BOOK VIII

Lecture 1

Opinions on the beginning and end of motion

965. After showing in the preceding book that it is necessary to posit a first mobile, and a first motion, and a first mover, the Philosopher intends in this present book to inquire after a description of the first mover, and first motion, and first mobile, The book is divided into two parts:

In the first he premisses something necessary to the following investigation, namely, that motion is sempiternal;

In the second he proceeds to investigate what is proposed, (L. 5).

About the first he does three things:

First he raises a problem;

Secondly, he states the truth according to his own opinion, (L. 2);

Thirdly, he answers possible objections to the contrary, (L. 4)#

In regard to the first he does three things:

First he proposes his problem;

Secondly, he gives opinions for both sides, at 968;

Thirdly, he shows the usefulness of this consideration, at 970.

About the first he does two things:

First he proposes the problem he intends to investigate;

Secondly, he responds to a tacit question, at 967.

966. In regard to the first it should be known that Averroes says that Aristotle in this book does not intend to inquire whether motion is sempiternal universally, but limits his question to the first motion.

But if one considers both the words and procedure of the Philosopher, this is entirely false. For the words of the Philosopher speak of motion in a universal sense. He says in effect: “Was there ever a becoming of motion before which it had no being and is it perishing again so as to leave nothing in motion?” From this it is clear that he is not inquiring about one definite motion but about motion universally, asking whether at any time there was no motion.

The falseness of Averroes’ statement appears also from the very procedure of Aristotle. First, it is Aristotle’s custom always to argue to his proposition from proper causes. Now, if anyone will consider the arguments he adduces, he will see that in none of them does Aristotle argue from a middle term that refers properly to the first motion, but he argues rather from a middle proper to motion in general. Hence this alone shows that he intends to inquire here about the sempiternity of motion in general.

Secondly, if he had already proved that there is one or a number of sempiternal motions, he would have been foolish to ask below whether anything is eternally in motion, for that question would have been already answered. It also is ridiculous to say that Aristotle would repeat from the start his consideration of a problem he had already settled, and act as though he had omitted something, as the Commentator pretends. For Aristotle had the opportunity to correct his book and fill in at the proper place any section he had omitted, so as not to proceed in a disorderly way. For if this chapter had been treated in the way charged by the Commentator, everything that follows would be confused and disorderly. This is not strange, for, having supposed an initial impossibility, others then follow.

Furthermore, the correctness of our view is shown by the fact that Aristotle later on uses what he proves here, as a principle to prove the eternity of the first motion. He would never have done this, had he already proved that the first motion is eternal.

The reason which moved Averroes is wholly frivolous. For he says that if Aristotle is here intending to inquire into the eternity of motion in common, it will follow that the consideration of Aristotle has been diminished, because it is not evident from what he proves in this place, how motions could be always continued one to the other.

But this has no weight, because it is enough for Aristotle to prove in this chapter in a general way that motion has always been. But how the eternity of motion is continued—whether it is because all things are always in motion, or because all things are sometimes in motion and sometimes at rest, or because some things are always in motion and others sometimes in motion and sometimes at rest—is a question he raises immediately after the present one.

Thus the present chapter must be explained according to this intention, namely, that he intends to inquire about motion in common. According to this, therefore, he asks: “Did motion in common begin to be at some time, so that previously there had never been any motion, and so that at some time it will perish so as to leave nothing in motion, or, on the other hand, did it never begin and will it never cease, so that it always was and always will be?

And he gives an example taken from animals, for some philosophers have said that the world is a certain large animal. For we see animals as alive so long as motion is apparent in them, but when all motion ceases in them they are said to be dead. Accordingly, motion in the whole universe of natural bodies is taken as a kind of life. If, therefore, motion always was and always will be, then this sort of life of natural bodies will be immortal and never-failing.

967. Then at (749) he answers a tacit question. For in the preceding books Aristotle had discussed motion in common, without applying it to things; but now, inquiring whether motion has always existed, he applies his general doctrine about motion to the existence it has in things. Therefore, someone could say that in this consideration the first question should have been about whether motion has existence in things rather than whether it is eternal, especially since there are some who have denied that motion exists.

To this he responds that all who have spoken about the nature of things admit that motion exists. This is evident from their statements that the world was made, and from their consideration of the generation and ceasing-to-be of things, which cannot occur without motion. It is therefore a common supposition in natural science that motion has existence in things. Hence there is no need to raise this question in natural science any more than in other sciences are raised questions about the suppositions of the science.

968. Then at (750) he presents opinions for both sides of the question he proposed.

First he gives the opinions which declare that motion is eternal;

Secondly, those who declare that motion is not eternal, at 969.

In explanation of the first part (750), therefore, it should be known that Democritus supposed that the first principles of things are bodies that are per se indivisible and always mobile and that the world came to be by the chance aggregation of these bodies—not only the world in which we exist but an infinitude of other worlds, since these bodies congregated to form worlds in diverse parts of infinite void. Still he did not posit these worlds as fated to endure forever; rather, some came into existence as a result of atoms combining, and others passed out of existence as a result of the same atoms scattering. Therefore all the philosophers who agree with Democritus assert the eternity of motion, because they say that the generation and ceasing-to-be of certain worlds i’s always going on-and that necessarily involves motion.

969. Then at (751) he gives the opinions of the other side. And he says that whoever declare that there is just one world which is not eternal, also declare what reasonably follows with respect to motion, namely, that it is not eternal.

Therefore, if there be supposed a time in which nothing was in motion, this could happen in two ways, just as it is in two ways that this world could be supposed not always to have been: in one way, that this world began in such a way that previously it never existed at all, as Anaxagoras held; in another way, that the world so began to be that it did not exist for some time previously, but that it again had existed before that time, as Empedocles held.

In like manner with respect to motion, Anaxagoras said that at one time all things were a mixture of one thing with another and nothing was segregated from anything else—in which mixture it was necessary to posit that all things were at rest, for motion does not occur without separation, since whatever is in motion separates from one terminus in order to tend to another. Therefore Anaxagoras posited the pre-existence of this mixture and rest in infinite time, in such a way that at no time before (the present world) had there been any motion at all, and that it was Mind, which alone was unmixed, that caused motion in the first instance and began to separate things one from another.

Empedocles, on the other hand, said that in one period of time some things are in motion, and again in another period all things are at rest. For he posited Friendship and Discord as the first movers of things: Friendship’s property was to make a unity of all things, and Discord’s to make many things from the one. But because the existence of a mixed body requires a mingling of the elements so as to form one thing, whereas the existence of a world required that the elements be dispersed in orderly fashion, each to its respective place, he posited that Friendship is the cause of the coming-to-be of mixed bodies, and Discord the cause of their ceasing-to-be; but that, contrariwise, in the whole world Friendship was the cause of its ceasing-to-be and Discord the cause of its coming-to-be.

Accordingly, he posited that the whole world is being moved, when either Friendship makes one from the many or when Discord makes many of the one; but during the intermediate times, he supposed there was rest—not in the sense that there was no motion at all, but none with respect to the general change of the world.

Because Aristotle had mentioned the opinion of Empedocles, he also gave the very words, which are difficult to interpret because they are in metre.

Thus, therefore, did Empedocles express his opinion in this arrangement of words : “It has learned to be born,” i.e., it is customary for something to be generated, “the one from the manifold”; “and again,” i.e., in another way, “from the one commingled,” i.e., composed of a mixture, “the manifold arises,” i.e., the many come to be through separation—for some things are generated by combining with others, and others by separating.

