clearer, we should consider that of all qualities in a thing, it is figure that both follows upon the species and indicates the species. This is particularly evident in animals and plants in which there is no more sure way to judge a diversity of species than by a diversity of figure. The reason for this is that just as quantity is the nearest of all the accidents to the substance, so the figure, which is a quality affecting quantity, is nearest to the substantial form. Hence, just as some philosophers supposed that dimensions were the substances of things, so they supposed that their figures were their substantial forms. It is for this reason that an image, which is an express representation of a thing, is based especially on the figure rather than on the color or something else. And since art imitates nature, and an artifact is an image of a natural thing, the forms of artificial things are the figure or something close to the figure. And therefore, on account of the similarity of forms and figures to substantial forms, the Philosopher says that the receiving of form and figure is not alteration but perfection. And that is also why the matter is not predicated of them except denominatively, similarly to the case of natural substances—for we do not say that a man is earth but of earth (terrenus).

918. Then at (701) he shows that there is not alteration in the first species of quality.

First in regard to habits and dispositions of the body;

Secondly, in regard to habits and dispositions of the soul, (L. 6).

In regard to the first, he gives this argument: Habits which are in the first species of quality, even if they be bodily, are called virtues and vices. For in general the virtue of a thing is what makes it good and renders its work good; hence a virtue of the body is that according to which it is well kept in itself and acts well, e.g. health; or, on the other hand, it is a vice, as is sickness.

Now every virtue and vice is spoken of in reference to something else. And this he makes clear by examples. For health, which is a virtue of the body, is a definite harmony of the hot and the cold, and I say that this harmony is in respect to the due proportion of the things beneath, i.e., of the humors, of which the body is composed, both in relation to themselves and to what contains them, i.e., to the whole body. For a proportion of humors that would be health in a lion, would be not health, but destruction, for a man, for his nature would not stand it.

The Commentator refers the phrase “to what contains them” to the surrounding air. But the first explanation is better, because the health of an animal is not considered in relation to the air; rather the disposition of the air is called healthy in relation to the animal.

Likewise, beauty and agility are said in relation to something (“agility” is taken here for the disposition whereby one is disposed for motion and action). For such dispositions are in a thing that is perfect in its nature in comparison to the best, i.e., to the end, which is operation. For, as it was said, such dispositions are called virtues because they make their possessor good and his work good,. Therefore these dispositions are described in reference to their due work, which is the best of a thing.

There is no use trying to explain “best” in terms of something extrinsic, as in the case of what is most beautiful or most healthy, as the Commentator does, for it is accidental to beauty and health that they be related to something extrinsic disposed in the best possible manner; rather what is per se is their relation to a good work.

And lest anyone understand by “perfect” a thing that has already attained its end, he says that “perfect” is here taken in the sense of what is healthy and disposed according to nature. But it must not be supposed here that such habits and dispositions are of their very nature relations, for otherwise they would not be in the genus of quality. The point is that their definition depends on a relation Of some sort.

Therefore, because habits of this kind imply a relation, and in relation there is neither motion nor generation nor alteration, as was proved in Book V, it is clear that in habits of this kind there is not alteration primarily and per se; rather a change follows upon a previous alteration of the hot and the cold or of something of this sort, just as relations begin to exist as a consequence of certain motions or changes.

Lecture 6

No alteration in the first species of quality as to habits of the soul

919. After showing that alteration does not occur in the first species of quality in respect of dispositions of the body, the Philosopher shows the same about the habits of the soul.

First as to the appetitive part of the soul;

Secondly, as to the intellectual part of the soul, at 923.

About the first he does two things:

First he shows that there is no primary and per se alteration in changes that affect virtues and vices;

Secondly, that changes involving virtue and vice are consequences of other alterations, at 921.

920. He concludes therefore first (702) from the foregoing that with respect to virtues and vices which pertain to the appetitive part of the soul there is no primary and per se alteration. And he mentions this as a conclusion, because he will proceed to prove it with the same arguments as he proved the previous points.

Accordingly, in order to prove this he makes the assumption that virtue is a kind of perfection. And this he proves in the following manner: A thing is perfect when it can attain to its own virtue (or power); for example, a natural body is perfect when it can make something like unto itself, and this is a virtue (or power) of the nature. He also proves this by the fact that a thing is most according to nature when it has the virtue of its nature (for virtue in a nature is a sign that the nature is complete), and when a thing has its nature completely, it is said to be perfect. And this is true not only in natural things, but also in mathematical, where their form is taken as the nature, for it is then that a figure is a perfect circle, namely, when it is most according to nature, i.e., when it has the perfection of that form. In this way, then, it is evident that since the virtue of a thing follows upon the perfection of its form, a thing is perfect when it possesses its virtue. Consequently, virtue is a kind of perfection.

