BOOK V

Lecture 1

Per se notion is distinguished from per accidens

638. After discussing motion and the things that accompany motion in general, the Philosopher now undertakes to give various divisions of motion. And his treatment falls into two parts:

In the first he divides motion into its species;

In the second he divides motion into quantitative parts in Book VI.

In the first he makes two parts:

First he divides motion into its species;

Secondly, he discusses unity and opposition of motion, at L. 5.

The first is divided into two sections:

In the first he distinguishes motion per se from per accidens;

In the second he divides motion into its species, at L. 2.

The first is divided into two parts:

In the first he distinguishes per se motion from per accidens;

In the second he shows that per accidens need not be discussed but that per se motion must, at 647.

In regard to the first he does two things:

First he distinguishes per se from per accidens motion;

Secondly, he makes a summary at 646.

In the first part he distinguishes per se motion from per accidens motion in three ways:

First, on the side of the mobile;

Secondly, on the side of the mover, at 640;

Thirdly, on the side of the termini of motion, at 641.

639. He says therefore first (465) that whatever changes, i.e., whatever is being changed, is described as doing so in three ways. First, per accidens, as when we say that a musician is walking, because the person who is walking happens to be a musician. Secondly, a thing is described as being changed without qualification even though only some part of it is changing, i.e., in statements which refer to part of the thing in question: thus the body is said to be restored to health, because the eye or the chest, which are parts of the body, are restored to health. Thirdly, there is the case of a thing that is in motion neither accidentally nor in respect of something that belongs to it as a part but in virtue of its being directly and per se in motion. And he says “directly” to exclude motion of a part, and per se to exclude motion that is per accidens. Now this per se mobile is a different thing according to the various kinds of motion: for example, it may be a thing capable of alteration—in which case it is called alterable—or it may be capable of growing—in which case it is called augmentable. Again, in the sphere of alteration it is called heal-able, if it is moved in respect of health, and heat-able, if it is moved in respect of heat.

640. Then at (466) from the side of the mover he distinguishes per se from per accidens motion, And he says that the preceding distinctions which were posed from the side of the mobile can be found in the mover. For a thing is described in three ways as causing motion. First, per accidens, as “the musician is building”. Secondly, by reason of a part (when some part of the mover causes motion), e.g., the man is said to strike, because his hand strikes. In a third way, something is described as acting or moving directly and per se, as “the healer heals”.

641. Then at (467) looking at the terminus of motion, he divides motion once more in the same manner.

First he lays down some presuppositions;

Secondly, he gives his division, at 645.

About the first he does three things:

First he declares how many things are required for motion;

Secondly, he mutually compares them, at 642;

Thirdly, he settles a question, at 644.

He says therefore (467) that five things are needed for motion, First, there must be a first mover, i.e., a source from which the motion originates; secondly, a mobile that is being moved; thirdly, a time in which the motion occurs. In addition to these three are required the two termini; one from which the motion starts and another into which the motion tends; for every motion is from something into something.

642. Then at (468) he compares these five things:

First he compares the mobile to the two termini;

Secondly, he compares one terminus with the other, at 643,

He says therefore (468) that whatever is being moved directly and per se is distinct from the terminus into which the motion tends and from the terminus from which the motion begins, as is evident in these three things: wood, hot and cold. For in the motion called heating, the wood is the mobile subject, whereas the hot which is the terminus into which, is something else, as is the cold, which is the terminus from which.

Now he says that what is moved directly is distinct from both termini, because there is nothing to prevent what is being moved per accidens from being either of the termini: for a subject, such as wood, is what becomes hot per se; but the privation, which is a contrary, namely, cold, is what becomes hot per accidens, as was explained in Book I.

That the mobile is distinct from each terminus he proves on the ground that motion is in its subject, for example, in the wood, and not in either of the termini, i.e., not in the species “white” or in the species “black”. This is clear from the fact that that in which the motion exists is what is being moved. But the terminus of motion neither moves nor is moved: whether the terminus be a quality, as in alteration, or a place, as in local motion, or quantity, as in the motion called growing and decreasing. However, the mover moves the subject, which is being moved, into the terminus ad quem, Therefore, since motion exists in the subject being moved but not in the termini, it is clear that the mobile subject is distinct from the termini of the motion,

643. Then at (469) he compares one terminus with the other. And he says that a change gets its name from the terminus ad quem rather than from the terminus a quo; for example, a change into non-being has the special name “corruption’, while, on the other hand, “generation” is the change into being, even though it starts from non-being. Consequently, the name “generation” pertains to being and “corruption” to non-being. The reason for this is that through change the terminus a quo is taken away, but a terminus ad quem is acquired: for which reason, motion seems to have a repugnance for the terminus a quo and a kinship to the terminus ad quem—that is why it gets its name from the latter.

644. Then at (470) he settles a doubt, About which he does three things:

First, he mentions two things that are clear from the foregoing: first, that we have already pointed out in Book III what motion is; secondly, that in the immediately foregoing we have said that qualities and place and passible qualities that are the termini of motion are not themselves being changed, since there is no motion existing in them, as we have already said and as is clear from heat, which is a passible quality, and from science, which is a quality.

Secondly, at (471) he mentions a matter about which there is doubt, saying that someone may wonder whether passible qualities, such as heat and coldness and whiteness and blackness might not be types of motion, since none of them is a subject of motion.

Thirdly, at (472) he mentions a discrepancy that would arise if such a view were posited. For since whiteness is a terminus into which a motion tends, then if whiteness itself were a motion, it would follow that there is motion in the terminus of a motion, which cannot be, as will be proved later. And from this he arrives at the truth that it is not whiteness but whitening that is motion, But he adds “perhaps” because he has not yet proved that a motion cannot end up in a motion.

645. Then at (473) from the fact that termini of motion are distinct from the mover and from the mobile, he shows that in addition to the divisions of motion taken on the side of the mover and of the mobile, there is a third, i.e., one taken on the side of the terminus. And since it is from the terminus ad quem rather than from the terminus a quo that motions are named, he develops his division not on the side of the latter but of the former. And he says that even on the side of the termini it is possible to find in motion (1) a goal that is so per accidens or (2) partially, i.e., with reference to a part or to something other than itself or (3) directly and not with reference to something else.

And first of all, per accidens: when it is said of what is becoming white that it is being changed into something that can be understood or recognized by someone—that will be per accidens for it is accidental to the color white that it is recognized.

But if it is said of what is becoming white that it is being changed into a color—this will be according to a part: for it is said to be changing into a color because it is becoming white, which is a part of the genus color. Likewise, if I should say of someone who is going to Athens that he is going to Europe, for Athens is a part of Europe.

However, if it is said of what is becoming white that it is being changed into the color white, this will be directly and per se.

The Philosopher does not divide motion from the viewpoint of time (which was one of the five things required for motion) because time is related to motion as an extrinsic measure.

646. Then at (474) he summarizes what he has said. And he says that it is clear how something is in motion per se and how per accidens and how in respect of something not its entire self, i.e., in respect of a part, and again how what is referred to as directly and per se is found both in the mover and in the mobile, For it has been said what a direct and per se mover is and also what is being moved directly and per se. Finally, we have said that there is no motion in the quality which is the terminus of motion; rather motion is in what is being moved, i.e., in the actually mobile, which is the same thing.

647. Then at (475) he shows which kind of motion needs to be discussed.

First he states his proposition;

Secondly, he explains something he said, at 648.

He says therefore first that per accidens change will not be the subject of our discussion, whether it be per accidens on the side of the mover or of the mobile or of the terminus. The reason for this is that per accidens motion is indeterminate: for it is present in all things, in all termini, in all times, in all subjects and in all movers, and an infinity of things can be per accidens in something. But a change that is not per accidens is not found in all things; it is found only in situations (1) that involve contraries or the intermediate between contraries in respect to motions that affect quantity, quality and place, or (2) that involve contradictories, for example, generation and corruption, whose termini are being and non-being—and all this is evident by induction. Now art concerns itself only with things that are determinate, and there is no art to deal with the infinite.

648. Then at (476) he explains his statement that motion can be in the intermediates. And he says that an intermediate may be a starting point of change and go to either of two contraries, inasmuch as we can take the intermediate as being contrary to both extremes. For the intermediate, inasmuch as it is akin to both extremes is in a sense either of them. Hence, we speak of the intermediate as in a sense contrary relatively to the extremes and of either extreme as a contrary relatively to the intermediate; for instance, the central note is low relatively to the highest and high relatively to the lowest, and grey is light relatively to black and dark relatively to white.

Lecture 2

The species of change; which one is motion

649, After distinguishing per se from per accidens motion, the Philosopher now divides per se change and motion into its species.

Here it should be noted that in Book III when Aristotle defined motion, he took it as being common to all species of change. It is in this sense that he now uses the word “change”. And he is beginning to use the word “motion” in a stricter sense, i.e., for a certain species of change. Therefore, this section is divided into two parts:

In the first he divides change into its various species, of which one is motion;

In the second he subdivides motion into its species, at L. 3.

About the first he does two things:

First he gives his division of change;

Secondly, he explains the parts of the division, at 654.

About the first he does three things:

First he states certain things that must be mentioned before dividing change;

Secondly, from these he concludes to the division of change, 651;

Thirdly, he answers an objection at 652,

650. He says therefore first (477) that since every change is from something to something—as is clear from the very word “change” which denotes something after something else, i.e., something earlier and something later—it follows from all this that what changes must change in one of four ways. (1) For both termini might be affirmed, in which case something is said to be changed from subject to subject; or (2) the terminus a quo is affirmed and the terminus ad quem negated, in which case something is changed from subject to non-subject; or (3) on the other hand, the terminus a quo is negated and the terminus ad quem affirmed, in which case something is moved from non-subject to subject. Finally (4), both termini might be negated, in which case something is said to be changed from non-subject to non-subject. (Here the word “subject” is not taken in the sense of that which sustains a form; rather, anything that is affirmatively expressed is here called a “subject”.

651. Then at (478) he derives from these premisses his division of change. And he says that it necessarily follows from these premisses that there are three kinds of change: one is from subject to subject, as when something is changed from white to black; another is from subject to non-subject, as when something is changed from being to non-being; the third is from non-subject to subject, as when something is changed from non-being to being,

652. Then at (479) he precludes a possible objection. For someone might object that since he mentioned four ways in which change can take place, he should have derived four kinds of change and not merely three. But he dismisses this objection by saying that there cannot be any kind of change from non-subject to non-subject, because every change takes place between opposites and two negations are not opposites. For they are neither contrary nor contradictory. A further proof of this is that any pair of negatives may chance to be true of one and the same thing at the same time; for example, a stone is neither healthy nor sick. Hence, since per se change occurs only between contraries and contradictories, as was pointed out above, it follows that there is no per se change from one negation to another. Such changes would always be per accidens, for when something changes from white to black, it changes at the same time, but per accidens, from non-black to non-white. This is the way that something is changed from non-subject to non-subject. However, what is per accidens in any genus cannot be a species of that genus. Therefore, there can be no species of change from non-subject to non-subject.