And according to what we observe in regard to particular instances of coming-to-be, so “thus do things come to be,” i.e., the same must be understood in the universal coming-t-o-be of things with respect to the whole world. “Nor is their era one,” i.e., there is not just one period of duration of things; but at one time a world is generated, at another it is destroyed, and in between there is rest: for “era” is taken to mean the measure of the duration of a thing..

He expresses the distinction of these eras when he adds, “Thus are they changed,” i.e., as though stating that the time in which things pass through the cycle of combining or separating is called one era. And lest anyone suppose that the generation of a world does not require an era, i.e., a period of time, but that the universe comes to be in an instant, Empedocles adds, “nor are they made perfect all at once,” but after a long interval of time.

Then speaking of the other era he adds, “thus are they always immobile,” i.e., in the time between the generation and corruption cycle, he supposed that things are at rest.

And lest anyone believe that before there was always change, and that later there will be continual rest, he excludes this by saying “alternately,” i.e., as though saying that this happens in cycles, namely, that things change and then rest, and then change again, and so on ad infinitum.

Then the words of Aristotle are added to explain the foregoing words of Empedocles, especially the expression, “thus they change.” He says therefore that following the words, “thus they change,” must be understood the addition, “from then hence,”, i.e., from a definite beginning up to the present—not in the sense that motion always was, or that after it began it had been interrupted.

970, Then at (752) he shows the usefulness of considering the question he has proposed. And he says that we must consider just what is the truth about this question, for to know the truth about it is most necessary not only for natural science but the science of the first principle as well, since both here and in the Metaphysics he uses the eternity of motion to prove the first principle.

This method of proving the existence of a first principle is most efficacious and irresistible. For if on the supposition that both motion and the world existed forever, it is necessary to posit one first principle, then, if the eternity thereof should be rejected, it is all the more necessary, for it is clear that every new thing requires a principle bringing it into being. Now the only reason why it could seem that no first principle would be necessary, would be if things were ab aeterno. But if the existence of a first principle follows even on that supposition, i.e., that the world existed ab aeterno, it is clear that the existence of a first principle is absolutely necessary.

Lecture 2

Arguments for the eternity of motion

971. After raising the problem of the eternity of motion, the Philosopher now intends to show that motion is eternal. His treatment is divided into two parts:

In the first he explains his proposition;

In the second he solves objections contrary to his proposition, (L.4).

About the first he does two things:

First he presents arguments to show the eternity of motion;

Secondly, he answers opinions to the contrary, (L. 3).

About the first he does two things:

First he shows that motion always has been;

Secondly, that it always will be, at 895.

About the first he does two things:

First he explains his proposition with an argument from motion;

Secondly, with an argument from time, at 979.

About the first he does three things:

First he premisses something needed for his proposition;

Secondly, he presents a proof that manifests his proposition, at 976;

Thirdly, he shows that his argument proceeds necessarily, 977,

972. He says first (753) therefore, that in order to demonstrate the proposition we must begin with things determined at the very beginning of the Physics and use them as principles. By this he gives us to understand that the preceding books, in which he determined about motion in general and which for this reason are given the general title “About Natural Things,” are set off from this Book VIII, in which he begins to apply motion to things.

He assumes, therefore, what was said in Physics III, namely, that motion is the act of a mobile precisely as such. From this it appears that in order for motion to exist there must exist things which can be moved with some sort of motion, because an act cannot exist without the thing of which it is the act. Accordingly, from the definition of motion it is evident that there must be a subject of motion, if there is to be motion at all.

But even without the definition of motion that fact is per se evident from the general consent of all, for everyone admits as a necessary fact that nothing is moved except what can be moved—and this with reference to any and all motion; for example, nothing can be altered except what is alterable, or be moved with respect to place unless it be changeable with respect to place.

And because the subject is by nature prior to what is in the subject, we can conclude that in individual changes—both from the viewpoint of the mobile and of the mover—the combustible subject is prior to its being set afire, and the subject capable of setting it afire is prior to its setting afire, prior, I say, not always in time but in nature.

973. From this argument of Aristotle, Averroes took occasion to speak against what is held by faith about creation. For if coming-to-be is a kind of change and every change requires a subject, as Aristotle here proves, it is necessary that whatever comes to be does so from a subject, therefore, it is not possible for something to come to be from nothing.

He confirms this with another argument: When it is said that the black comes to be from the white, this is not to speak per se, in the sense that the white itself is converted into the black, but it is to speak per accidens, in the sense that upon the departure of the white, the black succeeds it. Now whatever is per accidens is reduced to what is per se. But that from which something comes to be per se, is the subject, which enters into the substance of what comes to be. Therefore, whatever is said to come to be from its opposite comes to be from it per accidens, but per se it comes to be from the subject. Accordingly, it is not possible for being to come to be from non-being absolutely.

In further support of his position Averroes adduces the common opinion of the early philosophers that nothing comes to be from nothing.

He also gives two reasons from which he considers that the position arose that something should come to be from nothing. The first is that ordinary people do not consider as existing anything but what is comprehensible by sight; therefore, because they see something visible come to be which previously was not visible, they think that it is possible for something to come to be from nothing.

The second reason is that among the common people it could be thought to be a weakening of the virtue of the agent that it should need matter in order to act, which condition, however, does not derive from the impotency of the agent, but from the very nature of motion. Therefore, because the first agent does not have a power which is in any way deficient, it follows that it should act without a subject.

974, But if one considers rightly, he was deceived by a cause similar to the cause by which he claimed we are deceived, namely, by considering particular things. For it is clear that a particular active power presupposes the matter which a more universal agent produces, just as an artisan uses the matter which nature makes. From the fact therefore, that every particular agent presupposes matter which it does not produce, one should not suppose that the first universal agent—which is active with respect to all being—should presuppose something not caused by it.

Nor, moreover, is this in keeping with the intention of Aristotle who in Metaphysics II proves that the supremely true and the supreme being is the cause of being for all existents. Hence the being which prime matter has—i.e., a being in potency—is derived from the first principle of being which is in a supreme way a being. Therefore, it is not necessary to presuppose for its action anything not produced by it.

And because every motion needs a subject—as Aristotle proves here, and as is the truth of the matter—it follows that the universal production of being by God is neither motion nor change, but a certain simple coming forth. Consequently, “to be made” and “to make” are used in an equivocal sense when applied to this universal production of being and to other productions.

Therefore, just as, if we should understand the production of things to be from God ab aeterno—as Aristotle supposed, and a number of the Platonists—it is not necessary, indeed, it is impossible, that there have been a pre-existing but unproduced subject of this universal production, so also, in accord with the tenets of our faith, if we posit that he did not produce things ab aeterno but produced them after they had not existed, it is not necessary to posit a subject for this universal production. It is evident, therefore, that what Aristotle proves here, namely, that every motion requires a mobile subject, is not against a tenet of our faith—for it has already been said that the universal production of things, whether ab aeterno or not, is neither a motion nor a change. For in order that there be motion or change, it is required that something be other now than previously, and thus there would be something previously existing, and consequently this would not be the universal production of things about which we are now speaking.

975. Similarly, Averroes’ statement that something is said to come to be from its opposite per accidens and from a subject per se is true in particular productions according to which this or that being comes to be, e.g., a man or a dog, but is not true in the universal production of being.