With the premiss proved thus, the Commentator says that the full argument will be this: Every perfection is simple and indivisible; but no alteration or motion can affect what is simple and indivisible; therefore, in respect of virtue there can be no alteration,

But this reasoning will not apply to what Aristotle adds about vices, which are the removal and ceasing-to-be of a perfection. For although a perfection is simple and indivisible, yet the departure from perfection is not simple and indivisible, but occurs in many different ways. Again, it is not the custom of Aristotle to ignore a fact on which the conclusion chiefly depends, unless that fact is implied by something else he mentions.

Therefore, it is better to say that the argument here must be like the one used above for form and figure. For nothing is said to be altered, when it is being made perfect, and for the same reason, when it is being corrupted. Hence, if virtue is a perfection and vice a corruption, there will be no alteration in respect of them any more than there is in respect of forms and figures.

921. Then at (703) he shows that a change in virtue and vice is a result of some alteration. And first he proposes what he intends and says that the receiving of virtue and the removal of a vice, or vice versa, take place when something is altered in such a way that on the occasion of that alteration, there follows the receiving and loss of virtue and vice. Nevertheless, neither of these is a primary and per se alteration.

Then at (704) he proves the proposition and says that it is clear from the following that something must be altered in order that it receive or lose a vice or a virtue.

This is seen to be proved in two ways. First, according to two opinions that men have about virtue and vice. For the Stoics declared that virtues are impassibilities and that no virtue can exist in the soul unless all the passions of the soul are first removed, i.e., fear, hope, and so on, For they said that such passions are disturbances and ailments of the soul, whereas virtue is a peaceful and healthy state of soul. Accordingly, they said that the very capacity to undergo emotion is an evil or vice of the soul.

However, the opinion of the Peripatetics, derived from Aristotle, is that virtue consists in a defined control of the passions. For a moral virtue establishes a mean in the passions, as is said in Ethics II. And according to this, even the vice opposed to a virtue is not any kind of passibility at all, but a certain inclination to the passions contrary to the virtue, which are reckoned in terms of excess and defect.

Now, whichever may be true, the reception of virtue depends on some modification in the realm of the passions, i.e., either that the passions be entirely removed or that they be controlled. But the passions themselves, since they exist in the sense appetite, are subject to alteration. What remains, therefore, is that the receiving and loss of virtue and vice occur as a result of an alteration.

922. Then at (705) he proves the same thing in this way: Every moral virtue consists in some delight or sadness—for a person is not just unless he enjoys just works and becomes sad at their contrary; and the same is true of the other moral virtues. The reason for this is that the activity of every appetitive power, in which moral virtue exists, is terminated at delight or sadness, since delight follows upon the attainment of what the appetite seeks and sorrow upon the attainment of what the appetite dislikes. Hence, a person who desires or hopes is delighted when he attains what he desires or hopes. In like manner, the angry person is delighted, when he punishes. On the other hand, one who fears or hates something becomes sad when the evil he sought to escape occurs. But all sadness and delight are caused either by the actual presence of a thing or by the memory of a past thing or by hope of a future thing. Therefore, if delight concerns an actual present thing, the cause of this delight is a sense, for an agreeable thing does not delight unless it be sensed. Likewise, if the delight is based on memory or on hope, it proceeds from a sense, as when we remember sense pleasures we experienced in the past, or ones we hope to experience in the future. From which it is clear that delight and sadness are based on the soul’s sensitive part, in which alteration occurs, as was said above. If, therefore, delight and sadness are involved in moral virtue and moral vice and it is possible to undergo alteration in respect of delight and sadness, then it follows that the reception and loss of virtue and vice are consequent upon some alteration.

It is significant that he said the whole of moral virtue consists in delights and sadnesses, in order to distinguish it from intellectual virtues, which also have their own delight. But that delight is not according to sense. Consequently, it has no contrary, nor can there be alteration in respect to it, except in a metaphorical sense.

923. Then at (706) he shows that alteration is not found in the intellectual part of the soul.

First he proves this in general;

Secondly, more in detail, at 924.

In regard to the first (706) he gives this argument. Knowing is especially spoken of as in relation “to something else,” i.e., to the knowable, the likeness of which, existing in the knower, is science. This he now proves: It is only in “to something” (relation), and in no other genus, that something happens to a thing without its being changed; for something can become “equal” to something else without itself being changed, the other alone having been changed. Now we can see that even though no change occurs in the intellectual power, knowledge begins to exist in it—for merely on the occasion of something existing in the sensitive part science comes to be. In effect, from experiencing particular things, which pertain to the sensitive part, we receive knowledge of the universal in the intellect, as is proved in Metaphysics I and in Posterior Analytics II. Therefore, since there is no motion in “to something,” as was proved above, it follows that there is no alteration involved in receiving science.

924. Then at (707) he shows in detail that there is no alteration in the intellectual part.

First in the case of one who already has science and speculates upon it, which is to use science;

Secondly, in the case of one who receives fresh science, at 925

He says therefore first that, although there is no alteration in the intellectual part of the soul, it cannot be said that the use of science, which is to consider, is a type of generation, any more than we can say that when the eye externally regards an object or when one touches, there is generation. For just as seeing is the act of the visual, and touching is the act of the tactual, potency, so to consider is an act of the intellectual potency. Now, act does not imply that a principle is being generated, but rather that there is a proceeding from some active principle. Consequently, to understand is neither generation nor alteration. However, there is nothing to prevent an act from following upon generation and alteration, as, subsequent to its generation, fire heats, In like manner, on the occasion of a sense being altered by the sensible, the act of seeing or touching occurs.