653. Then at (480) he explains the parts used in his division. About this he does three things:

First he explains the first two parts;

Secondly, he shows that neither of them is motion, at 656;

Thirdly, he concludes that the remaining part is motion, at 659.

About the first he does two things,,

First he explains one part of the division;

Secondly, he explains a second part, at 655.

654. He says therefore first (480) that the change from non-subject to subject takes place between contradictories and is called generation, which is the change from non-being to being. Now this can take place in two ways: one is unqualified generation, by which something comes to be in the strict sense of the word; the other is a particular kind of coming to be, i.e., in a qualified way, And he gives an example of both kinds. First of all, of the second kind, saying that when some thing is changed from non-white to white, it is not an unqualified coming to be of the whole thing, but a mere coming to be of its whiteness. Then he gives an example of the first: and he says that generation from non-being to being in the order of substance is generation in an unqualified way, in regard to which we say that a thing comes to be without qualification. And since generation is a change from non-being to being, a thing is said to be generated when it is changed from non-being to being.

However, when something passes from non-white to white, it is not being changed from absolute non-being to absolute being. For, speaking strictly, what is being changed is the subject, and the subject of white is an actually existing being. Hence, since the subject remains throughout the whole change, there already was an actually existing being at the beginning of the change, although it was not a being actually existing as white. Consequently, it was not a case of unqualified coming to be but a coming to be white. But the subject of substantial form is not an actual being but a merely potential one, namely, prime matter, which at the beginning of generation is under privation and at the end under forms And so, in the case of a substance being generated, it is said that something comes to be in an unqualified sense.

From this it can be concluded that when it is a case of the coming to be of a form that presupposes another form remaining in the matter, it is not unqualified generation but generation in a particular way; because each form makes a being actual.

655. Then at (481) he makes clear the other part of the division and states that that change which is from subject to non-subject is called “corruption”. Rut there is a corruption which is so absolutely speaking and which, namely, is from substantial being to non-being; while there is a certain corruption which is into the opposite negation of any affirmation, as from white to non-white, which is the corruption “of this”, as has already been said of generation.

656. Then at (482) he shows that neither of these cases is motion.

First that generation is not motion;

Secondly, that corruption is not motion, at 658.

He proves the first by two arguments. In the first of which he says: What is not unqualifiedly a “this something” cannot be moved, because what does not exist is not moved; but what is unqualifiedly generated is not a “this something” for it is strictly speaking a non-being. Therefore, what is unqualifiedly generated is not being moved. Hence, unqualified generation is not motion.

In explanation of the first premiss he says that non-being is spoken of in three senses: in the first two senses, non-being is not subject to motion, but in the third it is subject to per accidens motion.

In one sense, being and non-being refer to the affirmation and negation of a predicate in a proposition, where they refer to truth and falsity; in which sense being and non-being exist only in the mind, as is said in VI Metaphysics. Hence, they are not subject to motion.

In another sense, what is in potency is called non-being insofar as being in potency is the opposite of unqualified being in act. Taken in this sense no motion is possible,

In a third sense, that is called “non-being” which is in potency, in such a way as to exclude not unqualified actual existence, but actually being such-and-such; for example, when non-white is called nonbeing and non-good. Such non-being is subject to motion per accidens, inasmuch as such non-being is attached to an actually existing thing subject to motion; as when a man is said to be non-white.

Now, why is it that what is not unqualifiedly a “this something” is not subject to motion at all, i,e., neither per se nor per accidens? It is because it is impossible for the non-existent to be moved, Consequently, it is impossible for generation to be a motion; for generation concerns itself with what is not. And although it was said in Book I that something comes to be per accidens from non-being and per se from a being in potency, yet it is true to say of what is absolutely coming to be that, strictly speaking, it is non-being; hence, such a thing cannot be moved and, for the same reasons cannot be at rest. Hence, generation is neither motion nor rest,

But if anyone insists that generation is motion, he will be forced to admit the strange proposition that non-being can be moved and can be at rest.

657. At (483) he gives a second reason: Whatever is moved is in a place; but what does not exist is not in a place, otherwise its place could be pointed out, Therefore, what does not exist is not moved.

The truth of the first statement is evident from the fact that since local motion is the first of all motions, whatever is moved has to be moved in respect of place and, consequently, must be in a place. But if you remove the previous, you remove whatever depends upon it.

658. Then at (484) he proves that ceasing-to-be is not a motion, because nothing is contrary to a motion but motion and rest, whereas the contrary of ceasing-to-be is generation, which is neither motion nor rest, as we have shown. Therefore, ceasing-to-be is not a motion.

659. Then at (485) he concludes that the remaining member of the above-given division is motion: for since motion is a definite kind of change, because there is in it something following something (which pertains to the very idea of motion), whereas motion is neither generation nor ceasing-to-be (which are changes between contradictories), it follows of necessity, since there are only three species of change, that motion is from subject to subject.

By two subjects is understood two that are affirmative, whether they be contraries or intermediates; because even privation is a kind of contrary that is expressed affirmatively, as nude, which is a privation, and as white and black, which are contraries.

Lecture 3

Per se motion is not in other predicaments than quantity, quality, and place

660. After dividing change into generation, ceasing-to-be and motion, the Philosopher now subdivides motion into its parts. And because it is the same science that deals with a thing and with its opposite,

            He first derives the species of motion;

            Secondly, he explains the various senses of immobile, at 683,

About the first he does two things:

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

Secondly, he explains this conditional proposition, at 662.

661, He concludes therefore (487) from the previous lecture that, since motion goes from subject to subject, and subjects are involved in certain genera of the predicaments, the species of motion must be distinguished according to the genera of predicaments, especially since motions derive their nature and name from the terminus, as was said above. Therefore, if the predicaments are divided into ten genera of things; namely, substance, quality, etc. (as is explained in the book of Predicaments and in V Metaphysics) and motion is found in three of these genera, there must be three species of motion, i.e., in the genus of quantity and in the genus of quality and in the genus of where, which is motion in respect of place.

The way in which motion is present in these three genera as well as how it is related to the predicaments of action and passion has been explained in Book III. Hence it is enough to mention briefly that a motion is in the same genus as its terminus, not that the motion itself would be in the genus, for example of quality, but it is placed there by reduction. For just as potency is reduced to the same genus as its act, inasmuch as every genus is divided by potency and act; so it is necessary for motion, which is an imperfect act, to be reduced to the genus of its perfect act. But when motion is regarded as being in something, though originating from something else, or as originating from one thing and being in something else, then it belongs to the predicaments of action and passion.

662. Then at (487) he explains the conditional proposition.

First, that there is no motion in any but the three genera mentioned;

Secondly, how motion is present in those three genera, at 678.

About the first he does three things.,

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

Secondly, that it is not in the genus of relation, at 666;

Thirdly, that it is not in the genera of action and passion, 668.

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

That motion (487) is not found in the genus of substance he proves by saying that every motion is between contraries, as we have said; but nothing is contrary to substance. Therefore, there is no motion in re8pect of substance.

663. Now, there seems to be a disagreement between this doctrine of the Philosopher and what he says in the book On Generation, that fire is contrary to water. And again in the book On the Heavens he says that the heaven is capable neither of coming to be nor ceasing to be, because it does not have a contrary—which seems to imply that things which cease to be are either contrary or composed of contraries.

To reconcile this, some assert that one substance can be contrary to another, as fire to water, in respect to form but not in respect to their subject. But if that were so, Aristotle’s proof at the end of 662 would be worthless; for then there would be motion in substance as long as the substantial forms were contrary. For motion is from form to form, because even in alteration subject is not contrary to subject, but form to form.

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

But even this answer presents a difficulty. For it is clear that properties originate from the principles of the subject, i.e., from matter and form. Now, if the properties of fire and water are contrary, then since the causes of contraries are themselves contrary, it seems that the substantial forms are contrary. Moreover, it is proved in X Metaphysics that every genus is divided by differences that are contrary, and differences are traced to the forms, as VIII Metaphysics explains. Therefore, it seems that there is contrariety between substantial forms.

664. Consequently, it must be asserted that contrariety of differences are all the genera is based on the common root of contrariety, which is excellence and defect, to which set of contraries all others are reduced, as was explained in Book I. For all differences that divide a genus are so related that one is like abundance and the other is like defect in relation to the first. For which reason Aristotle says in VIII Metaphysics that the definitions of things are like numbers in which the addition or subtraction of unity makes a different number. However, it is not necessary that there be in every genus the same detailed contrariety between species as exists in some genera; for a contrariety of excellence and deficiency is enough. For since contraries are things most distant, then in order to have contrariety in a genus there must be found two extremes that are most distant, so that between them fall all the things in that genus.

Yet that is not enough for positing motion in a genus, unless it is possible to pass without a break from one extreme to the other. Now these two conditions are lacking in some genera; for example, in numbers. For although all numbers differ according to excellence or defect, yet there cannot be found in that genus two extremes that are most distant; for it is possible to find a lowest number, i.e., 2, but not a greatest. In like manner, there are breaks between the species of number, for each number is formally constituted by unity, which is indivisible and not continuous with another unity.

Likewise, in the genus of substance. For the forms of diverse species differ in respect to excellence and defect, inasmuch as one form is more noble than another, for which reason diverse qualities can be caused by diverse forms, as the objection mentions.

Yet one form of a species is not contrary to another, if you consider it in regard to its own specific nature. First of all, because when you are speaking of substantial forms, there is no maximum distance between any two forms, such that you must pass through an orderly array of intermediate forms to go from the one extreme to the other. Rather, matter when it doffs one form can indiscriminately receive any other form in just any order. For which reason Aristotle says in II On Generation that when fire comes to be from earth, it is not necessary that the intermediate elements be involved at all.

Secondly, because, since the substantial essence of anything consists in an indivisible, no continuity can be found in substantial forms so as to make a continuous motion from one form to another by one form growing weak and the other growing strong.

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

665. In qualities of the third species, the two above-mentioned characteristics of contraries (namely, continuity and maximum distance between the extremes) are clearly manifest: first, because qualities can be weakened and strengthened so as to make for a continuous motion from quality to quality, and, secondly, because there exists a maximum distance between two definite extremes of one genus, as black and white in the genus of color, and sweet and bitter in the genus of taste.