This is clear from what the Philosopher said in Physics I. For he said there that if this animal comes to be inasmuch as it is this animal, it ought not come to be from “non-animal” but from “non-this-animal”—for example, if a man comes to be from non-man or a horse from non-horse. But if animal is produced precisely as animal, it must come to be from non-animal. Accordingly, if some particular being comes to be, it does not come to be from absolute non-being; but if the whole being comes to be, i.e., if being precisely as being comes to be, it must be made from absolute non-being—if, indeed, this process should be called “being made,” for it is an equivocal way of speaking, as has been said.

What Averroes introduces about the early philosophers has no value, for they were unable to arrive at the first cause of all being but considered the causes of particular changes.

The first of these philosophers considered the causes solely of accidental changes, and posited all “being made” to be alteration. Those who succeeded them arrived at a knowledge of substantial changes, but those who came still later, such as Plato and Aristotle, arrived at a knowledge of the principle of all existence.

Consequently, it is clear that we are not moved to assert that something comes to be from nothing because we suppose only visible things to be beings; rather it is because we do not content ourselves with considering merely the particular productions of particular causes, but go on to consider the universal production of all being from the first principle of being. Nor do we assert that to need matter in order to act is due to a diminished power, in the sense of such a power’s lacking its natural energy, rather, what we say is that this is proper to a particular power, which does not extend to all being but makes a particular being.

Hence one can say that it is characteristic of a “diminished power” to make something from something in the sense that we would say that a particular power is less than the universal power.

976. Then at (754), assuming that a mobile and a mover are required in order that there be motion, Aristotle argues in the following manner: If motion has not always existed, it is necessary to say either that mobiles and movers were at some time made, having previously not existed, or are eternal. If, therefore, it is held that each mobile has been made, it is necessary to say that previous to the change which is taken as the first, there was another change and motion according to which was made the very mobile which is able to be moved and to have been moved. This inference, indeed, depends on the preceding. For if it is granted that motion has not always been but that there is some first change before which there was none, it will follow that that first change involved a mobile, and that that mobile was made, for previously it did not exist—since it is being supposed that all mobiles have been made. Now, whatever comes to be after having previously not existed, comes to be through a motion or a change. But the motion or change through which a mobile comes to be, is prior to the change by which the mobile is moved. Therefore, prior to the change which was presumed to be first is another change and so on ad infinitum.

But if it is held that things which are mobile always pre-existed even when no motion existed, this seems to be unreasonable and a sign of ignorance. For it immediately appears that if mobiles exist, motion ought to exist, for natural mobiles are at once also movers, as is clear from Book III. But if natural mobiles and movers are existing, there must be motion.

But to enter more deeply into our search for the truth, it is necessary that this same thing happen—if mobiles and movers are assumed to be eternally existing prior to motion—that followed from the assumption that they were made, namely, that prior to the change supposed to be the first, there is other change ad infinitum. This is evident in the following way: If it be supposed that certain mobiles and certain movers exist, and yet the first mover begins at some time or other to cause motion and something is moved by it, and before this nothing is being moved but is at rest, it will be necessary to say that there was another change in the mover or mobile made prior to that which was assumed to be the first one produced by the mover beginning to cause motion, The truth of this is clear from the following:

Rest is the privation of motion. Privation, however, is not present in a thing capable of habit and form except on account of some cause. Therefore there was a cause—either on the part of the mover or on the part of the mobile—why there was rest. Therefore, as long as that cause prevailed, there was always rest. If, then, a mover begins at some time to cause motion, the cause of rest must be removed. But it cannot be removed except by a motion or change. Therefore, it follows that before that change which was said to be first, there is a prior change by which the cause of rest is removed.

977. Then at (755) he proves the necessity of the foregoing argument. For someone could say that it happens that things are at rest at some time and in motion at some time, without any pre-existing cause of rest to be removed. Hence he wishes to refute this. And about this he does two things:

First he premisses something needed for his proof;

Secondly, he presents the proposed proof, at 978.

He says therefore first that among movers, some move “singularly,” i.e., in just one way, while others move with respect to motions that are contrary. Things that cause motion in just one way are natural things, as fire always heats and never cools. But beings that act through intellect are causes of motions that are contrary, for one and the same knowledge seems to deal with things and their contraries, as medicine is the science of health and of sickness. Hence one sees that a doctor by means of his science can cause motions that are mutually contrary.

Now Aristotle mentioned this distinction among movers, because in things that act through intellect it does not appear that what he had said is true, namely, that if something is moved when previously it had been at rest, the cause of the rest ought first be removed. For things that act according to intellect seem to be ready to move to opposites without any change of themselves being involved; hence it seems that they can cause motion and not cause it, without any change.

Therefore, lest his argument be forestalled by this objection, he adds that his reason holds both for things that act according to intellect and that act by nature. For things that act by nature do always per se move to one, but per accidens they sometimes move to the contrary, and in order that such an accident occur, some change is necessary; thus cold always per se causes coldness, but per accidens it produces warmth.

But that cold should per accidens cause warmth is due to some change affecting the cold object, either inasmuch as it is moved to another location, thus making it differently related to the object which is now made warm by it than it was when it was making it cold, or inasmuch as it completely departs.

For we say that cold is the cause of warmth by departing in the way that a captain is by his absence the cause of the sinking of a ship; again, cold becomes per accidens the cause of warmth either by moving farther away or by approaching closer, as in the winter the interior of animals is warmer, because their heat retreats inward on account of the surrounding cold.

The same applies to things that act by intellect, For knowledge, although it is one thing dealing with contraries, does not deal equally with them both but with one principally, as medicine is per se ordained to causing health. Therefore, if it happens that a doctor uses his knowledge for the contrary purpose of causing sickness, this will not be per se from this science but per accidens, on account of something else. And in order that that something else occur when previously it did not exist, some change is required.

978. Then at (756) he sets forth the proof which manifests his proposition. He says therefore that from the fact that things are such, i.e., that a similar situation prevails with respect to things that act by nature and things that act by intellect, then, speaking universally of all, we can say that whatever things are possible to make, or to be acted upon, or to cause motion, or to be moved, cannot cause motion or be moved in just any disposition in which they find themselves, but according as they are in some definite state and nearness with respect to each other.

And this he concludes from the premisses, because it has already been said that both in things that act according to nature and in things that act according to will, none is the cause of diverse things except as it is a different state. Accordingly, it is necessary that when the mover and the moved approach one another according to a suitable distance and likewise when they are in whatever disposition is required for one to cause motion and for the other to be moved, then the one must be moved and the other must cause motion.

If, therefore, there was not always motion, it is clear that existing things were not in that state that allowed for one to cause motion and another to be moved; rather, they were in the state of not being able to cause motion and of being moved at that time. But later they reached that state in which one moves and the other is moved. Therefore, one or the other of them changed.

For we see that in all things which are said to be “to something” it does not happen that a new relation arises except through a change affecting one or other or both, as, for example, if something which previously was not “double” has now become double, even though not both of the extremes were changed, yet at least one of them was. Accordingly, if there newly arises a relationship by which something causes motion and something is moved, then one or other or both had to be previously moved. Hence, it follows that there is a change prior to the one assumed to be the first.

979. Then at (757) he explains his proposition with an argument from time.

First he premisses two things necessary for his proposition. The first of these is that “prior” and “subsequent” cannot occur unless there is time, since time is nothing else than prior and subsequent precisely as numbered. The second is that time cannot be, unless there is motion. This, too, is clear from the definition—given in Book IV—describing time as the number of motion with respect to prior and subsequent.

980. Secondly, at (758) he concludes to a conditional proposition from statements made in Book IV, For there, according to his doctrine, he stated time to be the number of motion; according to the doctrine of the other philosophers time is a motion, as he there stated. But whichever of these is true, it follows that this conditional is true: If time always exists, it is necessary that motion be perpetual.