925. Then at (708) he shows that there is not generation and alteration when science is newly received.

For whatever accrues to a thing solely through the subsiding of certain disturbances and motions does not accrue through generation and alteration. But science, which is speculative knowledge, and prudence, which is practical reason, accrue to the soul through the subsiding of bodily motions and sensible passions. Therefore, neither science nor prudence accrue to the soul through generation and alteration.

To elucidate this argument he gives examples. For let us suppose that some person who possesses science is asleep or drunk or sick. It is clear that he cannot at such a time use his science and act according to it. But it is also clear that, when the disturbance subsides and the mind returns to its normal state, he can then use his science and act according to it, Yet, we do not say that when a sleeping person is awakened, or someone drunk becomes sober, or when the life of a sick person is restored to due order by health, that he then becomes a knower as though science were newly generated in him, for there already existed in him a habitual potency “to the congruousness of science,” i.e., to be restored to a congruous state in which he could use his science.

Now, he says that something like that happens when a person newly acquires science. For this seems to take place on account of a certain quieting and subsiding of “turbulence,” i.e., of disordered motions, which are present in boys both in respect of their bodies, because their whole nature is undergoing change by reason of growing, and in respect of their sensitive part, because in them the passions rule.

Hence when he says “quieting,” he seems to be referring to disturbances of the body, which are calmed when nature arrives to full estate; and when he rays “subsiding,” he seems to refer to the passions of the sensitive part, which are not completely at rest but subside by reason of their being controlled by reason to the extent that they do not disturb the reason. It is in this way that we say that certain liquids have subsided when the dregs descend to the bottom and what is pure remains at the top.

Why is it that youths cannot learn by taking in what is said by others, and why is it they cannot with their internal senses judge about what they hear or somehow comes to their knowledge, as well as older persons can? It is because the former are subject to many disturbances and many commotions, as we said. But disturbances of this sort can be entirely removed or at least mitigated, sometimes by nature, as when a person reaches old age, in which motions of this kind are put to rest, and sometimes by other causes such as by training and habit. It is then that they can learn and judge well. That is why the exercising of the moral virtues, through which passions of this kind are bridled, is of great value in acquiring science.

Therefore, whether the passions are made to subside by the exercise of virtue or by nature, an alteration is involved, since these passions are located in the sensitive part, just as an alteration takes place in the body when a sleeping person arises, and becomes awake, and starts to act.

From this it is clear that newly to acquire science is not an alteration but is a consequence of an alteration.

From this, however, he further concludes universally that alteration can occur in the external senses, in sensible bodies, and in the entire sensitive part of the soul (which he says on account of the interior passions), but in no other part of the soul, except per accidens.

926. What Aristotle says here about receiving science seems to agree with Plato’s opinion. For Plato taught that just as separated forms are the cause of the generation and existence of natural things, in the sense that corporeal matter participates these separated forms in some way, so also they are the cause of science in us, for our soul somehow participates of them, in such a way that it is the very participation of separated forms in our soul which is science. In this way, it will be true that science is newly acquired, not by its being generated in the soul, but merely by the subsiding of bodily and sensitive passions, which prevented the soul from using its science. And in this way it will also be true that even though no change occurs in the intellect, a man becomes a knower by the mere presence of the sensible things of which he has experience, as occurs in relative things. This means that sensible things are not required for knowledge except for the purpose of arousing the soul.

However, Aristotle’s opinion is that science comes to be in the soul through the intelligible species, abstracted by the agent intellect, being received in the possible intellect, as is said in On the Soul III. For which reason, he says in the same place that to understand is certain “undergoing” (passio), although the way the intellect “undergoes” differs from the way the senses do.

It is not unfitting that Aristotle should here make use of the opinion of Plato. For it is his custom to make use of the opinions of others before giving his own, just as in Book III he used Plato’s opinion that every sensible body has heaviness or lightness, the contrary of which he will prove in On the Heavens I.

927. Nevertheless, these arguments based on the opinion of Aristotle are saved. To make this clear it must be considered that a receiver can be related in three ways to a form that is to be received.

For sometimes the receiver is in the final disposition for the reception of the form and no impediments exist either in it or in anything else. Under these conditions, as soon as the active principle is present, the receiver accepts the form without any further alteration, as is evident when air is illumined, the sun being present,

But sometimes the receiver is not in the final disposition required for receiving the form. In that case a per se alteration is required to put into the matter a disposition for this particular form, as, for example, when fire comes to be from air.

Sometimes the receiver is in the final disposition for the form but an obstacle is present, as when air is prevented from receiving light either by closing a shutter, or by the presence of clouds. In these cases, an alteration or changed is required per accidens, i.e., the removal of the obstacle.