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

666. Then at (488) he shows that there is no motion in the genus to something, i,e., relation. For in any genus in which per se motion exists, nothing can newly arise in that genus without its being changed, just as new color is never found in a colored object without that object’s being changed. But it does happen that something can be newly said truly of one thing relative to another, where the latter is changed but the former not. Therefore, in relation motion is not found per se but only per accidens, inasmuch as a new relation follows upon some change; for example, equality or inequality accompany a quantitative change and resemblance or dissimilarity qualitative change.

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

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

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

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

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

668. Then at (489) he proves that motion is not in the genera of action and passion. For action and passion do not differ really from motion, but they add to it something of reason, as we said in Book III. Hence, it is the same thing to say that motion is present in acting and being acted upon as to say that motion is present in motion, Therefore in regard to this he does 3 things:

First he proposes what he intends;

Secondly, he proves his proposition, at 669;

Thirdly, he posits a distinction that will explain the proposition, at 677.

Accordingly, he says at (489) that just as motion is not found in something relative, so also there is no motion of an agent or a patient and, strictly speaking, not even of the mover and moved: for there cannot be motion of motion or a coming-to-be of coming-to-be, which are types of change, nor even a change of change (which is the genus) or a ceasing-to-be of a ceasing-to-be.

669. Then at (490) he proves that there cannot be change of changes. And he does this with six arguments.

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

670. In another way it can be interpreted that there be change of change as of a terminus, so that subject A is moved from one type of change to another; for example, from getting hot to getting cold or healthy, so that two changes are understood to be the termini of one change, as sickness and health are taken as the two termini of a change when a man is changed from health to sickness. But it is not possible for a subject to be moved per se from one change to another but only per accidens. And that it is impossible per se, he proves in two ways: for every motion is a change from one definite form to another definite form. Even generation and ceasing-to-be, which are co-divided with motion, have their definite termini; but there is this difference, namely, that generation and ceasing-to-be are to opposite termini “thus”, i.e., according to contradiction, whereas motion tends to an opposite terminus “not in a like way” but according to contrariety.

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

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

671. He proves this same point again with another argument: If the passing from a previous changing to a subsequent change were motion per se, it would not be necessary that the passing be always to a “contingent” change, i.e., one which could co-exist with the previous change: as becoming white can co-exist with becoming sick, but getting well cannot co-exist with getting sick, because these are contrary changes. But it is possible that just as becoming white can follow becoming sick in the same subject, so also could becoming well. And this is what he says: that the passing from one change to another will not always be to a contingent change, since it is sometimes to a non-contingent, and that non-contingent change proceeds from something to something else, that is, it is between two other termini, Hence that non-contingent change into which something passes from the change called “getting sick” will be “getting well”, which is the opposite of “getting sick”.

Now that this is strange is evident from what we have said above, that while the first change is still going on, it is being changed to the second change: therefore, while something is being moved to sickness, it will be changing to another change called “getting well”. Hat the goal of getting well is health (for it is from something to something, as was said). Hence it remains that while something is being moved to sickness it is at the same time being moved to health, which means it is being moved toward two contraries at the same time and intends them at the same time—which is impossible. Consequently, it is clear that no change from one change to another is per se.

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

672. Before giving the second of the six reasons he promised, he presents (491) two conditional propositions: the first of which is that if there is change of change and generation of generation, in either case it would be necessary to go on ad infinitum; because, for the same reason the second generation will have another generation, and so on ad infinitum.

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

This second conditional he now proves: Let fire be the thing that is unqualifiedly generated; if, then, there is a generation of generation, it is necessary to say that that unqualified generation was itself generated and that its coming-to-be came to be. When, however, that coming-to-be was being generated, the fire was not existing (for it is being assumed that the fire is being unqualifiedly generated): because a thing does not exist while it is coming to be, but it exists for the first time after it has come to be. Therefore, as long as the coming-to-be of fire was in the state of coming to be, the fire had not yet come to be; therefore, it was not yet existing. And again the very coming-to-be of its coming-to-be was itself (for the same reason) coming to be. Consequently, just as when the coming-to-be of the fire was coming to be, the fire did not exist, so also as long as the coming-to-be of the coming-to-be was taking place, the coming-to-be of the fire was not existing.

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

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

673. He gives the third reason at (492) and it is this. One and the same motion has as its contraries both motion and rest; for example, both descending and rest in the lower place are contrary to ascending. In the same way are generation and ceasing-to-be contrary. But contraries are apt to affect the same thing. Therefore, whatever comes to be can cease to be. But if there is coming-to-be of coming-to-be, then coming-to-be must come to be. Therefore coming-to-be ceases to be. But what ceases to be must be: for just as it is what is not that comes to be, so it is what is that ceases to be. Therefore, it is necessary that when what comes to be comes to be, i.e., when something-comes to be and the coming-to-be exists, then the very coming-to-be ceases to be, not indeed as soon as the coming-to-be is finished or some time after it is finished, but during the coming to be-which seems absurd.

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

674. At (493) he gives the fourth reason, In every coming to be there must be matter from which that which comes to be is generated, just as every change requires some matter or subject: for example, in alteration the subject is the body, if you are dealing with bodily qualities, or the soul, if you are dealing with soul qualities. If, therefore, coming-to-be comes to be, there must be some matter involved which passes into the form coming to be as the matter of generated fire passed into the form fire. However, such matter is not discoverable.

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

675. At (494) he gives the fifth reason: Genus is to genus as species is to species. If, therefore, there is coming to be of coming-to-be, then the coming to be of teaching is itself teaching. But this is evidently false: for teaching is the generation of science and not of teaching. Therefore, neither can there be a coming to be of coming-to-be.

676. The sixth reason is given at (495) and it is this: If there is change of change, whether as of a subject or as of a terminus, then, since there are three species of motion, as was said above (motion to where and quantity and quality), it will follow that one of these species could be the subject and terminus of some other species or even of its own species. Therefore, it will follow that local motion can be altered or even be moved locally. Such a thing is more plainly absurd when you get down to cases than when you speak in general. Therefore, it cannot be admitted that there is change of change or coming to be of coming-to-be.

677. Then at (496) he shows in what sense there can be change of change. And he says that since there are three ways in which something can be moved, (namely, in respect to an accident or in respect to a part or per se, it is only per accidens that there could be change of change, i.e., only inasmuch as the subject of the change changes: for example, if someone, while he is becoming healthy, would run or learn; for then the healing process would be running or learning per accidens, just as a musician builds per accidens. But it is not our intention to treat of per accidens motion, for we have already decided to pass it by.

Lecture 4

Motion is solely in quantity, quality, and place

678. Having shown that there is no motion in substance or in relation or in action and passion, the Philosopher now tells in which genera motion does exist. And about this he does three things:

First he arrives at the intended conclusion;

Secondly, he shows how motion is found in each of three genera, 679;

Thirdly, he answers a difficulty, at 682.

He says therefore first at (497) that since motion is neither in substance nor in relation nor in acting and being-acted-upon, as has been explained, there remain but three genera in which there is motion: quantity, quality and where, for in each of these genera there is apt to be the contrariety which motion requires.

He has already explained both why he omits the three genera of when, situs and habitus and how there is contrariety in the three genera in which motion is found.

679. Then at (498) he explains how motion is found in the three genera:

First in quality;

Secondly, in quantity, at 680;

Thirdly, in where, at 681.

He says therefore first that motion in the genus of quality is called “alteration”. And he refers to this genus a common name—alteration; for in Latin the word alterum (other) is customarily applied to things that differ in respect of quality. And we are speaking of quality not in the sense in which it is found in the genus of substance, where the substantial difference is said to be predicated in regard to that which qualifies, but in the sense of a passive characteristic (contained in the third species of quality) in virtue of which something is said to receive or not receive a quality such as hot and cold, black and white, and so on. It is in respect to these that things are said to be “altered”, as will be shown in Book VII.

680. Then at (499) he shows how there is motion in quantity, And he says that motion in respect to quantity does not have a name for its genus, as quality has the generic name “alteration”. Rather it is named according to its species, which are “growth” and “decrease”. For the movement from imperfect size to perfect is called “growth”; the one from perfect size to imperfect is called “decrease”.

681. Then at (500) he explains how there is motion in where. And he says that motion in respect of place has neither a common name for its genus nor a particular name for its species, yet he gives it the general name latio—although this is not the generic name of every type of local motion. For it is properly used of things which are so moved in respect of place that it is not due to their own power that their local motion stops; in other words, things that are moved not by themselves but by others.

The reason why the common name could be applied to motion in quality is that qualities are contrary in the very notion of their species according to which they are contained under the genus of quality. But quantities are contrary, not according to the very characteristics of their species, but according to “perfect” and “diminished”; and it is according to these that the species of quantity derive their name. However, in place the only contrariety that exists is founded on motion in respect to which two termini are most distant, Consequently, because such contrariety is based on something entirely foreign to place, no motion in this genus could possess a name based either on the genus, or the species under the genus.

682. Then at (501) he clears up a point about which there could be doubt and shows to which species of motion should be reduced a change from lesser to greater or greater to lesser; for example, when something white becomes less white or more white. For at first sight it might seem that it should be reduced to the motions called “increase” and “decrease”. But he shows that it should be reduced to alteration, saying that any change within the same species of quality, for example, change to whiteness or to more or less whiteness, is alteration.

He proves this by the fact that alteration, which is change from one contrary to the other in respect of quality, can occur in two ways: first, unqualifiedly, as when something changes from white to black or vice versa; or secondly, qualifiedly, when something changes from more white to less white, and vice versa. And that such a change is a change from contrary to contrary he now proves: for when something is changed from more white to less white, such a thing is said to be changed from one contrary to its opposite, because it is approaching the true contrary, which is black. And when it is changed from less white to more white, it is as though it were changed from one contrary to its opposite, namely, from black to white. For it becomes more white by becoming further removed from black and acquiring more perfect possession of whiteness.

In order for there to be alteration, it makes no difference whether the change is unqualifiedly from contrary to contrary, or from more to less or less to more, except that in the former case the termini of the alteration must be two actual contraries; whereas the change in regard to more and less involves the subject’s having or not having in a greater or lesser degree one or another of the contraries.

At the end of (502) he concludes that it is now clear that there are only these three kinds of motion.

683. Then at (503) he explains the various senses of “immobile”, giving three. The term “immobile” is applied in the first place to what is absolutely incapable of being moved, as God; just as we correspondingly apply the word “invisible” to sound’, In a second sense, it is applied to what is moved with difficulty (in two ways) either because, after it has begun to be moved, it continues slowly and with great difficulty (as when we call a lame person “immobile”) or because it is difficult to get it started both on account of the labor and time involved, as when we say that a mountain or a large rook is immobile, In a third sense something is called “immobile”, when it is capable of being easily moved, but it is not in motion when and where and in the manner in which it is capable. This alone is called “rest”, because rest is the contrary of motion. Here “contrary” is used in a wide sense, i.e., in the sense that includes even privation. Hence he concludes that rest is privation of motion in that which is capable of motion. For “contrary” and “privation” are applied only to things that are susceptible of opposites.