981. Thirdly, at (759) he proves in two ways the antecedent of this conditional. First, from the opinions of others. And he says that all the philosophers but one, namely, Plato, seem to be in accord with regard to the opinion that time is not begotten, i.e., that it did not begin to exist after previously not existing. Whence, Democritus also proved that it is impossible that all things should have been made in the sense of newly beginning to be, because it is impossible that time have been so made that it begin newly to be.

Only Plato generates time, i.e., says that time was newly made. For he says that time was made at the same time as the heavenst and he supposed that the heavens were made, i.e., that they have a beginning of their duration, as Aristotle here claims, and as Plato’s words seem at first glance to indicate—although Platonists say that Plato asserted that the heavens were made in the sense that they have an active principle of their existence but not as having a principle of their duration. Thus, therefore, does Plato alone seem to have conceived that time cannot be without motion, for he did not suppose that time existed before the motion of the heavens.

982. Secondly, at (760) he proves the same point by an argument, namely, from the fact that it is impossible to say or to understand time to exist without the “now,” just as it is impossible that there be a line without a point, The “now,” however, is something intermediate, having as part of its nature that it be at once a beginning and an end, i.e,, the beginning of a future time, but the end of a past. From this it appears that it is necessary for time always to be. For whatever time is taken, its boundary is a “now” in both senses. And this is clear from the fact that nothing is actual in time but the Itnow,” because what is past has gone by, and what is future does not yet exist. But the “now” which is taken as the boundary of time, is both a beginning and an end, as has been said. Therefore it is necessary that from both aspects of whatever time is taken, time always be; otherwise the first “now” would not be an end, and the last not a beginning.

But from the fact that time is eternal, he concludes that motion too must be eternal; the reason for this conclusion being that time is a property of motion, for it is its number, as was said.

983- But the argument of Aristotle does not appear efficacious. For the “now” is to time as the point is to the line, as was explained in Book VI. But it is not necessary that a point be an intermediate, for some points are merely the beginnings of lines and others the ends, although every point would be both a beginning and an end if the line were infinite. One could not, therefore, prove that a line is infinite from the fact that every point is a beginning and an end; rather it is the other way around: from the fact of a line’s being infinite, one would go on to prove that every point would be both a beginning and an end. Accordingly, it also appears that the claim that every “now” is a beginning and an end is not true, unless time is assumed to be eternal. Therefore in assuming this as a middle term, i.e., that every “now” is a beginning and an end, Aristotle seems to suppose the eternity of time—the very thing he ought to prove.

Now Averroes, in trying to save Aristotle’s argument, says that the attribute of always being both a beginning and an end belongs to the “now” inasmuch as time is not stationary like a line but flowing. But this does not pertain to the proposition. For from the fact that time is flowing and not stationary, it follows that one “now” cannot be taken twice in the way that one point is taken twice, but the flow of time has nothing to do with the “now” being at once a beginning and an end. For the notion of begining and end is the same in all continua whether they be permanent or flowing, as is clear from Book VI.

984. And therefore another explanation must be furnished in accord with the intention of Aristotle, which is that he wishes to derive the fact that every “now” is a beginning and an end from what he had first supposed, namely, that “prior” and “subsequent” would not be, if time did not exist. For he uses this principle which he supposes for no other purpose, but deduces from it that every “now” is a beginning and an end. For let us suppose that some “now” is the beginning of a time; but it is clear from the definition of a beginning, that the beginning of a time is that before which nothing of the time existed. Therefore, there must be taken something “before” or “prior” to the “now” which is assumed as the beginning of the time. “Prior,” however, does not exist without time. Therefore, the “now” which is taken as the beginning of a time is also the end of a time. In the same way, if a “now” be taken as the end of a time, it too will be a beginning, because an end is by definition that “after which” nothing of a thing exists; but “after” cannot be without time. Therefore, it follows that the “now” which is the end of a time is also a beginning.

985. Then at (761) he shows that motion will always be. And he shows this on the part of motion, because the argument from motion given above concluded only that motion never began, whereas the argument from time concluded both, i.e., that it never began and that it never ceases. He says therefore that the very argument by which it was proved that motion never began can prove that motion is indestructible, i.e., that it will never end. For just as from the assumption that motion began it followed that there was a change prior to the change assumed to be first, so too, if it be supposed that motion at some time ceases, it follows that a change will occur after the one assumed to be the last,

How this follows he explains by abbreviating the more diffuse explanation he gave with regard to the beginning of motion. For he had supposed that if motion began, the mobiles and movers either began or always were. The same alternatives can be taken here, namely, that if motion should cease, the mobiles and movers will remain or they will not. But because he had previously shown that the same conclusion follows from either alternative, here therefore he uses only the one alternative, i.e., the supposition that motion ceases in such a way that the mobiles and movers also pass away.

Therefore, beginning with the assumption mentioned, he says that both the actual motion and the mobile do not pass away simultaneously, but just as the generation of a mobile is prior to its motion, so the ceasing-to-be of a mobile is subsequent to the passing away of its motion. This is so because something combustible can remain after combustion ceases.

And what was said of the mobile must also be said of the mover, because a mover in act does not in ceasing to be cease at the same time to be a mover in potency. Accordingly, it is evident that if even the mobile cease to be after the destruction of its motion, then there has to be a process by which the mobile passes out of existence.

And again, because we are supposing that all mobiles and motions are ceasing to be, it will be necessary later that even the cause of their ceasing-to-be cease to be. But because ceasing-to-be is a type of motion, it will follow that after the final change, other changes occur. But since this is impossible, it follows that motion endures forever.

986. These, therefore, are the arguments by which Aristotle intends to prove that motion always has been and will never cease, The first part of which, i.e., that motion always existed, conflicts with our faith, For our faith admits nothing as eternally existing but God alone, Who is utterly immobile—unless, of courset you wish to refer to the act of the divine intellect as a motion, but that would be an equivocal sense, and Aristotle is not here speaking of motion in that sense but of motion properly so called.

The other part of the conclusion is not entirely contrary to the faith, because, as was said above, Aristotle is not treating of the motion of the heavens in particular but of motion universally. Now we believe according to our faith that the substance of the world indeed began, yet so as never to cease. For we posit that some motions will always exist, especially in men who will always remaing living an unceasing life either of happiness or misery.

But some, vainly trying to show that Aristotle concluded nothing contrary to the faith, have said that Aristotle does not intend here to prove as a truth that motion is eternal but to allege reason for both sides of a question that is doubtful. Rut this is a foolish statement to anyone who investigates Aristotle’s procedure here. Moreover, he uses the eternity of time and of motion as a principle to prove the existence of a first principle both here in Physics VIII and in Metaphysics XII. That shows he considered it proved.

987. But if one rightly considers the arguments here given, the truth of the faith is not assailed by them, For they prove that motion did not begin through the way of nature, as some taught it did, but that it did not begin by things being created by a first principle of things, as our faith holds, cannot be proved by these arguments. And that will be evident to anyone who considers each of the inferences here drawn by Aristotle.

For when he asks whether, if motion did not always exist, the movers and mobiles always existed or not, the reply must be that the first mover always existed; other things—movers or mobiles—did not always exist, but began to exist from the universal cause of all existence. But it has been pointed out above that the production of all being by the first cause of being is not a motion, whether this coming-forth be taken to be ab aeterno or not. Accordingly, it does not follow that before the first change there was a previous change. But this would follow if the movers and mobiles were newly brought into existence by some particular agent acting upon some presupposed subject that would be changed from non-being to being, or from privation to form—and Aristotle’s argument concerns this way of coming into existence.