Now the possible intellect, considered in itself, is always in the final disposition for receiving the intelligible species. Therefore, if there be no obstacle, then, whenever there are present objects received through experience, there will arise in the intellect an intelligible species, just as an image will appear in a mirror when a body is present. It was on this basis that Aristotle took his first argument, in which he said that science is “to something.” However, if there be an obstacles as happens in youths, then these obstacles must be removed in order to allow the intelligible species to be received in the intellect. In this case an alteration is necessary per accidens.

Lecture 7

The comparing of motions; what is required

928. After the Philosopher has shown that it is necessary to posit a first in mobiles and movers, now, because things which are of one order seem capable of being compared, and because to be “prior” and “subsequent” implies a comparison, he wishes to inquire about comparison of motions. Concerning this he does two things:

First, he shows which motions can be mutually compared;

Secondly, how motions are mutually compared, (L. 9).

About the first he does three things:

First, he raises a question;

Secondly, he objects against both parts of the question, at 929;

Thirdly, he settles the question, at 933.

First he raises a general question (709) and asks whether just any motion at random may be compared to just any other motion or not. Then he raises a special question about motions in some one genus. Now if any motion at random may be compared to just any other motion with respect to swiftness and slowness (it having been said in Book VI that the equally swift is what is moved in equal time over an equal space), it will follow that a circular motion will be equal, or greater, or less, in swiftness than a rectilinear one, and further, that a curved line will be equal to a straight line in quantity, or larger or smaller, from the fact that the equally swift is that which traverses an equal distance in equal time.

Then he raises a question about motions in diverse genera. For if all motions may be compared with respect to speed, it will follow that if in an equal time A is altered, and B is moved locally, then a local motion is equal in swiftness to an alteration. Further, by virtue of the definition of the equally swift, it will follow that a passion, i.e., passible quality, in respect of which there is alteration, is equal to the length of the distance traversed by the local motion. But this is plainly impossibles because they do not agree in the same notion of quantity.

929. Then at (710) he raises objections against the question proposed:

First, he objects against comparing alteration with local motion;

Secondly, against comparing circular motion with rectilinear, at 930.

First (710), therefore, from the foregoing argument which leads to an impossibility, he concludes to the contrary of what he posited, as though saying that, since it has been said that it is not feasible for a passion to be equal to a length, while whenever something is moved through an equal space in equal time, it is said to be equally swift, therefore, since no passion is equal to a length, it follows that a local motion is not equal in swiftness to an alteration, or greater or less. From this it may be further concluded that not all motions can be compared.

930. Then at (711) he considers the other part of the question, i.e., concerning circular and rectilinear motion.

First he objects against a circular motion’s being as equally swift as a rectilinear motion;

Secondly, he takes the contrary position, at 932.

About the first he does two things:

First he objects against the proposition;

Secondly, he dismisses a quibbling response, at 931.

He objects first (711) in the following manner. Circular motion and rectilinear are differences of local motion, just as upward and downward are. But as soon as something is moved upwards and something else downwards, it is at once necessary that one be being moved faster or slower than the other—the same is true if the same thing is moved now upwards and later downwards. It seems therefore that in like manner we must say that a rectilinear motion is swifter or slower than a circular one, whether it be the same thing that is being moved in a straight line and in a circular one, or two different things.

It should be noted that in this argument he makes no mention of the equally swift but of the swifter and slower, because this argument is based on the likeness of an upward motion—whose principle is lightness—to a motion which is downward—whose principle is heaviness. Some, indeed, have held that heaviness and lightness are the same as swiftness and slowness—an opinion he rejected in Book V.

931. Then at (712) he rejects a quibble. For someone could concede on account of the foregoing reason that a circular motion is either swifter or slower than a rectilinear ones but not equally swift.

This he rejects, saying that it makes no difference, so far as the present discussion is concerned, once someone grants that it is necessary for what is being moved circularly to be moved more swiftly or more slowly than what is being moved in a straight line. For according to this the circular motion will be faster or slower than the rectilinear. Hence it follows that it could also be equal.

That this follows he now proves. Let A be the time in which the swifter traverses B, which is a circles and let something slower traverse the straight line C in the same time. Now, since the swifter traverses more in the same time, it will follow that circle B is larger than the straight line—that is the way the swifter was defined in Book VI. But we also said in that place that the swifter traverses an equal distance in less time. Therefore, we can take of time A a part during which the circularly moving body will traverse a part of this circle B and during which it will traverse C, while the slower body is traversing C in the entire time A. It will follow, therefore, that that part of the circle is equal to the entire C, because one and the same object traverses an equal distance in equal time. And in this way, a circular line will be equal to a straight line and a circular motion will, consequently, be as fast as a rectilinear.

932. Then (713) he takes the contrary position. For if circular and rectilinear motions may be compared with respect to swiftness, it follows, as just said, that a straight line will be equal to a circular one, for the equally swift is what traverses an equal distance. But a circular line and a straight line cannot be compared, so as to be called equal. Therefore, neither can a circular motion be said to be as swift as a rectilinear.