Finally, at (504) he summarizes and says that it is now clear what motion is and what rest is and what are the varieties of change and which of them can be called motion.

Lecture 5

The definitions of “in contact,” “consecutive,” “continuous”

684. After dividing change and motion into its species, the Philosopher now begins to discuss the senses in which motion is said to be one, and the senses in which motions are said to be contrary. About this he does two things:

First he establishes a background of preliminary notions that will be of use;

Secondly, he pursues his main objective, at L. 6.

About the first he does three things:

First he states his intention;

Secondly, he pursues it, here at 684;

Thirdly, he makes a summary, at 694.

He says therefore first that we must now define the terms together, extraneous or separate, touching [in contact], intermediate [or between], consecutive to.

The reason for positing these definitions now is that they will be used in later demonstrations, just as in the beginning of Euclid are posited definitions that serve as principles of later demonstrations.

685. Then at (5o6) he carries out his plan.

First he defines the terms he mentioned;

Secondly, he compares one to the other, at 692.

About the first he does three things:

First he defines those that pertain to contact, i.e., touching;

Secondly, those which pertain to consecutiveness, at 686;

Thirdly, those that pertain to continuum, at 691.

Since “together” occurs in the definition of in contact, the Philosopher defines it first (506) and says that those things are said to be together in respect of place which are in one first place, where first place refers to proper rather than common place. For things are said to be together not because they are in one common place but in one proper place; otherwise, we should be able to say that all bodies are together, since they are all contained under the heavens.

He speaks of such things that are together in respect of place, in distinction to those that are said to be together in time—a point we are not now discussing, Conversely, whatever things are one in one place, and another in another place, are said to exist separate or apart.

But in contact is said of things whose termini are together. The termini of bodies are surfaces and of surfaces, lines, and of lines, points. Therefore, if two lines are in contact as to their termini, the two points of the two lines in contact will be contained under one point of the place containing them. From this, however, it does not follow that the thing in place is greater than the place, for point added to point does not make anything larger. And the same holds for the others.

686. Then at (507) he defines the things that pertain to consecutiveness, About this he does three things:

First he defines between, which is placed in the definition of consecutive to;

Secondly, he defines consecutive to, at 689;

Thirdly, he draws a corollary, at 690.

He says therefore first (507) that the between is what a naturally and uninterruptedly changing thing is apt to arrive at before it reaches the ultimate terminus of the motion, into which terminus it is being changed; for example, if something is changing from A to C through B, then, provided it is a continuous motion, it reaches B before C.

In some cases there are a number of “betweens” to be traversed as you pass from one extreme to the other, as from black to white there are many colors between; but there must be at least three things involved, two of which are extremes and one the between. Consequently, the between is what must be passed through before arriving at the terminus of a change: but the terminus of a change is a contrary; for it has already been stated that motion goes from contrary to contrary.

687. Because the definition of between made mention of continuity of motion, he now shows what continuous movement means. Now continuity of motion may be viewed from two aspects: first, from the time during which the movement occurs and, secondly, from the thing through which the motion takes place for example, the magnitude, in local motion.

For a motion to be continuous it is required that there be no interruptions in time, because even the slightest interruption of the motion as to time prevents the motion from being continuous.

But on the side of the magnitude through which the motion passes there can be slight variations without prejudice to the continuity of the motion. This is clear in crossings over streets, at which stones are placed slightly distant from each other, and over which a person passes from one side of the street to another without interrupting his motion. This, therefore, is what he says: that continuity of motion is present when there is no gap or only the slightest in the thing, i.e., when there is no interruption in the thing over which the motion passes or, if there is, it is very slight. But there cannot be the slightest interruption of time, if the motion is to be continuous.

How there can be a gap in continuous motion he explains by adding that a motion will be continuous even if there is a gap in the material, as long as there is no time-gap; for example, if in playing the harp one strikes the highest note immediately after having sounded the lowest and none of the intermediate ones. But this is not a gap in time, but in the material in which the motion takes place.

What has been said about the continuity of motion applies not only to local motion but to all the others as well.

688. But because it is not evident how the terminus of a local motion is a contrary, since one place does not seem to be contrary to another, he now gives an explanation. And he says that the contrary in respect of place is the greatest rectilinear distance, where greatest distance is taken in relation to the motion and the mobiles and the movers, for example, for the motion of heavy and light things the distance from the center of the earth to the extremity of the sky is the greatest distance, while in regard to my motion and your motion, the greatest distance is the interval between where we start and where we intend to arrive.

What he means by the phrase “in a straight line” he explains by adding “that the shortest line is definitely limited”. To understand this, consider that the shortest distance between two points is a straight line, for between any two points there is only one straight line. But there are any number of curved lines between two points, where by curved lines we mean the arcs of major or minor circles, Now since every measure should be finite (otherwise there would be no way of knowing the quantity of a thing—for that is the purpose of measuring), the greatest distance between two objects is not measured by a curved line but by a straight line which is finite and determinate.

689. Then at (508) he defines what is meant by consecutive to and a species of it, namely, contiguous. And he says that two things are required in order that something be called consecutive to another. One is that it be after the first and in a certain order: either according to position, as things that are in order in place; or according to species, as 2 comes after 11 or in any way in which things can be in order, as according to virtue, according to dignity, according to knowledge, and so on. The other requirement is that between that which is consecutive and that to which it is consecutive there not be anything of the same kind intervening; for example, one line is consecutive to another, if there is no line between—likewise from one unit to another and one house to another. However, this does not forbid something else intervening. For example, an animal could be found between two houses.

Why he said “to which it is consecutive” and “that it is after the first” he explains by adding that whatever is said to be consecutive is so in respect to something else, not as being prior to it but as following it. For 1 is not said to be consecutive to 2, or a new moon to a second new moon; rather, it is just the opposite.

Then he defines a certain species of consecutive called contiguous. And he says that not everything consecutive is also contiguous, but only when it is consecutive and in contact, so that there is nothing at all between, i.e., nothing of the same genus or of any other genus.

690. Then at (509) he concludes from the foregoing that since the between is that through which something is changed into what is final, and since every change is between opposites which are either contrary or contradictory, although there is no between in contradictories, it follows that it is between contraries that the between is found.

Then at (510) he shows what a continuum is and he says that it is a species of the contiguous. For when the terminus of two things in contact is one and the same, then something is continuous. And the very word “continuum” denotes this. For “continuum” is derived from “continere” (to hold together): when, therefore, many parts are held together in a unit and, as it were, keep themselves together, then there is a continuum. But this cannot be while the endings are two but only when they are one.

From this he further concludes that continuity can occur only in things from which a unity through contact is naturally apt to come about. For in whatever way a whole is naturally one and continuous in the same way is a continuous unity formed from many things, whether by riveting, by glueing or by any form of contact that makes one terminus for two parts, or even by being born of another, as fruit is born of a tree and forms a sort of continuum with it.

692. Then at (511) he compares three of the foregoing with one another; namely, the consecutive to the continuous, and the continuum. About this he does three things:

First he compares consecutiveness to contact;

Secondly, contact with continuum, at 693;

Thirdly, he draws a corollary, at 694.

He says therefore first (511) that it is clear why among these three, consecutiveness is naturally first in the order of nature, for in the cases of contact there is always consecutiveness, since there must be an order, at least of position, among things that are in contact. Bat not all cases of consecutiveness involve contact, for an order can exist among things in which there is no contact, as in substances separated from matter. Hence, consecutiveness is present in things that are prior in definition, for it is found in numbers, in which there is no contact, which is present only among continua. Numbers, however, are prior to continuous quantities in definition, for they are more simple and more abstract.

693. Then at (512) he compares in contact with continuous and says that for the same reason in contact is prior to continuous, because if a thing is continuous it must be in contact, but it does not necessarily follow that if it is in contact it is continuous,

And he proves this from the definitions of the two. For it is not necessary that the endings of things be one (which is implied in the notion of continuum), if they are together (which is implied in the notion of contact). But, on the other hand, if the endings are one, they must be together, for what is one is together unto itself.

However, if “together” implies a relationship between distinct things, then things that are together are not one: and according to this, continua are not in contact. But they are, if we do not speak so precisely. Hence he concludes that natural junction, i.e., continuity, in which one part is joined to another at one terminus, is last in coming to be, in the sense that what is specific comes to be after what is general, as animal comes to be before man. And, therefore, I say that natural junction is last, because things must mutually touch if their extremities are naturally united; however, it is not necessary that all things that touch be naturally joined to one another. But in regard to things which cannot touch, it is clear that continuity is impossible.

694. Then at (513) he draws a corollary from the preceding: i.e., if point and unit have an independent existence of their own, as some say who suppose a separated existence for mathematical objects), it follows that unity and point are not the same.

And this is clear for two reasons: first, because points are present in things that are capable of mutual contact and certain things touch at points; but in units contact is never found, but only consecutiveness. Secondly, because there must be something existing between two points, but between two unities there is not necessarily anything

between. For it is evident that between the two unities that form 2 and the very first unity, which is 1, there is nothing intermediate.

Finally, at (514) he makes a summary and says that we have defined what is meant by together and apart, contact, between, consecutiveness, contiguous and continuous. Also we have shown in which circumstances each of these terms is applicable,

Lecture 6

Generic, specific, and numerical unity of motion

695. After positing some definitions to be used later, the Philosopher now proceeds to discuss unity of motion and contrariety of motions.

First he treats of the unity and diversity of motion;

Secondly, of its contrariety, which is a kind of diversity, L.8,

About the first he does three things:

First he shows how motion is said to be generically one;

Secondly, how it is specifically one, at 697;

Thirdly, how it is numerically one, at 699.

696. He says therefore (515) that there are a number of ways in which a motion is one, just as one itself has many senses: i.e., generically, specifically and numerically. A motion is said to be generically one according to the different predicaments. For all motions that are assigned to one and the same predicament can be called generically one; thus every local motion is one generic motion, because each is in the predicament where, and differs generically from alteration, which is in the predicament quality, as has been said above.

697. Then at (516) he shows how motions are specifically one.

First he shows this;

Secondly, he raises a question, at 698.

He says therefore first (516) that a motion is called specifically one when, besides being a generic one, it also takes place in a species incapable of subdivision. For some species can be subdivided into other species, as color, which is a species of quality, is capable of differences that make for sub-species. Hence motions in regard to color can be diverse in species, as whitening and blackening; but all cases of whitening are specifically the same (just as all cases of blackening are), for there are no sub-species of whitening.