988. But because we posit that at least a first mover always existed, we need to give an answer to his subsequent deduction that, if movers and mobiles pre-exist, and motion begins newly to be in them, then the movers or mobiles could not have been previously in that disposition in which they are while there is motion, and therefore, some change must have preceded the first change.

Now, if we are speaking of the motion itself, the answer is easy: the mobiles were not previously in that disposition in which they now are, because previously they did not exist; hence they could not be moved. But, as it has been said, they received their existence not through a change or motion but through coming forth from the first principle of things; accordingly, it does not follow that before the first change there was a change. But there still remains the question about the first production of things. For if the first principle, which is God, is no different now than before, then neither does he produce things now any more than before; but if he is different, at least the change affecting him will be prior to the change which is supposed to be the first.

And indeed, if he were a cause that acts only through nature and not through intellect and will, this reason would conclude necessarily. But because he acts through will, he can through an eternal will produce an effect which is non-eternal, just as by his eternal intellect he can understand a thing that is non-eternal—the thing understood being in a certain way the principle of action in causes that act by intellect, as a natural form is in causes that act by nature.

989. But a further point must be pursued. For we do not say that a will postpones doing what it wants, unless something is expected in the future that does not yet exist in the present, as for example, when I will to make a fire not now but later, because in the future it is expected to be cold, on account of which I make the fire; or at least a presence of time is awaited. But that time succeeds time does not occur without motion. Therefore, it cannot be that a will, even if it be immutable, postpones doing what it wills, without some motion being involved, Accordingly, the new production of things cannot come forth from the eternal will except by means of motions succeeding one another ad infinitum.

Now those who raise this objection fail to see that it assumes a thing acting in time, i.e., something that acts on the assumption that time exists; for in this kind of action which occurs in time, one must consider some determinate relationship to this time or to things that exist in this time to explain why it be performed in this time rather than in some other time. But this reasoning has no place in the universal agent, which produces time itself at the same time that it produces other things.

For when we say that things have not always been produced by God, we do not understand that an infinite time preceded, in which God refrained from acting and that later, at a definite time, He began to act; rather, we understand that God produced at once both time and things after they did not exist. Accordingly, we must not consider in the divine will that it willed to make things not then but later, as though time were already existing; rather, we must solely consider the fact that he willed that things and the time of their duration should begin to be after they had no existed at all.

If it be asked why he willed this, it must be said without a doubt that it was for his own sake. For just as he made things because of himself, in order that in them the likeness of his goodness be manifested, so he willed that they not always be, in order to show his self-sufficiency, from the fact that, although nothing else existed, he in himself had all sufficiency of happiness and of power to produce things.

And this can indeed be said as far as human reason can grasp divine things, saving, of course, the secret of divine wisdom which cannot be comprehended by us.

990. Because the solution of this argument proceeded on the supposition that time did not always exist, there remains the problem of solving the argument which seems to prove that time always existed. And perhaps Aristotle, after the argument from motion, gave one from time, because he thought that the one from motion would be inefficacious, unless time was assumed to be eternal. His statement, therefore, that whenever there is time there must be a “now” existing, must be granted without demur. But the statement that every “now” is both a beginning and an end should not be conceded, unless it be also granted that motion always existed, so that every indivisible of motion (which is called a “moment”) should be both a beginning and an end of motion—for the “now” is to the moment as time is to motion. If, therefore, we suppose that motion has not always existed, but that we can take some first indivisible in motion before which nothing of motion existed, we can also take some “now” in time before which there was no time.

Now we have already shown, in explaining the text, that what Averroes says to bolster this argument is inefficacious. But neither is there any efficacy in what Aristotle cites to bolster his own position, namely, that “before” and “after” do not exist without time.

For when we say that a time’s beginning is “that before which nothing of the time existed,” we are not thereby compelled to say that the “now” which is the beginning of the time, is preceded by a time signified by the word “before,” any more than in magnitudes, if I say that the beginning of a magnitude is “that beyond which nothing exists of that magnitude,” it is necessary to say that the phrase, “beyond which beginning,” signifies some real place existing in nature—for it signifies an imaginary one only. Otherwise, it would be necessary to posit a place beyond the universe, whose magnitude is finite and has a beginning and an end.

Similarly, the first “now” which is the beginning of time is not preceded by a time existing in reality but only in our imagination. And this is the time that is described when one says that the first “now” is the beginning of time, “before which” nothing of time exists.

Or it may be said that in the expression, “the beginning of time is that before which nothing of time exists,” the word, “before,” is not affirmed but denied—and so it is not necessary to posit a time before the beginning of time. For in things which exist in time, it happens that some certain time precedes their beginning, as, when it is said that the beginning of youth is that before which there was nothing of youth, the word “before” can be taken in an affirmative sense, because youth is measured by time. But time is not measured by time; hence no time preceded its beginning; hence the word “before” in the definition of time is not taken affirmatively but negatively.

But before time there does exist a duration, namely, the eternity of God. But this eternity has no extension or any before or after as time does; rather, it is all at once—and is not of the same nature as time any more than the divine magnitude is of the same nature as a bodily magnitude.

Therefore, just as when we say that “outside” the universe there is nothing but God, we are not positing some dimension outside the world, so too, when we say that “before” the universe nothing existed, we are not positing any sort of successive duration before the universe.

Lecture 3

Arguments against Anaxagoras and Empedocles

991. After presenting the reasons showing that motion always existed, the Phillosopher here gives arguments against Anaxagoras and Empedocles who posited the contrary. About this he does two things:

First he gives an argument against their position;

Secondly, against the argument they presupposed, at 992.

He says therefore first that since it has been shown that motion always exists, it is wrong to say, as Empedocles and Anaxagoras did, that at some time motion exists and at another time it does not; for to make such a claim is a figment, because it has no basis. Something stated without a reason or the support of divine authority seems, indeed, to be a fiction. However, divine authority has more value than human reason, much more indeed than the authority of a philosopher is more valuable than the weak argument some child might give. Therefore, what is held by faith, even though it be believed without an argument is not a figment of the mind, because we believe on the divine authority approved by miracles —works that God alone can produce.

992. Then at (763) he objects against the argument on which they rested. About this he does three things:

First he suggests that their argument is unsuitable;

Secondly, that it was more unsuitable to Anaxagoras’ position than to that of Empedocles, at 993;

Thirdly, he shows that even according to Empedocles’ opiniont it is unsuitable, at 994.

He says therefore first (763) that it also seems a fiction that anyone, positing that motion at one time exists and at another time does not, should give as his reason that this is so because it is natural for it to be that way, and then adds that this statement must be accepted as a principle. Now that is what Empedocles seems to say, namely, that the situation whereby during one period of time things maintain friendship, and during another are ruled by discord that sets things in motion, but in the interim are at rest, is due to a sort of necessity in things. That is like saying that the reason why heat warms is that it has to be that way, and that heat warms should then be accepted as a principle. This is exactly what Empedocles does, when he takes as a principle that it is due to an ordinance of nature that things are at one time being moved by friendship, and at another time by discord, and at another time are at rest.

Perhaps Anaxagoras, too, and others who posit one active principle would speak in a similar vein, namely, that we must accept as a principle that moti6n began to exist after not existing for an infinite period of time.