933. Then at (714) he settles the difficulty he raised.

First he asks in general what may be compared to what;

Secondly, he adapts this to his proposition, (L. 8).

About the first he does three things:

First he states one thing that is required for comparison;

Secondly, a second thing, at 937.

Thirdly, he concludes a third requirement, (at 939)

About the first he does three things:

First he mentions what is required for comparisons;

Secondly, he takes the contrary position, at 935;

Thirdly, he settles the matter, at 936.

934. He says therefore first (714) that things seem to be capable of being compared so long as they are not equivocal, that is, in the line of things not predicated equivocally the subjects of predication may be compared. For example, “sharp” is an equivocal term: for in one sense it is applied to magnitudes, as when an angle is said to be “sharp” (acute) and when a pen-point is said to be “sharp”; in another sense it is applied to savors, as when wine is said to be “sharp” (dry); in a third sense it is applied to notes, as when the ultimate, i.e., highest, note in a melody, or a chord of a lyre is said to be “sharp.”

Now, the reason why no answer can be made to the question, “Which of these is sharpest, the point, the wine or the voice?” is because “sharp” is predicated of them in an equivocal sense. But the highest note can be compared with respect to sharpness to another which is next to it in the scale, because in this case “sharp” is not taken equivocally, but is predicated of both in the same sense.

Therefore, according to this, it could be replied to the proposed difficulty that the reason why a straight motion cannot be compared to a circular one is because the word “swift” is being used equivocally. And much less is the meaning of “swift” the same in respect to alteration and local motion. Consequently, these two are even less capable of being compared.

935. Then at (715) he objects against what was just said. And he says that at first sight it does not seem to be true that things may be compared so long as they are not equivocal. For there are some non-equivocal things which cannot be compared; for example, “much” is used in the same sense when applied to water and to air, yet water and air cannot be compared with respect to muchness.

Now if someone refuses to admit that “much” signifies the same thing on account of its general nature, he will at least grant that “double,” i.e., twice as much as, which is a species of muchness, signifies the same thing in regard to air and to water; for in both cases it signifies the ratio of 2 to 1. Nevertheless, air and water cannot be compared in terms of double and half, so as to be able to say that the amount of water is double that of the air or vice versa.

936. Then at (716) he answers this objection. About this he does two things:

First he gives the solution;

Secondly, he confirms it by raising another question, at 937.

He says therefore first that it could be said that in “much” and “double” we discern the same reason for their inability to be compared, when they are applied to water and to air, as was discerned in “sharp” when it was applied to pen and wine and note; for “much” itself is equivocal.

Now, because someone could object against this on the ground that the same notion of “much” is referred to when it is applied to both, then in order to reject this, he states that even the notions, i.e., definitions, of certain things are equivocal. For example, if someone should say that the definition of “much” is that it is “this amount and yet more,” “to be this amount” and “to be equal,” which is the same thing, is equivocal, for “to be equal” is to have one quantity, but the definition of “one quantity” is not the same in all things. (The notion of “much,” as used here, implies a comparison in the sense that it is the opposite of “a little,” i.e., it is not taken in its absolute sense of being the opposite of “one.”)

And what he said of “much” he says consequently of “double.” For although the notion of “double” is that there is a ratio of 2 to 1, yet even that notion contains an equivocation, for it could be said that “one” is equivocal; and if “one” is equivocal, it follows that “two” is, because “two” is nothing more than “one” taken twice.

Now it should be observed that there are many things which, when considered in an abstract way in logic or mathematics, are not equivocal, but which are in a certain sense equivocal when they are taken in a concrete way, as the philosopher of nature takes them when he applies them to matter, for they are not taken according to the same aspect in all matter. For example, quantity, and unity (which is the principle of number) are not found according to the same aspect in the heavenly bodies, and in fire and air and water.

937. Then at (717) he confirms what has been said by raising a certain other question. For if it be held that there is one nature of “much” and of “double” and of other like things which cannot be compared, as there is also one nature of things that are predicated univocally, the question still remains, why it is that among things having one nature some can be compared and some not. For it seems that when things are similar, there should be a same judgment about them.

Then at (718) he answers this question by positing the second requirement for things to be compared. About this he does two things:

First he mentions the second requirement;

Secondly, he shows that even that one is not enough, at 938.

He says therefore first (718) that the reason why some things possessing one nature can be compared, while other things having one nature cannot, could be that when some one nature is received according to one first subject in diverse things, they will be comparable, as horse and dog can be compared with respect to whiteness, one being able to be said “whiter” than the other, because not only is the same nature of whiteness in both, but there is one first subject in which whiteness is received, namely, the surface. In like manner, the magnitude of each may be compared, so that one can be called “larger” than the other, because there is one same subject of magnitude in each, namely, the substance of a mixed body. But water and a note cannot be compared with respect to magnitude so as to say that the note is “greater” than the water or vice versa, because although magnitude in itself is the same, the receiver of it is not the same. For when magnitude is said of water, its subject is a substance, but when it is said of a note, its subject is sound, which is a quality.