But when it happens that the species is at the same time a genus, then the motions found in a subalternate species are qualifiedly one, although, strictly speaking, they are not of the same species. Thus science is a species of knowledge, as well as a genus of the various types of science. Hence all indoctrination, which is a movement toward science, is in some sense specifically the same, although, strictly speaking, it is not, for the indoctrination by which grammar is taught is absolutely different in species from that by which geometry is taught.

Now it should be observed that in the foregoing the Philosopher has based the unity and diversity of motion on the genera and species in which motion can occur, because motion is in a certain way reduced to the genus in which the motion is.

698. Then at (517) he raises a question about the foregoing: Whether a motion is specifically one and the same when the same thing changes frequently from the same to the same, e.g., when a point (according to the geometers who imagine that a point can be moved) changes again and again from this place to that. Now according to the foregoing it seems that the answer should be Yes. For if all motions that tend to the same species, e.g., whiteness, are specifically the same, a fortiori two motions from the same origin to the same terminus should be specifically one. But if that were so, then it would follow that a rectilinear motion is specifically the same as a circular motion. For it is possible to pass from this place to that by means of a circular motion, i.e., by describing an arc, and after by going in a straight line. Likewise, it would follow that in the motions of animals, walking (which is in a straight line) would be specifically the same as whirling, which consists in turning oneself in circles.

However, he answers this difficulty in the light of the foregoing. For it has been decided that if that in which the motion takes place is specifically different (as in the present instance the circular path is specifically different from the straight), the motion itself is also different. Consequently, in order that two motions be specifically the same, not only must the goal be specifically the same but also that through which the motion passes. Now it is clear that a straight line is specifically different from the curved. Consequently, a circular and a rectilinear motion, as well as walking and whirling, are not specifically the same, even though they tend to the same goal, because the paths are not specifically the same.

But if the goals are identical and the paths specifically the same, then the motions are specifically the same; and much more so, if the goals and the path are numerically the same, the same repeated motions will be specifically the same.

699. Then at (518) he posits the third way in which a motion is said to be one; namely, numerically. About this he does two things:

First he explains when a motion is numerically one;

Secondly, he raises some question on this point, at 700.

He says therefore first at (516) that in the first two senses motions are not unqualifiedly one, but they are one only in a sense, i.e., in genus and species. But in the third sense a motion is unqualifiedly one, i.e., when it is numerically one in its essence.

Which motion is one in this way will be clear, if we distinguish the things required for motion: for numerically there are three things on which the unity of a motion depends: first, the subject which is being moved; secondly, the genus or species of the motion; thirdly, the time in which the motion takes place. And he explains each of these individually.

A subject of motion is required, because in every case of motion there must be something that is being moved, as a man or gold or some body. Likewise the subject must be affected by some genus or species of motion, such as place or a passible quality. Again, the time must be considered, because whatever is moved is moved in time.

Now among these three things, the generic or specific unity of the motion can depend on the thing in which there is motion; for example, on the place or quality. But the time does not account for the generic or specific unity of the motion, for there is only one specific time; rather it accounts for the continuity of the motion, i.e., that it flows on without interruption.

But unity of motion, in the sense of unqualified unity, depends on all three. For that in which the motion exists must be one and indivisible in the way that a species incapable of further subdivision is said to be one. Further, the time during which the motion occurs must be continuous without any breaks. Thirdly, the subject in motion must be one.

However, there are two types of unity of subject which are not sufficient to guarantee that the motion is unqualifiedly one. The first type is accidental: for example, Coriscus and white are accidentally one, but the motion proper to Coriscus in not the same as the motion proper to white. For the proper motion of white is to become black and the motion proper to Corisicus is to walk; and these are different. The second type is generic and specific unity. For in order that a motion be numerically one, it is not enough that the subject be one as something common either generically or specifically. For it is possible that two men are being healed during the same period of time in regard to the same thing; for example, from inflammation of the eye, so that the time is one and the species of motion is one, and the subject is one in species. Yet these two healings are not one numerically but only specifically.

700. Then at (519) he raises a question. And about this he does three things:

First he mentions what at first glance seems to be a motion numerically one;

Secondly, he raises a question about this, at 701;

Thirdly, he gives the true solution, at 702.

He says therefore first (519) that it is possible for one mobile, e.g., Socrates, to be altered at two different times with respect to the same specific disease, for example, if he is twice healed of eye-inflammation. This repeated healing will at first sight be numerically one motion, if the health acquired is numerically the same in both cases. And this will be so, if it is possible for that which ceased to be to come again into being as the same numerical thing—which seems impossible. For the health acquired after the first alteration was later lost and the same numerical health cannot be regained.

But it seems that if the same numerical health were regained, the second alteration would be numerically the same motion as the first; whereas if the same numerical health is not regained, the motion will not be numerically the same but specifically.

701. Then at (520) he raises another difficulty on this point. It is this: if someone continually perseveres in health or any other accident, could the health, or any other habit or passion in bodies, be one? It seems not, because certain philosophers believe that all subjects that possess certain qualities or habits are in continuous motion and flux.

If, therefore, in the case of a person who remains healthy, there is one and the same health at dawn and at noon and in the evening, there seems to be no reason why in the case of a person who gets sick and then recovers, the health recovered is not numerically the same as the one previously possessed.

Aristotle does not settle this question: first, because it is not ad rem, since it pertains to metaphysics, whose province is to consider the one and the many, the same and the diverse; and, secondly, because this difficulty is based on the false assumption that all things are in a state of continuous change and flux, as Heraclitus believed—an opinion which Aristotle refutes in IV Metaphysics. Moreover, the two cases are not the same: for as long as health remains in spite of fluctuations in degree, the original health is not interrupted, as it is in the case of one who completely loses his health.

?02. Then at (521) he determines the truth in regard to the case mentioned in 700. For he mentioned there that if it is the same quality that is recovered, the second alteration will be numerically the same motion as the first; if the same numerical quality is not recovered, then it is not numerically the same act.

Having presented a certain difficulty as though giving a reason for what was set down above, he adds that the reason for raising the difficulty was that at first sight it seemed that the same argument would hold good for the unity of quality and of motion.

But there is a difference: for it does follow that if two motions are the same in the manner in which a motion is said to be numerically one, then the habit, i.e., the quality, acquired by the motion is one; because numerically the same quality is produced by an act numerically one. However, if the quality that returns is one, not everyone would agree that the act is one; for if the terminus of two motions is numerically one, it does not mean that the motions were numerically one. This is evident in local motion. For when a person interrupts his walk, the act of walking ceases; but when he resumes, the act resumes. Now, if you were to say that the whole journey is one act of walking that ceases to be and is then revived, then it would follow that one and the same thing can exist and cease to exist any number of times—which is impossible. In like manner if the same numerical health is again and again recovered, it does not follow that the second healing was the same motion as the first, any more than a second walk is the same as a first, even though both go toward the same numerical goal.

Finally, he concludes that these difficulties lie outside the present enquiry and are for that reason to be passed over.

Lecture 7

Numerical unity of motion (continued)

703. After positing that three things are required in order that a motion be unqualifiedly one, namely, unity of time, unity of that in which the motion takes place and unity of subject, the Philosopher now intends to prove this.

Now while there are a number of ways in which things are unqualifiedly one, one being the way in which an indivisible is one and another the way in which a continuum is one, no motion can be unqualifiedly one in the way that an indivisible is one, because no motion is indivisible. Consequently, it remains that a motion is one to the extent that it is continuous and that, insofar an a motion is concerned, to be continuous is to be unqualifiedly one, so that the very continuity of motion suffices for its unity. For if it is continuous, it is one. Accordingly, whatever is required to make a motion be continuous is also required to make it one.

704. Now, in order that a motion be continuous, three things are required. The first of these is oneness in species. For there will not be continuity between one motion and another indiscriminately any more than there is continuity between just any two continuous things chosen at random in any other sphere. There can be continuity only when the extremities of the two things are one—this is implied in the very notion of continuity, as was explained above. Now, some things have no extremities at all; for example, forms and all indivisibles. Therefore, in regard to such things there can be no continuity. Other things have extremities which are divisible and have quantity. Some such things are equivocal, i.e., not agreeing in name and notion. Such things afford no means of forming continuity; indeed, in many cases no contact is possible. For how could a line and walking be in contact, or how could they possess a common extremity, so as to make continuity possible?

This shows that continuity is impossible with things that belong to genera or species that are diverse.

However, motions that differ generically or specifically can follow one upon the other, as a person immediately after running can start to get a fever—running and getting a fever being in diverse genera. And even in the same genus, e.g., in local motion, one change of place could follow upon another without the motion being continuous, as is evident in the spreading of the lamp (the torch-race), when the torch is passed from hand to hand. In this case we have diverse non-continuous motions. Or the phrase “spreading of the lamp” could refer to the local motion of the flame—which is signified by the word “lamp”—which is moved according to the local motion of the fuel that feeds the flame—such local motion being called spreading.

Therefore the changes mentioned in the preceding paragraph, since they differ either generically or specifically, are not continuous, since they cannot have one extremity, which is required for a continuum. Consequently, motions that differ generically or specifically may be consecutive and “had”, i.e., in contact somehow without any time interruption, inasmuch as time is continuous and has its continuity in the same way that motion has, namely, because there is one extremity (joining two parts). Now there is nothing to prevent one motion from being ended and another of an entirely different kind from beginning at the same instant that two parts of time are being joined. In that case the two motions will be contiguous but not continuous. Therefore, according to our premises, it follows that in order that a motion be continuous, it is necessary that it be one in species: this unity of species being in the motion from the thing in which the motion is, insofar as it is incapable of division according to species.

705. In the second place, continuity of motion requires unity of subject, for the motions of diverse subjects cannot be continuous, though they can be contiguous, as was said about transferring a lamp from hand to hand.

706. Thirdly, in order that a motion be continuous and one, it must be one as regards the time, so that no period of immobility or rest intervene. For if there is a time in which it was not moving, then it was at rest during that time, and if a state of rest intervenes, the motion is not one but many; for motions that are interrupted by rest are not one but many. Consequently, if a motion is interrupted by rest, it will be neither one nor continuous. But it is interrupted by rest, if there is a time in the middle of it, as was shown. Hence for continuity of motion, there must be one continuous time.

But mere continuity of time is not enough, because a motion that is not specifically one is not continuous, even though time is not interrupted: for although it be one in regard to time, it will be other in regard to species. In other words, in order that a motion be one and continuous, it must be specifically one; but it does not follow that a motion specifically one is unqualifiedly one,

Thus, it is clear that the three aforementioned things are required in order that a motion be unqualifiedly one. And so he concludes that we have now explained which motion is unqualifiedly one.

707. Then at (523) having posited the three principal ways in which a motion is one, he mentions two secondary ways, although these pertain more to a certain form of unity than to unity itself. The second of these is given at 708.