993. Then at (764) he shows that Anaxagoras used this argument in a more unsuitable way than did Empedocles. For it is clear that when something is laid down as a principle, it should be accepted as being according to the nature of a thing, i.e., that the nature of a thing is such that such a thing belongs to it. Thus we accept the principle that the whole is greater than its part, because it is the very reason and nature of a whole that it exceed the quantity of a part. Hence, when Empedocles says, “It is natural that it be that way,” he gives us to understand that it should be accepted as a principle. Anaxagoras would have said the same, although he did not express it.

But it is clear that no natural thing nor anything that belongs to things naturally, can exist without ordert because nature is a cause of order. For we see that nature in its works proceeds in an orderly fashion from one thing to another. Therefore, whatever does not possess order is not according to nature and cannot be called a principle.

But two infinites have no order, one to the other, because there is no ratio between one infinite and another, whereas every order is a kind of ratio. Accordingly, it is evidently not a work of nature that things rest for an infinite time and later begin to be moved for an infinite time without there being, between this time and that, any difference to explain why motion comes to be now rather than before; any more than it is a work of nature not to assign some other order between the two thingst so that when one fails the other begins and motion comes to be, as Anaxagoras posited. These are not works of nature, because whatever is in nature either is always the same and not sometimes this way and then that way—as fire always moves upwards—or there is some reason why it is not always the same, as for example, animals do not always continue growing but reach a point when they start to decrease—and for this there is a reason.

Accordingly, it does not seem to be according to nature that for an infinite time things be at rest and later begin to be moved, as Anaxagoras assumed.

Hence it is better to say, as Empedocles said—and those who believed as he—that the whole universe is at rest at one time and in motion at another, because at least in this case there would be order, for there can be a ratio between one finite and another.

It should, however, be considered that the tenet of our faith is not akin to Anaxagoras’ position, for we do not assume before the world any infinite reaches of time that have to be related to a later time; rather, before the world began, only the simple eternity of God existed, and that is outside the genus of time.

994. Then at (765) he shows that the above-mentioned argument is not appropriate in Empedocles’ situation either.

First he explains the proposition;

Secondly, he rejects a false interpretation, at 995.

He says therefore first (765) that even the holder of Empedocles’ theory ought not to assert the fact only but also should explain the cause of his statement and not go beyond what is required by the cause he assigns. Nor should he accept anything as an axiom, i.e., as a principle without reason; rather, whatever is accepted as a principle should be explained either by induction, as is done in the case of natural principles based on sense experience, or by demonstration, as in the case of those principles which are proved by prior principles. But Empedocles does not do that. Granted that he posits friendship and discord as causes, yet it is not the property of friendship or hostility that one should cause motion after the other. For it is not the nature of friendship to be changed into hostility, or vice versa; though it is of the nature of friendship to gather and of hostility to scatter.

But if it is further determined that at one time the one gathers and that at another time the other scatters, it must be further made clear by definite instances in which this occurs. For example, that friendship gathers and discord scatters is manifested among men, because by the former men are united but by the latter they fly from one another. So Empedocles supposed that this is what happens in the whole universe, because it seems to happen in certain cases. But that according to equal periods friendship should move at one time and discord at another, needs to be supported by argument, since that is not seen to happen among men.

995. Then at (766) he rejects a false assumption. For someone could believe that whatever is eternal has no cause, since whatever we observe as being caused among us is something that begins newly to be. Consequently, it seemed to some that when a discussion reached something that always existed, there was no need to inquire any further for a cause or a reasons In this vein Empedocles could say that friendship and discord had always caused motion according to equal times and therefore no reason for it need be sought. But Aristotle disqualifies this by saying that it is a wrong assumption to suppose that we have an adequate first principle in virtue of the fact that something always is so or always happens so. In this way Democritus reduced all the causes that explain nature to something existing always: he assigned a principle for things that begin newly to be, but would not look for a principle of what has always been, Now this is true in some things and not in others. For it is clear that a triangle always has three angles equal to two right angles, but even of this eternal property there is a cause other than the fact. But some things are indeed eternal, such as principles, that do not have a cause.

996. Very special attention should be paid to what is here said, because, as is mentioned in Metaphysics II, the arrangement of things in existence and in truth is the same. Therefore, just as some things are always true and yet have a cause of their truth, so Aristotle understood that there are some eternal beings, namely, the heavenly bodies and separated substances, which nevertheless have a cause of existence.

From this it is evident that although Aristotle posited a world that was eternal, he did not believe that God is not the world’s cause of existence but of its motion only, as some maintained. Finally, he concludes his main proposition with a summary. And he says: “Let this conclude what we have to say in support of our claim that there never was a time when there was not motion and there will never be a time when there will not be motion.”

Lecture 4

Solution of arguments concluding motion was not always

997. After giving arguments proving that motion always exists, the Philoper accidenssopher now intends to answer objections to the contrary. About this he does two things:

First he gives the arguments;

Secondly, he answers them, at 1000.

In regard to the first he gives three arguments, after first stating that it is not difficult to solve the objections contrary to his position. And he says that there are three main arguments from which it seems to follow that motion began to be at some time after previously not existing at all.

The first of these is that whereby he proved in Book VI that no change is infinite, because by the same argument it can be proved that no change is eternal. For no terminated change is eternal any more than it is infinite. But every change is terminated. For every motion is naturally from something to something, and these two are contraries; hence, of necessity, the termini of any change are the contraries within the sphere of that change. But because contrariety of termini is not evident in all cases of local motion, Aristotle adds something common to every motion, namely, that nothing is moved to infinity, because nothing is moved to what it cannot reach, as has been said in Book VI, Accordingly, it is clear that no motion is perpetual, just as it is not infinite. If, therefore, no motion is perpetual, it also seems possible to posit a time in which there is no change. This first argument is taken from motion.

998. The second argument is based on the mobile, at (768). It is this: If motion cannot newly come to be when previously it was not, it seems fitting to say of anything that either it is always in motion or never in notion; because if motion can sometimes be and sometimes not be in one particular mobile, why not for the whole universe? But we see that it is possible for something to be moved that previously was not moved as a whole, and that had no motion in itself with respect to any of its parts, as is apparent in non-living things, among which some mobile begins at one time to be moved when previously no part had been moved, nor the whole itself, but it was completely at rest. It remains, therefore, that in the whole universe there can be motion where previously there was none.

999. But because in non-living things, even though motion is seen to begin anew in something when previously there was none at all, yet motion appears to have been pre-existing in something external by which it is moved, he accordingly gives a third argument from animals, which are moved not from without but by themselves.

This argument is at (769). and it says that it is more evident in animals than in the non-living that motion begins after previously having not existed. For when we have rested for a time so that ho motion exists in us, we begin at a certain time to be moved and the principle of our motion is from our very selves even if nothing external moves us. This, however, does not happen in non-living things, because they are moved always by something external, such as the cause that generates them, or a cause that removes an obstacle, or a cause that subjects them to force. From this it follows, if an animal is at one time entirely at rest, that motion begins to exist in an immobile being after previously not existing in it, which motion does not originate from an external mover but from the very thing that is moved. And if this can occur in an animal, there is nothing to prevent its occuring in the universe. For an animal and especially man possesses a likeness to the world; wherefore it is said that man is a small world. Accordingly, if in this small world, motion can begin after previously not existing in it, it seems that the same can happen in the large world. And if this happens in the world, it can happen in the infinite whole, which some assumed exists beyond the world—provided, of course, that there is something infinite that can rest and be moved.