938. Then at (719) he shows that this second requirement does not complete the list of requirements, for two reasons. The first of these is this: If things were comparable just because there is a non-differing subject, it would follow that all things have one nature, for it could be said of all things whatsoever that they do not differ except insofar as they exist in some one or other first subject. And according to this, it would follow that “to be equal” and “to be sweet” and “to be white” are one and the same nature, differing only by reason of being received in one or another receiver. And this is seen to be unacceptable, namely, that all things have one nature.

But it should be noted that positing a diversity of things on the sole ground of diversity of subject is a Platonist opinion, which attributed unity to form and duality to matter, so that the entire reason of diversity came from the material principle. That was why he stated that “one” and “being” are predicated univocally, and that they signify one nature but that the species of things are diversified by reason of a diversity of receivers.

The second reason which he gives, at (720), is that not just anything is capable of receiving just anything else at random, but one is primarily the receiver of one; consequently, the form and what receives it are in proportion. Therefore, if there are many first receivers, there must necessarily be many natures capable of being received; or if one nature has been received, then necessarily there is one first receiver.

939. Then at (721) he concludes that there is a third requirement for things to be comparable. And he says that things which can be compared must be not only non-equivocal (which is the first requirement) but must also not possess any difference either on the side of the first subject in which something is received (which is the second requirement) or on the side of what is received, which is a form or a nature (and this is the third).

And he gives examples of this third requirement. For “color” is divided into various species of color; hence it cannot be compared solely on the ground that it is predicated of these colors, even though it be not predicated equivocally, and even though it have one first subject, which is a surface, and which is a first subject of the genus “color”, but not of any species of color. For we cannot say which is more colored, white or black, because this comparison would not be in terms of some definite species of color, but in terms of color in general. But in terms of whiteness, which is not divided into various species, all white things may be compared, so that it can be said which one is whiter.

Lecture 8

Which motions may be compared

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.

First in general;

Secondly, by comparing motions that belong to diverse genera, at 941;

Thirdly, by comparing one motion to another in the same genus, at 942.

He says therefore first (722) that just as in other matters the requirements for comparability are that the things compared be not equivocal, and 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, with respect to a change of the same kind.

941. Then at (723) he discusses the comparison of motions in diverse genera. And he asks, in keeping with what went before, “If one mobile be altered and another moved locally, can the alteration be said to be ‘as swift as’ the local motion?” To say “yes” would be unacceptable. The reason is that the two motions are of different species—and it has already been said that things not of the same species cannot be compared. Therefore, since local motion is not of the same species as alteration, the swiftness of the two cannot be compared.

942. Then at (724) he discusses the comparison of motions in some one species within some one genus.

First as to change of place;

Secondly, as to alteration, at 949;

Thirdly, as to generation and ceasing-to-be, at 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;

Secondly, he shows that one factor which seems to be required is not, at 945;

Thirdly, he concludes to what he chiefly intended, at 946.

About the first he does two things:

First he concludes to the impossibility that would follow if all local motions could be compared;

Secondly, he tells why not all can be compared$ at 944.

943. He says therefore first (724) that if the equally swift are things moved locally through an equal magnitude in equal time, and if 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, secondly, 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 impossible.

944. Then at (725) he investigates the reason why rectilinear motions cannot be compared with circular ones. For since he had concluded that if they are equal, then the magnitudes are equal—which is seen to be impossible—someone might wonder whether the reason for this inability to be compared is due to the motion or to the magnitude. And this is his question: “Is the reason why a straight motion is not as equally swift as a circular one due to 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 because line is a genus containing under it straight and circular as species?” Of course, time cannot be the reason, for all time is “atomic,” i.e., indivisible, as to species.

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

945. Then at (726) he rejects a factor that might seem to be required for identity of species and comparability in local motions. And he says that sometimes changes of place are diversified by reason of “that in which,” i.e., by reason of that through which, as through an instrument, a local motion takes place; 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, as the Commentator says.

However, it could possibly better be 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 lean more to the mobile, whereas figures are on the part of that in which the motion occurs.

946, Then at (727) he concludes his proposition. Concerning this he does three things:

First he concludes to the main proposition;

Secondly, he draws from the conclusion a fact to be considered, at 947;

Thirdly, he investigates the problem of diversity of species, at 948.

He concludes therefore first (727) that since motions are not comparable unless they are of the same species, and local motions are not of one species unless they traverse the same specific magnitude, it follows that those are equally swift which 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 accidentals, they can be.

947. Then at (728) he draws from the foregoing a fact worthy of consideration, namely, that 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; and secondly, from the preceding lecture, in which it was stated that the nature of comparable things is one. 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 ultimate form, which is absolutely one in the universe of things, but the genus is not taken from a form that is one in the universe of things but from one that is so in conception only. For the form on account of which man is animal is not distinct from the one on account of which man is man. Therefore, all men who are of one species agree in the form which constitutes their species, because each has a rational soul. But there is not in man, horse, and ass, some common soul which makes them animal, over and above the soul that makes one a man, or 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, because according to the diverse forms existing in the universe of things, diverse species are capable of receiving a same genus as a predicate. Consequently, a genus is one thing logically but not physically.