He says therefore first (523) that whether a motion be one in genus or in species or in substance, i.e., numerically one, it is also called one if it is perfect, just as in other things, “perfect” and “whole” pertain to the notion of unity. For we do not speak of one man or one shoe, unless they are whole.

However, there are times when we speak of something imperfect as being one, provided it is continuous. And the reason for this is that unity can be regarded from the viewpoint of quantity, in which sense mere continuity suffices for the unity of a thing, or from the viewpoint of the substantial form, which is the perfection of the whole. Thus, what is perfect and whole is said to be one.

708. Then at (524) he gives the other secondary way; that a motion is called one when it is regular, i.e., uniform, just as in other things an object is said to be one, if its parts are alike. About this he does three things:

First he posits this mode of unity in the sense that a regular motion is one;

Secondly, he shows in which motions regularity and irregularity are found, at 709;

Thirdly, he explains the modes of irregularity, at 710.

He says therefore that in addition to the above-mentioned rays of being one, a motion is called one, if it, is regular, i.e,,, uniform. For an irregular or non-uniform motion does not seem to be one, whereas a regular, i.e., uniform motion does (as a motion which is entirely straight is uniform).

The reason why an irregular motion does not seem to be one is that it can be divided into parts which are not alike, whereas indivisibility pertains to the notion of unity, because that which is one is undivided. However, an irregular motion is one in a sense. But the unity of irregular and regular motions seem to differ according to more and less: because a regular motion is more perfectly one than an irregular one; just as a body whose part’s are alike is more perfectly one than a body of parts that are not alike.

709. Then at (525) he shows in which motions irregularity and regularity are found. And he says that they are found in every genus and species of motion: for some things can be altered in a regular manner, as when the entire alteration is uniform, and some things can be moved along a magnitude that is regular and uniform, as things that are in circular motion or in rectilinear motion. The same is true of growing and decreasing.

710. Then at (526) he approaches the task of deciding about irregular motion.

First he mentions ways of being irregular;

Secondly, he shows how an irregular motion is one, at 713.

About the first he does two things:

First he assigns two ways in which irregularity is present in motions;

Secondly, he draws certain conclusions from all this, at 712.

He says therefore first (526) that the variations that make for irregularity in motion are caused sometimes from the thing in respect to which there is motion, as is evident especially in local motions for it is impossible for a motion to be regular and uniform unless it passes over a magnitude that is regular, i.e., uniform. Now a magnitude is said to be regular or uniform when each part of it follows its neighbor in a uniform manner, so that any part could be superimposed upon any other, as is clear in the case of arcs or straight lines. But a magnitude is irregular, if one part does not uniformly follow another, as is evident in two lines that form an angle, of which one part does not fit perfectly over the other in the way that one part of a line fits perfectly over another,

Therefore, a circular motion is regular and so is a rectilinear one: but reflexed or oblique motions, whose path forms an angle, are not regular and do not take place on a uniform magnitude; likewise any motion on a magnitude that is not such that any part of it taken at random fits on any other taken at random, For if the part (of the motion) that contains the angle is superimposed on a part that does not form an angle, they will not match,

711. The second difference that makes for irregularity is found neither in the place nor in the time nor in the goal (for the goal of a motion is not merely a place but also quality or quantity) but in the manner of the motion, For in some cases the motion is differentiated by swiftness and slowness; because a motion that has the same velocity throughout is said to be uniform, while one in which one part is swifter than another is said to be irregular.

712. Then at (527) he draws two conclusions from the foregoing. The first of which is that swiftness and slowness are neither species of motion nor specific differences, because they can be found in all types of motion, since they determine regularity and irregularity, which follow upon each species of motion, as was said above. And no species or difference is common to every species of a genus.

The second corollary is that swiftness and slowness are not the same as heaviness and lightness, because each of the latter has its own motion, for the motion of earth, which is heavy, is always toward a downward place and the motion of fire is always toward an upward. On the other hand, swiftness and slowness are common to diverse motions, as was said.

713. Then at (528) he shows how an irregular motion is one; Secondly, he draws a corollary at 714.

He says therefore first that an irregular motion can be said to be one insofar as it is continuous, but it is less perfectly one than a regular motion, just as a line having an angle is less perfectly one than a straight line. This is especially clear in a reflected motion, which seems to be, as it were, two motions.

Now, since an irregular motion is less perfectly one, it appears to share in the notion of multitude, for a thing is said to be less, because it has an admixture of the contrary, as what is less perfectly white has an admixture of black, at least in being closer to black than a perfectly white object is.

714. Then at (529) he concludes from the immediately foregoing the conclusion which he had previously proposed; namely, that motions which are specifically diverse cannot form a continuity. For every motion that is one can be either irregular or regular. But a motion that is composed of specifically distinct motions cannot be regular. For how could a regular motion be composed of alteration and local motion? For in order that a motion be regular its parts must agree. Consequently, the conclusion is that diverse motions that are consecutive but not all of the same species do not form a motion that Is one and continuous, as was stated above and explained by examples.

Lecture 8

Contrariety of motions

715. After discussing unity and diversity of motions, the Philosopher now discusses contrariety of motions, which is a kind of diversity, as is evident from Book I of Metaphysics. His treatment is divided into two parts:

In the first he shows how to understand contrariety in motion and in rest;

In the second he raises some questions about such contrariety, at 742.

About the first he does two things:

First he settles the problem of contrariety of motion;

Secondly, about contrariety of states of rest, at 727.

About the first he does three things:

First he distinguishes diverse ways according to which contrariety of motion might be taken;

Secondly, he rejects some of these ways, at 717;

Thirdly, he assigns the true way in which motions and changes are contrary, at 722.

716. He says therefore first (530) that it is now time to decide how one motion is contrary to another, as well as how rest is contrary to motion and rest to rest.

But in this treatment we must first distinguish the ways according to which the idea of contrariety in motions can be taken universally. And he distinguishes five ways. The first of which is that one idea of contrariety in motions is based on one motion approaching a definite terminus and another departing from the name terminus. And this is what he says: “...whether contrary motions are motions respectively from and to the same thing, e.g., a motion from health and a motion to health”. According to this, generation and ceasing-to-be seem to be contrary, because generation is a motion to being, and ceasing-to-be from being.

The second way is that the idea of contrariety of motions is based on contrariety of the termini from which the motions begin. And this is what he says: “...or motions respectively from contraries, e.g., a motion from health and one from sickness”.

The third way is that contrariety of motions is based on the contrariety of the goals at which they are terminated. And this is what he says: “...or motions respectively to contraries, e.g., a motion to health and a motion to sickness”.

The fourth way is to take contrariety of motions according to the contrariety existing between the start of one and the goal of the other. This is what he says: “...or motions respectively one from a contrary and the other to a contrary, e.g., a motion from health and one to sickness”.

The fifth way is based upon contrariety on the part of both termini of each motion. This is what he says: “...or motions respectively from a contrary to its opposite and from the latter to the former, e.g., a motion from health to sickness and a motion from sickness to health”.

Now contrariety among motions is necessarily based either on one of these five ways or on more than one, for there is no other possible way of one motion being contrary to another.

717. Then at (531) he rejects two of these five:

First of all the fourth, which based contrariety on the opposition between the start of one and the goal of the other;

Secondly, the second, which based contrariety on the opposition between the start of one and the start of the other, at 716.

Thirdly, he concludes how two of the remaining ways are related, at 721.

He says therefore first (531) that a motion which begins at one contrary cannot be called contrary to a motion that tends to the opposite contrary, so as to say that a change from health is contrary to a change to sickness. For nothing is contrary to itself; but a motion from health is one and the same as a motion to sickness, although they differ in thought inasmuch as a change from health is not the same idea as a change to sickness—for one stresses the starting point and the other the goal of the same notion. Consequently, contrariety of motion must not be taken from the viewpoint of the contrariety existing between the start of one and the end of the other.

718. Then at (532) he shows that contrariety must not be taken from the contrariety existing between the two starting points of two motions: and this for three reasons, of which the first is the following. Two motions that tend to the same goal are not contrary; but two motions that start from contraries can tend to one and the same goal, for a motion can go either to a contrary or to what is intermediate between the contraries, as will be said later. Thus two motions that start from contraries could terminate at the same intermediate. Consequently, motions are not contrary just because they start at terms that are contrary.

719. He gives the second reason at (533), which is this. The idea of contrariety in motion must be based on that which more evidently makes the motion contrary, but contrariety between goals at which motions end seems to be a greater cause of contrariety in motions than is contrariety between termini at which motions start. For when I say that motions begin at contrary terms, I am stressing the removal of contrariety, but when I say that motions are approaching contrary goals, I am stressing the receiving of contrariety. Therefore, contrariety of motions is not based solely on the termini at which they start.

720. He gives the third reason at (534) and it is this. Things receive contrariety from that from which they take their name and species, for contrariety is a difference based on form, as in clear in Book X of Metaphysics. But every motion gets its name and species from the goal more than from the starting point, as healing is a motion to health and getting sick is a motion to sickness. This point was mentioned before. Therefore, contrariety of motions is taken rather from the goal than from the terminus at which they start. Thus our conclusion is the same as before.

721. Then at (535) he concludes that having rejected the two ways that were based on the contrariety of termini, there remain two other ways, namely, the third and the fifth. Of these, one is based solely on the contrariety of goals and the other on the contrariety of both sets of termini. Way #1 was not based on any contrariety of termini but on approach and departure from the same terminus. He further concludes that perhaps these two remaining ways are really the same, because motions that tend to contrary goals also start at contraries; but perhaps they are not the same in conception, on account of the various relationships that exist between motions and their termini, as was said above. For example, a motion to health is really the same as a motion from sickness, but they differ in conception. The same is true for a motion from health and a motion to sickness.

722. Then at (536) he explains how to take contrariety in motion.

First, when the motion tends toward a contrary;

Secondly, when it tends toward the intermediate, at 726.

About the first he does two things:

First he explains what makes for contrariety in motions;

Secondly, in changes, at 724.

About the first he does two things:

First he explains his proposition with a syllogism;

Secondly, by induction, at 723.

As to the first, he gives this reason at (536): The contrariety of things is based on their specific nature and definition. But the specific definition of motion is that it is a change which takes place from a definite affirmed subject to a definite affirmed subject and that two termini are involved—on this point, motion differs from change, which does not always require two affirmed termini. Therefore, we are left with the fact that for contrariety of motion there must be contrariety on the side of both termini. In other words, a motion which goes from contrary to contrary is, strictly speaking, contrary to one that is from contrary to contrary; for example, one that is from health to sickness is contrary to one from sickness to health.