1000. Then at (770) he answers these arguments in order.

In answer, therefore, to the first he says that it is correct to say that motion which occurs between contraries cannot always endure as one and the same numerical motion, because perhaps this is necessary, as will be proved later—and he leaves this in doubt, because it has not yet been proved. But because someone could say that even motion which is between contraries can be always numerically the same on account of maintaining the same mobile which is repeatedly moved from one contrary to another—for example, if it is first moved from white to black, and then from black to white, and so on throughout time—he then adds that it is not possible that a motion which is always in one and the same mobile be kept one and the same by repetition. And he explains this by an example: Let the same chord be continually struck on a lyre and let the striker be unvarying in his striking; one may ask whether the motion and sound of the one chord struck twice is one and the same or continually other and other.

Yet whatever be the case with other mobiles, there is nothing to prevent a motion which is not between contraries, such as a circular motion, from being the same continual and perpetual motion. This will be made clearer from later development. Therefore, although every motion is finite with respect to its termini, yet by repetition some motion can be continuous and perpetual.

1001. Then at (771) he answers the second argument. And he says that it is nothing unusual for a non-living thing to begin to be moved when previously it was not being moved, provided that this occurs because an external mover is present at one time and not at another. For it is clear that motion must pre-exist on the part of a mover which at some time becomes near but previously was not so. However, this seems to be a point to be looked into as a problem, namely, whether, if a mover exists, the same object can be at one time moved by this mover and at another not—for he had previously said that such a thing cannot happen unless there intervenes some change affecting either the mover or the mobile. Accordingly, motion always pre-exists, whether or not a mover pre-exists. Now this point seems to need investigation, because whoever proposed this argument seems to be certain about everything but one factor, namely, whr it is that things at rest do not always rest, and mobiles are not always in motion.

1002. Then at (772) he answers the third argument, And he says that the third objection causes the greatest problem about whether motion can exist after previously not existing, based on what is seen to happen in living things. For it seems that an animal which previously was at rest, later begins to move about without any external cause of motion; accordingly, it seems that that motion of the animal was not preceded by any motion, either in the animal or in anything else, as happens in non-living things.

But it is false that the motion of the animal does not come to be from something external. For we always observe in animals something naturally moved, whicht namely, is not moved through will. And the cause of its be,ing moved naturally is not the animal through its appetite, but perhaps the cause of this natural change is its surroundings, i.e., the air, and beyond that the heavens, as is plainly the case when the body of an animal is altered by heat or coldness of air.

And he says, “perhaps,” because in an animal something is also moved naturally by an internal principle, as is evident in those changes which occur in the vegetal soul, such as are the digestion of food and the subsequent transmutations, which are called “natural” because they do not follow upon apprehension and appetite. And because this seems to be contrary to what is proper to an animal, which is to move itself, he adds that when we say that an animal “moves itself,” we do not understand this of any and every motion, but of local motion, according to which an animal moves itself through apprehension and appetite.

Accordingly, there is nothing to prevent—indeed, it is necessary—many changes from taking place in the body of au animal on account of its surroundings, i.e., the air and the heavens, some of which changes move the understanding or the appetite, by which in turn the whole animal is moved.

1003. It should be noted that Aristotle here declares the way in which heavenly bodies act upon us. For they do not act directly on our souls but on our bodies; but when our bodies are moved, then per accidens a change occurs in the powers of the soul, which are acts of bodily organs, but not necessarily in the intellect and the intellective appetite, which do not use bodily organs. Yet the intellect and will sometimes follow upon some of these changes, as when a person through his reason chooses either to pursue or to reject or to do something on account of a passion which began in the body or in the sensitive part. And therefore Aristotle does not say that all motions caused by the surroundings move the intellect or appetitet but that some of them do. In this way he excludes necessity from the intellective powers.

Of the things he said he gives an example from sleeping things, in which there seems to be maximum rest with respect to animal motions. But even though during sleep there be no motion that is sensible, i.e., proceeding from sense apprehensiong animals rise awakened by some motion existing within, due either to the work of the nutritive soul, as when, as a result of the food’s being digested, the vapors which caused sleep vanish and the animal is aroused, or when the body is altered by its surroundings, from heat or cold.

Thus it is clear to anyone who considers the matter diligently that no motion ever newly appears in us unless some other motion preceded. And he promises to give a fuller explanation of this later.

Lecture 5

Five ways in which things may be disposed with respect to motion or rest.

Two first excluded.

1004. Having shown in Book VII that there is not an infinite process in movers and in mobiles but that a first must be reached, and having now shown that motion has always been and always will be, the Philosopher goes on further to consider the condition of the first motion and of the first mover. And his treatment is divided into two parts.

In the first he shows that the first motion is eternal and that the first mover is entirely immobile;

Secondly, from this he proceeds to show the condition of the first motion and of the first mover, (L. 14).

The first is divided into three parts:

In the first he gives a division having five members;

In the second he excludes three members of this division, at 1006;

Thirdly, he investigates the two remaining members to see which of them is truer, because the truth of what he intends to settle depends on it, (L. 6).

1005. He says therefore first (773) that the reason for the following consideration, in which we intend to investigate about the first motion and the first mover, is that it pertains to a question he raised in answering the second argument (given in the preceding lecture), namely, that of whence it happens that certain things are at one time in motion and at another time at rest, and are not either always in motion or always at rest since motion in common is considered perpetual.

And he says that the ways in which things are disposed with respect to motion or rest are necessarily limited to three. The first of which is that all things be always at rest and nothing ever in motion; the second is that all things be always in motion and nothing at rest; the third way is that some things are in motion and others at rest.

But the third way is again divided into three ways. The first of these is that some things are in motion and some at rest in the sense that the ones in motion are always in motion and those at rest always at rest, and nothing is at one time in motion and at another time at rest.

The second way is the converse, ioeol that all things are apt to be in motion and to rest and that nothing is either always in motion or always at rest.

The third way is that certain things are always immobile and never in motion; others are always mobile and never at rest; still others may be taken with both, i.e., with motion and rest, so as to be in motion at one time and at rest at another.

This last member must be determined by us to be the truth, because in it are contained the solutions of all objections. And when we shall have shown this, we shall possess the end which we intend in this work, namely, to arrive at a first eternal motion and a first immobile mover.

Therefore, it is in the above manner that the third member of the first division is divided into three members, thus making a general division consisting of five members.

Now, it should be noticed that in three of these members all things are respectively put in one definite disposition; for example, in the first member all things are taken to be always at rest; in the second all things are always in motion; and in the fourth all things alternate between motion and rest. But in one member, namely, the third, beings are divided according to two dispositions, so that some are always in motion and others always at rest. Finally, in one member, the fifth, beings are divided according to three dispositions; namely, some are never in motion, others are never at rest, while the others are sometimes in motion and sometimes not. Notice, too, in this last member that it is not rest but immobility that is posited; because the first mover, who is never moved, can not strictly be said to be at rest, for, as was said in Book V, only what is apt to be moved, and is not being moved, is properly said to be at rest.

1006, Then at (774) he excludes three members of the division.

First he posits that not all things are always at rest;

Secondly, that not all things are always in motion, at 1007;

Thirdly, he excludes the third member, in which it was said that the things in motion are always in motion and those at rest are always at rest, (L. 6).

In regard to the first he posits three statements. The first of these is that it is due to a weakness of understanding that some affirm rest of all things and in support of their stand search for a sophistic reason without referring to sense. For it proceeds on the fact that the intellect is not capable of destroying sophistical arguments which conflict with things evident to sense. But it has been said in Topics I that there is no need to dispute against positions or problems that are in a mind which needs sense or punishment. Hence it is not necessary to dispute this position, due to its stupidity.