Now, because a genus, although not purely one, is still in some sense one, 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 a heavenly body, and the animal which 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.

Still 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 schools, the other in the house, Hence, on account of their close resemblance in genus or likeness things do not appear to be equivocal which nevertheless are.

948. Then at (749) because he had said that we must consider the question of the differences of motion, i.e., whether motions differ specifically, he now inquires how specific differences may be taken in motions and in other things as well. 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 some same thing is in one and another, except for the Platonists who posited that a genus is absolutely one. On this account, as though answering the question, Aristotle adds that a species is different, not because the same thing is in a different subject, but because a different nature is in a different subject.

The second question is about definition, and it is this: “What is a term, i.e., what is the definition which 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 some thing is the same or other, e.g. 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, because 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 (730) he discusses the comparison of alterations, About this he does two things:

First he shows that one alteration is as equally fast as another;

Secondly, he investigates from what aspect equality of quickness in alteration is considered, at 950.

He asks therefore first about alteration, how one alteration is as equally fast as another. And that two alterations are equally fast, he proves. 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 equally swift as another, for what is moved in an equal time is said to be moved with equal speed.

950. Then at (731), because equality of speed in local motion requires not only equality 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. And this is what he says: “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, equal is not found, so 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 as equality is found in quantity, likeness is found in quality.

To this question he responds at (732). And first he answers the question, and says that alterations should be called equally swift if in an equal time it is the same thing which has been changed, i.e., altered.

951, Secondly, 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 secondly, the subject in which the quality exists, the question arises: “Should a comparison of this sort be regarded from the viewpoint of the identity of the quality or of the identity of the subject in which the quality exists?”

952. Then at (734) 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, that the same specific quality be involved, for example, the same health, of the eye or of something similar; secondly, that the quality which is taken be present in the same way, and neither more nor less. But if the qualities in question differ specifically, e.g., if one alteration involves becoming white, and another healthy, 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, so 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 which are moved, i.e., 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 V.

953. Thirdly, at (735), having determined one part of the question he raised, he now attacks the other. The question is this: “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 which 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, i.e., to the quality involved and to 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 (736) he shows how comparison should be made with respect to generation and ceasing-to-be.

First, according to his own opinion;

Secondly, according to the opinion of Plato, at 955.

He says therefore first (736) 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 example, if in the time required for the generation of a dog, a horse should be generated, the generation of the horse would be swifter.

And because he had said that, in alteration, from the viewpoint of the quality involved, two things must be considered, 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: “For we do not have two things in which there is an otherness called unlikeness.” It is as if he said: “The reason why in generation the only thing to be considered is whether it is the same 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 (737) 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” which 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 yet 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, i.e., the diversity which arises from the largeness and smallness of number, whereas 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”, while 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.

Lecture 9

Rules for the comparison of motions

956. After showing which motions are mutually comparable, the Philosopher now teaches how they are compared:

First in local motions;

Secondly, in other motions, at 962.

About the first he does two things:

First he mentions the aspects according to which local motions ought to be mutually compared;

Secondly, he sets forth the rules of comparison in the light of the foregoing, at 957.

He says therefore first (738) that the mover in local motion always moves some mobile, in some definite time, and through some quantity of space. And this is required, because, as was proved in Book VI, something always moves and has moved, simultaneously. For it was proved there that whatever is being moved has already been moved through some part of a distance and through some part of time. Hence it follows that what is being moved is something quantitative and divisible, as are the distance and the time involved. However, not every mover is quantified, as will be proved in Book VIII; nevertheless, it is clear that some quantitative things are movers and it is in respect to those that he proposes the following rules of comparison,

957. Then at (739) he lays down the rules of comparison.

First according to division of the mobile;

Secondly, when the mover is divided, at 958.

He says therefore first (739): Let A be a mover, and B a mobile, and C the length of space traversed, and D the time in which A moves B through C. If therefore we take another moving power, equal to the power of A, it will follow that it will move half of the mobile B through a distance twice C in the same time; but in half the time D it will move half of mobile B through the entire length C,

From these statements of the Philosopher two general rules may be gathered. The first is that if some power moves a mobile through some certain distance in a given time, then it or an equal power will move half of that mobile through twice the distance in the same time or in an equal time.

The other rule is that an equal power will move half the mobile over the same distance in half the time. The reason behind these rules is that the same proportion is being kept. For it is clear that the swiftness of a motion results from the victory of the mover’s power over the mobile, because the weaker the mobile the more the strength of the mover prevails over it and the more swiftly will it move the mobile. The swiftness of a motion cuts down on the time and increases the length traversed, for the swifter is what traverses a greater distance in an equal time or an equal distance in less time, as was proved in Book VI. Therefore, according to the same proportion by which the mobile is diminished, either the time is diminished or the length traversed is increased, provided, of course, that the mover is the same or an equal mover.