723. Then at (537) he proves the same by induction. And first of all in bodily alterations: for to fall ill is contrary to getting well. In these two examples the first is from health to sickness and the other from sickness to health. This is also evident in changes that occur in the soul: for to learn is contrary to being led into error (not by oneself but by another). These two motions are also from contraries to contraries, because learning is a motion from ignorance to knowledge, and being deceived is from knowledge to ignorance.

He says “not by oneself”, because just as, in the case of knowledge, it is possible for a person to acquire it by himself (and this is called “discovery) or with someone’s help (and this is called “learning”), so also it can happen that a person is led into error sometimes by himself and sometimes by another. It is the latter that is properly opposed to learning.

Continuing, we take an example from local motion: for an upward motion is contrary to a downward (and these are contraries in respect of length); a motion to the right is contrary to one to the left (and these are contrary in respect of breadth); and a motion to the fore is contrary to one to the rear (and these are contrary in respect of depth).

But notice that Aristotle is here speaking of differences of position as they apply to man: for up and down are measured in respect to man’s length; left and right in respect to his breadth; fore and after in respect to his thickness, which is called height or depth.

Moreover, it should be noted that even in natural motions, there is a contrariety based on up and down; but in regard to right and left, or fore and aft, the contrariety is not according to nature but according to motions that originate from the soul, which has motions toward these contrary directions.

724. Then at (538) he shows how there is contrariety in changes.

First he explains how to take contrariety of change in things in which contrariety is found;

Secondly, how to take it in things in which there is no contrariety, at 725.

He says therefore first (538) that if contrariety is taken merely from the goal so that what tends to a contrary is said to be contrary, such a process does not make for contrariety of motion, but of change, which is generation and ceasing-to-be, as becoming white and becoming black are contrary. Now the contrariety of these instances of generation is not based on the contrariety of starting point; because in generation the starting point is not something affirmed but something negated, for the white comes to be from the non-white and not from something affirmed. For a change from subject to subject is not change but motion.

Then at (539) he shows that in things in which there is no contrariety, for example, in substances and the like, contrariety of change is based on approach and departure from the same terminus, as accession to the form of fire, which pertains to the generation of fire, and receding from the same form, which pertains to its ceasing-to-be, are contraries. Hence generation is contrary to ceasing-to-be and any loss is contrary to any gain, But these are changes, not motions.

It is evident, therefore, that of the five ways listed above, the second and fourth are of no use; one of the remaining is suitable for knowing contrariety of motions, and the other two are suitable for contrariety of changes.

726. Then at (540) he decides about contrariety of motion from the viewpoint of the intermediate between contraries. And he says that wherever a pair of contraries admit of an intermediate, motions to that intermediate must be held to be somehow motions to one or other of the contraries, for the intermediate serves as a contrary for the purposes of motion, no matter in which direction the change may be. For example, grey in a motion from grey to white takes the place of black as starting point, but in a motion from white to grey, it takes the place of black as goal. For the middle is, in a sense, opposed to either of the extremes, as has been said above.

Finally, he concludes what he mainly intended; namely, that motions are contrary to one another, only when one is a motion from a contrary to the opposite contrary and the other is a motion from the latter to the former.

Lecture 9

Contrariety of rest to motion, and of rest to rest

727. After discussing contrariety of motions, the Philosopher now determines about contrariety of states of rest.

First, in motions;

Secondly, in changes, at 732.

About the first he does two things:

First he shows how rest is contrary to motion;

Secondly, which is contrary to which, at 728.

He says first (541) that since not only motion but also rest seem to be contrary to motion, we have to decide how rest is contrary to motion, for, strictly speaking, it is motion that is perfectly contrary to motion. However, even rest is opposed to motion, since it is the privation of motion, and privation is somehow a contrary. For privation and possession form the fundamental contraries, as is said in Book X of Metaphysics, since the idea of privation and possession are involved in every type of contrary, inasmuch as in any set of contraries, one of them is as privation in respect of the other; for example, black in relation to white and sweet in relation to bitter.

728. Then at (542) he shows which rest is contrary to which motion. About this he does three things:

First he phrases the question;

Secondly, he determines the truth, at 729;

Thirdly, he proves it, at 731.

In the question which he proposes (542) he assumes that not any state of rest is indiscriminately opposed to just any state of motion, but a definite type of rest to a definite type of motion; for example, rest in place is opposed to motion in regard to place. But because the question here is a general one, there still remains another problem: whether the opposite of that rest which consists in possessing its goal, for example, whiteness, is the motion to whiteness, i.e., whitening, or the one from whiteness, namely, blackening.

729. Then at (543) he determines the truth.

First as to the contrariety of motion to rest;

Secondly, as to the contrariety of rest to rest, at 730.

He says therefore first (543) that since motion is between two affirmed termini, the contrary of a motion from A to its contrary B is rest in A; for example, the contrary of a motion from whiteness to blackness is rest in whiteness, while the contrary of a motion from the contrary B to A is rest in B. For example, the contrary of a motion from black to white is rest in black.

730. Then at (544) he treats of the contrariety of one state of rest to another. And he says that those states of rest which are in contrary termini are mutually contrary. For it is not suitable to have motions contrary to one another and states of rest not contrary. And how states of rest in opposites are opposite, he explains with the example that rest in health is the opposite of rest in sickness.

731. Then at (545) he proves what he had said about the contrariety of rest to motion. And he says that the opposition of a motion from health to sick is rest in health; for it is not reasonable that rest in health be the opposite of a motion from sickness to health. This he now proves: Rest in the very goal toward which something else is in motion is the consummation and perfection rather than the opposite of that motion. And that rest in the goal toward which there is motion is its perfection is evident from the fact that the state of rest is coming to be during the motion, because the very movement toward the goal means that rest is coming to be. Hence, since motion is the cause of that rest, it cannot be its opposite, because a thing is not the cause of its opposite. Now the contrary of a motion must be either rest in its goal or rest in the starting point. For it is not reasonable to say that rest in some other species is contrary to a given motion or rest, any more than rest in whiteness is contrary to rest in health or motion to health. Consequently, since rest in the goal is not contrary to motion toward that goal, the only thing that remains is that it is contrary to rest in the starting point.

732. Then at (546) he determines about contrariety of rest in changes. About this he does three things:

First he repeats what has already been said about contrariety of changes;

Secondly, he shows that the opposite of change is not rest but non-change, at 733;

Thirdly, how non-change is contrary to change, at 736.

He repeats therefore first (546) that in changes that do not involve termini that are contrary, for example, in the generation and ceasing-to-be of substance, opposition is based on approach and departure from the same terminus. For a change from A is opposed to a change to A, as a change from existence, i.e., corruption, is opposed to a change to existence, i.e., generation. However, neither of these is called motion.

733. Then at (547) he shows that these changes do not have an opposing state of rest. About this he does three things:

First he proposes what he intends;

Secondly, he interposes a question, at 734;

Thirdly, he proves his proposition, at,133-5.

He says therefore first (547) that changes which do not pass from contrary to contrary have no states of rest opposed to them; rather what is opposed to them in the way that rest is opposed to motion can be called non-change.

734. Then at (546) he interposes a question on this matter. For it has been said that a change to being is contrary to a change from being, which is really a change to non-being. Now the expression “non-being” has two senses: In one sense, it implies a subject, which is either an actual being, as when non-white is in a body, or a potential being, as when privation of substantial form is in first matter. In a second sense, non-being can imply that no subject is involved, i.e., that we are dealing with absolute non-being.

If non-being is taken in the first sense, i.e., that a subject. is implied, then it would be possible to find out how one non-change is contrary to another non-change: for it could be said that a non-change in being is opposed to a non-change in non-being. For, since non-being has a subject, there is nothing to prevent that subject from persevering in non-being, which is the same as not changing.

Rut if there is nothing which is not, i.e., if non-being has no subjects then the question remains: to which non-change is the non-change or rest in being contrary? For what does not exist at all cannot be said to be at rest or to be unchangeably permanent. And since some kind of non-change must be contrary to non-change or rest in existence, it follows that that non-existence from which generation begins and toward which ceasing-to-be tends is a nonbeing that has a subject.

735. Then at (549) he explains something he had supposed, namely, that the opposite of generation and of ceasing-to-be is not rest. For if it were, then either of two things would follow: first, that not every rest is contrary to motion, or, secondly, that generation and ceasing-to-be are motions. So it is clear that whatever it is that is opposed to generation and ceasing-to-be, it is not rest, unless generation and ceasing-to-be are motion—which they are not, as we have proved above.

736. Then at (550) he shows how non-change is contrary to change. And he says that there is a parallel between the contrariety of non-change to change and that of rest to motion: for a non-change An being is contrary, either to no non-change (which would be, if non-being has no subject) or to that non-change which is in nonbeing (if non-being has a subject). And this contrariety is like the opposition between one rest and another.

Or we can say that a non-change in being is the opposite of corruption, as rest is of motion. However, it is not the opposite of generation, because corruption departs from non-change and rest in being, whereas generation tends to it. And we already know that the opposite of motion and change is not rest in the goal but rest in the starting point.

Lecture 10

Certain difficulties are resolved

737. After discussing the contrariety of motions and of rests, the Philosopher now raises some questions concerning these matters, About this he does two things:

First he raises questions and solves them;

Secondly, he explains certain matters that may still be doubtful in regard to these questions, at 747.

The first part is divided into three sections, one for each question he raises. About the first point he does two things;

First he raises a question;

Secondly, he solves it, at 740.

738. Therefore he first (551) raises the question why it is that in the genus of local motion, but not in the other general there are found some motions and rests that are according to nature and some not according to nature. For example, why in it that there are alterations according to nature but none not according to nature? For getting well does not seem to be according to nature or not according to nature any more than getting sick, since each originates from a natural intrinsic principle. The same is true in regard to getting white and getting black or in growing and decreasing, for the former motions are not so contrary to one another that one is according to nature and the other not, since each is a natural process. Nor is growing contrary to growing in such a way that one is according to nature and the other not. The same is true of generation and ceasing-to-be: for generation cannot be said to be according to nature and ceasing-to-be not according to nature, for growing old--which is the road to ceasing-to-be-is according to nature. Nor does it appear that one generation is according to nature and another not.

739. Now it seems that what he says here is opposed to a declaration in On the Heavens, that old age and every defect and ceasing-to-be are against nature. But it must be said that old age and ceasing-to-be and decreasing are against nature in one sense and according to nature in another. For if we consider the specific nature of anything, i.e., its particular nature, it is clear that all ceasing-to-be and all defects and decrease are against nature: because each thing’s nature tends to preserve the subject in which it exists, whereas the contrary of this happens when the nature is weak or defective.

But if we consider nature in general, all these things are the result of a natural intrinsic principle, as the destruction of an animal results from the contrariety of hot and cold; and the same is true for all the others.

740. Then at (552) he answers this question by invalidating it. About this he does two things:

First he shows that things according to nature and not according to nature are found in every genus;

Secondly, how these two things are contrary when they occur in motions and it states of rest, at 742.

About the first he does two things:

First he determines the truth;

Secondly, he removes an objection, at 741.

He says therefore first (552) that since what takes place through compulsion is contrary to nature (because compulsion arises from a principle outside a thing in such a way that the thing suffering compulsion does not cooperate, whereas what is natural comes from an intrinsic principle) it follows that compulsive ceasing-to-be is contrary to natural ceasing-to-be, just as a ceasing-to-be that is outside of nature is opposed to one according to nature.

According to the same argument, he concludes that some generations are compulsory and not according to fate, i.e., not according to the order of natural causes (because the order of natural causes. can be called “fate”), as when a person grows roses or fruits by artificial means out of season or when the generation of frogs or other natural things is procured artificially. Consequently, since these generations are compulsory, they are outside of nature and are contrary to generations according to nature.

He shows the same for growing and decreasing. For some cases of growth are compulsory and unnatural, as is evident in persons who reach the state of puberty in an abnormally short time, on account of soft living or on account of the food, i.e., they are fed abundantly and delicately. The same is also apparent in the growing of wheat, for sometimes the grains grow unnaturally through abundance of moisture and are not compact, i.e., made thick and solid by normal digestion.

Likewise in alterations. Some are compulsory and some natural, as is especially evident in the process of getting well. For some recover from fever on the critical days and some not on the critical days. The former are cured according to nature and the latter not according to nature.

741. Then at (553) he raises an objection against the foregoing. For since what is outside the nature is contrary to what is according to nature, then if there are generations that are according to nature and some not, and the same for ceasing-to-be, it follows that instances of ceasing-to-be are contrary not to generation but to one another, because one thing cannot be contrary to two.

But he solves this by saying that there is nothing to prevent generation from being contrary to generation, and ceasing-to-be to ceasing-to-be. This is true, even if you were to abstract from the contrariety between what is according to nature and what is against nature. For if you take the case of something sweet coming to be and then ceasing to be, and the case of something sad coming to be and ceasing to be, the two cases of coming-to-be would be contrary and the two of ceasing-to-be would be contrary. (When he speaks of the coming to be and the ceasing to be of the “sweet”, he means when “something more noble comes to be from the less noble that has ceased to be, as when fire is generated from air; on the other hand, the coming to be and ceasing to be of the “sad” refers to the less noble coming to be from the ceasing-to-be of the more noble, as when air is generated from fire).

Now even though ceasing-to-be is contrary to ceasing-to-be, it does not follow that it is not opposed to coming-to-be, for ceasing-to-be is opposed to coming-to-be when both are taken generically, while ceasing-to-be is opposed to ceasing-to-be in a specific sense. For example, avarice is contrary to liberality in the way that a vice is contrary to a virtue, but it is opposed to prodigality as one species to another. So that what he concludes is this: ceasing-to-be is contrary to ceasing-to-be, not in a generic sense, but one ceasing-to-be is this and another that, i.e., compulsory and beyond nature, or sweet and sad.

742. Then at (554) he explains contrariety in motion and rest on the basis of their being outside nature and according to nature. And he says that not only coming-to-be is contrary to coming-to-bg and to ceasing-to-be from the viewpoint of being outside nature and according to nature, but in general all motions and rests are contrary in this way. For example, an upward motion is contrary to a downward one (because up and down are contrarieties of place) and each of these motions is natural to certain bodies: for fire is naturally carried upward and earth downward. And again in regard to each of these motions, one can take as contrary differences that which is according to nature and that which is outside the nature. And this is what he means when he says that “these contrarieties in motion are differences”, or he might mean that in respect to the very bodies that are moved there are contrary differences in their motions, namely, according to nature and outside their nature. For an upward motion is natural to fire but a downward not. So it is clear that a motion which is according to nature is contrary to one that is outside nature.

Likewise for states of rest. For rest which is above is contrary to a downward movement. But rest above is not natural to earth, whereas a downward motion is. According to the foregoing then, it is clear that rest which is outside the nature is contrary to the natural motion of the body involved, for even in the same body, motions ate mutually contrary, in the sense that the natural motion of one body is contrary to an unnatural motion of the same body. The same is true of rest; for some contrary rests will be according to nature, as rest above for fire and rest down for earth; others are outside the nature? as down for fire and up for earth.

743. Then at (555) he raises the second question; Has every state of rest that is not eternal a becoming, which becoming is called a coming to a standstill? The answer seems to be “no” for two reasons. First of all, if there is coming-to-be of every state of rest that is not eternal, it will follow that there is coming-to-be for states of rest which are outside nature (as when earth is at rest above). Now rest can be produced only by a previous motion, and the motion preceding an unnatural state of rest is compulsory. Consequently, it follows that when earth is violently projected upwards, it is then that rest comes to be. But this cannot be, because “the velocity of that which comes to a standstill seems always to increase”, i.e., when rest is being generated through motion, it is true that as the state of rest gets closer, the motion gets swifter. For since the perfection of coming-to-be is the thing produced, and since each thing gets stronger and more intense as it gets closer to its perfection, it follows that the motion through which rest is produced is swifter the more it approaches rest, as is abundantly clear in natural motions.

But in things that are moved by compulsion the contrary happens: for the motion grows less intense the closer it gets to the state of rest. Consequently, compulsory rest is not generated. This is what he means when he says that some things come to rest by compulsion “without having become so”, i.e., in such a way that their rest is not generated.

744. He gives the second reason at (556) and it is this: Coming to a standstill, i,e., the coming-to-be of rest, is either entirely the same as the natural motion by which something is carried to its natural place or it is something that happens to accompany it. Now it is clear that both are the same reality though differing in conception. For the goal of a natural motion is to be in a natural place, but to be in a natural place and to be at rest in it are really the same thing. Consequently, a natural motion and the coming-to-be of rest are the same thing in reality and differ only in conception. However, it is evident that compulsory rest is not brought about by a natural motion. Therefore, coming to a standstill is not present in compulsory states of rest, i.e., such states are not generated.

745. Then at (557) he raises a third question about a point mentioned in Lecture 3, that rest in A is contrary to motion from A. Now this seems to be false, because when something is moved from A as from a place, or A is being abandoned, as in the case of a quality or quantity, while it is being moved it still seems to have that which is cast off or left behind. For a thing does not leave its entire place all of a sudden but successively; likewise, it is only gradually that it loses whiteness. Therefore, while it is being moved it still retains something of the starting point. If, therefore, the state of rest whereby something remains in a starting point is contrary to the motion by which departure is made therefrom, it follows that two contraries are together—which is impossible.

746. So at (558) he solves this difficulty. And he says that what is being moved by departing from its starting point is at rest therein not absolutely but in a certain sense only, i.e., in the sense that it is there not in its entirety but partly, because it is universally true that in all cases of motion, part of the mobile is in the terminus a quo and part in the terminus ad quem. Nor is it unacceptable that one contrary be mixed with another in a certain respect; but the less it is mixed, the more perfectly is it contrary. Therefore, a motion is more contrary to another motion (since they are never intermingled) than a rest is, which somehow intermingles.

Finally, in summary, he says that we have spoken about motion and rest and how unity and contrariety are found therein.

747. Then at (559) he states some things that will clarify the foregoing. (These passages are said not to be found in the Greek MSS. and, according to the Commentator, not even in the Arabic MSS.; consequently, these statements seem to have been lifted from the sayings of Theophrastus or some other expositor of Aristotle). Three things are here posited in an attempt to clarify the foregoing.

The first pertains to the question previously raised about the generation of unnatural rest. And he says that someone may wonder about “Coming to a standstill”, i.e., about the coming-to-be of rest, for if all motions that are outside nature have an opposing state of rest, i.e., an unnatural one, does that state of rest come to be? If it is held that there is no “coming to a standstill” in cases of compulsory rest, something unacceptable follows. For it is clear that a thing in compulsory motion will sometimes remain, i.e., come to rest, by compulsion. Consequently, it will follow that something will be at rest not eternally without having come to rest—which seems impossible. But it is plain that sometimes there is compulsory rest. For just as things are moved outside their nature, so also they rest outside their nature. Rut it should be observed that what is said here appears contrary to what was said above (at 743). Hence Averroes says that a solution is now being given to a question previously raised.

However, it is better to say that the previous doctrine contains more truth, although what is being said here is somehow true also. For compulsory rest is not, strictly speaking, generated in the sense that it proceeds from a cause that is essentially productive of rest, as happens when natural rests are generated. But compulsory rest is generated per accidens through lack of a productive force, because when the compulsion of the mover either ceases or meets an obstacle, the state of compulsory rest comes to be. This is why compulsory motions peter out at the end, whereas natural ones become more intense.

It should be noted also that there is found another text for this place, to which we should give our attention. For it reads., Someone may ask whether to a motion outside nature there is any contrary rest not according to nature? This does not inquire whether, properly speaking, a state of rest that is contrary to nature is opposed to a motion that is contrary to nature, as Aristotle taught above; rather, here one is now speaking in wide and loose terms in the sense of the general opposition between rest and motion. And he says that it seems unreasonable not to find unnatural states of rest. For it is clear that the violence of the mover will cease at some time and unless rest eventuates, the motion will not come to a standstill. Hence it is clear that. to compulsory motions are opposed compulsory states of rest, because to what is moved outside its nature there belongs to rest outside its nature.

748. Then at (560) he mentions a second fact to explain his doctrine on the contrariety of natural and compulsory motion. And he says that since certain things are subject to motions that are according to nature and outside their nature, as fire is moved upward according to nature and downward outside its nature, the question arises whether the natural upward motion of fire has for its contrary the compulsory downward motion of fire or the natural downward motion of earth.

He answers that both are contrary to the natural upward motion of fire but not in the same way. For the downward motion of earth is contrary to the upward motion of fire as something natural contrary to something natural, whereas a downward motion of fire is contrary to the upward motion of fire as something natural contrary to something compulsory. The same is true for the contrariety of states of rest.

749. Then at (561) he mentions a third point to explain what he previously said about contrariety of rest to motion. And he says that perhaps motion is not strictly opposed to rest, but only in some sense. For when someone is being moved from A, in which he was at rest, and is doffing it, it seems to retain something of A. Hence if rest in this place is contrary to a motion from this place to a contrary place, it follows that contraries are together. But yet a thing is somehow still at rest while it perseveres in A; indeed, speaking generally of a thing in motion, part of it is in the terminus a quo and part in the terminus ad quem. Consequently, rest is less contrary to motion than a contrary motion is, as was explained above.

Finally, he sums up, as is clear of itself.

Now the fact that the same words that appeared in an earlier passage (see end of 246 above) are repeated, lends support to the possibility that they are not the words of Aristotle, but of some expositor.