958. Then at (740) he teaches how motions are to be compared from the viewpoint of the mover,

First according to a division of the mover;

Secondly, and conversely, according to an assemblage of movers, at 9610

About the first he does three things:

First he sets forth a true comparison;

Secondly, he rejects some false comparisons, at 959;

Thirdly, from this he answers an argument of Zeno, at 960.

He says therefore first (740) that if a power moves the same mobile through a certain distance in a given time, it moves half the mobile the same distance in half the time, or it moves half the mobile through twice the distance in the given original time, as was said of an equal power. Further, if the power be divided, half the power will move half the mobile through the same distance in the given time. However, this must be understood of a mover that is not destroyed by division, for he has been speaking in a general way without making application to the particular natures involved. And he gives an example: Let E be half of power A and let Z be half of mobile B, then just as A moved B through C in time D, so E will move Z through the same distance in the same amount of time, because the same proportion of motive power to body mass moved is preserved. Hence, it follows that in an equal time the motion will traverse an equal distance, as was said.

959. Then at (741) he rejects two false comparisons. The first consists in adding to the mobile without adding to the motive power. Hence he says that if E, which is half the motive power, moves Z9 which is half the mobile, a distance C in time D, it is not necessarily true that the halved power E will move a mobile twice Z through half the distance in the given time, for it could happen that the halved power cannot move the doubled mobile at all. But if it can move it, the comparison will hold.

The second false comparison occurs when the mover is divided and the mobile is not divided. This he rejects at (742), saying that if the motive power A moves the mobile B through distance C in time D, it does not necessarily follow that half the motive power will move the entire mobile B in time D through a part of distance C such that this part of C is related to the entire distance C as A was related to Z in our other example. For when A was compared with Z, it was a suitable comparison, but in the present case it is not, for it can happen that half the motive power will not move the whole mobile any distance. For if some whole power moves some whole mobile, it does not follow that half of it will move the same mobile any distance, no matter how much time is allowed. Otherwise it would follow that a man by himself could move a whole ship a certain distance, if the combined power of the shiphaulers is divided by the number of haulers and the distance they haul it be so divided.

960. Then at (743) he uses the foregoing to answer an argument of Zeno who wished to prove that each grain of millet falling to the earth makes a sound, because an entire bushel of it, when poured to the earth, makes a sound. But Aritstotle says that this argument of Zeno is not true, i.e., that each grain of millet makes a sound when it falls to the earth. For there is no reason why any such part should in any length of time move the air to produce a sound, as does the whole bushel in falling.

And from this we can conclude that it is not necessary, if a part existing in a whole causes a motion, that this part, now existing in isolation from the whole, can cause a motion. For in the whole the part is not actual but potential, especially in continua. For a thing is a being in the same way that it is one, and “one” is that which is undivided in itself and divided from others. But a part, precisely as existing in a whole, is not actually divided from it but only potentially; hence it is not actually one but only potentially. For this reason, it is not the part but the whole that acts.

961. Then at (744) he sets forth a comparison based on an aggregate of movers and says that if there are two and each of them causes motion and if each by itself is moving its own mobile a certain distance in a given time, then when the two are united they will move the mobiles—which are now joined together—through an equal distance in the same time, because even in this case the same proportion is maintained.

962. Then at (745) he sets forth the same rules of comparison for other motions. About this he does three things:

First he shows that the things according to which the comparison of motions must be judged are divisible;

Secondly, he sets forth the true comparison, at 963;

Thirdly, he rejects some false comparisons, at 964.

He says therefore first (745), in respect to growth, that there are three things involved, namely, the cause of increase, the thing increased, and the time; and these three have a certain quantity. Also there is a fourth thing to be considered, namely, the quantity of increase produced by the cause and received by the growing thing. And these four things must be considered also in alteration, namely, the cause of alteration, the thing altered, the amount or degree of alteration (which is present according to more and less), and the amount of time. These four, of course, are the same as are involved in local motion.

963. Then at (746) he sets forth the true comparison and says that if a power moves something to a certain amount in a given time according to these motions, then it will move to twice the amount in twice the time; and if it moves to twice the amount, it will be in twice the time. Likewise, the same power will move to half the amount in half the time, or if it moves in half the time, then the motion will be to half the amount, Or if there is twice the power, it will move something to twice the amount in an equal time.

964. Then at (747) he dismisses a false comparison and says that if what causes alteration or increase causes a certain amount of increase or alteration respectively in a certain amount of time, it does not necessarily follow that half the force will alter or increase half the object or some given amount in half the time; for it may happen that there will be no alteration or increase at all, the case being the same as with the locally mobile that has weight.

It should be observed that when Aristotle says “half will be moved in half or double will be moved in an equal,” “double” and “half” (in the accusative case) refer, not to the mobile but to the sphere of motion, i.e., the quality or the quantity, which are related to alteration and growth as length of distance is related to local motion. For in local motion it was said that if a certain power moves a certain mobile, half will move half the mobile, but here it is said that half might not move anything. But it must be understood that we are speaking of an integral mobile whole, which will not be moved by a halved motive power to any amount of quantity or degree of quality, much less to half.