The second thing he says is that this problem does not concern a particular being but being in general. Nor does it affect natural science alone, but in a way all demonstrative sciences and all opinions, i.e., all the arts which use opinions, as do rhetoric and dialectics, for all the arts and sciences make use of motion. For the practical arts in a way direct certain motions, and natural philosophy speculates about the nature of motion and about mobile beings. Mathematicians, too, make use of motion, i.ee, of an imagined one, saying that a point in motion makes a line. The metaphysician, however, considers first principles. Accordingly, it is plain that to destroy motion conflicts with all sciences.

Now an error that affects all beings and all sciences is not to be reproved by the philosopher of nature but by the metaphysician. Thereforet it is not the business of natural philosophy to dispute this error.

The third thing he says is that unreasonable and inappropriate problems about the principles of mathematical sciences do not pertain to mathematics to be answered. The same is true in the other sciences. In like manner, it is not the business of the physicist to destroy an affirmation that is contrary to its principles. For in each science the definition of the subject is assumed as a principle; hence in the science which deals with nature, it is assumed as a principle that nature is a principle of motion. Accordingly, in the light of these three statements, it is apparent that it does not belong to natural philosophy to dispute this position.

1007. Then at (775) he excludes the second member, in which Heraclitus posited that all things are always being moved. And first he compares this opinion with the previous one which posited that all things are always at rest; and he says that to say that all things are always in motion, as Heraclitus said, is both false and contrary to the principles of natural science. Yet this position is not in as great conflict with the art as the first one is.

But that it does conflict with the art is clear, because it takes away the assumption of natural science that nature is principle not only of motien but also of rest, which supposition makes it clear that rest is something natural just as motion is. Hence, just as the first opinions which destroyed motion, was against natural science, so too is this one that destroys rest.

The reason why he says that this opinion is less against art is that rest is nothing more than the privation of motion. But it is less evident that there is no motion than that there is no privation of motion. For there are some motions so weak and insignificant that they can be scarcely noticed; for that reason it is easy to suppose that something is at rest when it really is not. But great and strong motions cannot be concealed; hence it cannot be said that the senses are deceived in perceiving motion as they are in perceiving rest.

Therefore, secondly, at (776) he shows how some posited this second opinion. And he says that some, such as Heraclitus and his supporters, have said that all things which exist are always in motion, and not some things only or just at some time, but this motion eludes our senses. Now, if they say this of some motions, they are correct; for some motions do elude us. But because they do not qualify their statement but speak of all motions, it is not hard to find arguments against them, for there are many motions which evidently could not have existed always.

1008. Thirdly, at (777) he forms the arguments against this position.

First with respect to the motion of growth;

Secondly, with respect to the motion of alteration, at 1009;

Thirdly, with respect to local motion, at 1012.

The reason he begins with growth is that Heraclitus was led to his doctrine as a result of considering growth. For he observed that a person grows a small amount in one year and, supposing that growth is continuous, he believed that in each part of that year he was increased with respect to part of that quantity; and yet that increase is not sensed, because it comes in a small portion of time, He reasoned, therefore, that the same thing happens in other things which seem to be at rest.

Against this Aristotle says that it is not possible for a thing to be continually increased or diminished so that the increased quantity can be divided according to time in such a way that in each part of time there is a corresponding increase. Rather, there is, after the increase of one part, a time in which there is no increase but a disposition is produced for the increase of the next part.

And this he explains with kindred examples. The first of these is that we see that the multiplication of drops of rain breaks a stone. The second example is that we see that things being born, i.e., that plants born in stones divide the stones. Now, we cannot say that, if the repeated drops dig out or remove a certain quantity of the stone in a given time, half of this number of drops in half the time would previously remove half of that quantity. But what happens here is what happens with regard to shiphaulars. For it does not follow, if 100 men pull a ship a certain distance in a given time, that fifty of them will move it half the distance in the same time or the full distance in twice the time—this was said in Book VII. So also it does not follow, if many drops cave in a stone, that some part of those drops had previously removed the half in some certain time.

The reason for this is that what is removed from the stone by many drops is indeed divisible into many parts, but none of them is removed separately from the stone, for all the parts are removed at once, in the sense that they are in the totality removed in potency.

And he is speaking here of the first total quantity that is removed, for there is nothing to prevent that, over a long period of time, such a large quantity, be removed from the stone by these drops that a certain part may have been removed previously by a part of these drops. But we must come to a removed quantity which is removed all together and not part after part. Therefore, in the removing of that whole, none of the preceding drops removed anything, but merely disposed for its removal. However, the last acts in virtue of all and removes what the others had disposed to be removed.

The same is true in the motion called decrease. For it is not necessary, if something decreases a certain amount in a given time (even though the quantity be divided ad infinitum), that in every part of that time a corresponding part of the removed quantity should depart; rather, at some time a given amount will depart all together. The same holds in increase. Consequently, it is not required that something be continuously increased or decreased.

1009. Then at (778) he contradicts the above-mentioned position of continuous motion with respect to alteration, and this with three arguments. First, he says that what was said about increase, applies also to alteration. For although a body that is being altered is infinitely divisible, that is no reason for supposing that alteration is divided ad infinitum, so that for each period of time a part of the alteration should occur. Rather, alteration very often takes place swiftly, i.e., many parts of the altered body are altered all at once, as happens when water is condensed or congealed. For a whole mass of water is congealed all at once and not part after part (although if it be a large mass of water, there is nothing to prevent part congealing after part).

It should be noticed that what Aristotle says here about alteration growth seems contrary to what was said in Book VI, where it was shown that motion is divided according to the division of the time, and of the mobile, and of the sphere of motion.

But it should be recognized that in Book VI Aristotle was talking about motion in common, without application to definite mobiles. Therefore, what he discussed there must be taken according to the requirements of motion’s continuity; but at present he is speaking of motion with application to definite mobiles, in which a motion can be interrupted and not be continuous, which, when viewed under the common aspect, could be continuous.

1010. He gives the second argument at (779), and he says that if a sick person is to get well, he has to become healed in a period of time and not in a terminus (an instant?) of the time. And it is further necessary that the very change, which is healing, tend to a definite terminus, ie., to health and not to anything else. Accordingly, every alteration requires a definite time and a definite terminus, because every alteration tends to a contrary, as was said in Book V. But no such change is always continuous. Therefore, to say that something is being always and continuously altered, is to speak against the facts.

1011. The third argument he gives at (780) and he says that a stone does not become harder or softer, even after a very great period of time; thus it is foolish to say that all things are always being altered.

1012. Then at (781) he contradicts the opinion at issue with respect to local motion, on two counts. First, indeed, because some local motions and rests are so evident that they cannot be hidden. For it would be strange if it were hidden from us when a stone is carried downwards or when it is at rest on the earth. Consequently, it cannot be said that, because of the concealment of local motions, all things should be supposed to be always being moved locally.

Tnl3. Secondly, at (782) he argues thus: Earth and any other natural body, when they are in their due placest rest from a necessity of nature and are not removed except by force. But it is evident that certain natural bodies are in their due place. Therefore, it is necessary to say that some things are at rest with respect to place and that not all things are being moved locally.

Finally, he concludes in summary that, from the foregoing and other things similar to the foregoing, anyone can know that it is impossible for all things always to be in motion, as Heraclitus said, or for all things always to be at rest, as Zeno and Parmenides and Melissus said,

Lecture 6

A third member of the division is rejected

1014. Having disposed of two members of the foregoing division, the Philosopher now rejects a third, in which it was posited that things are divided into two dispositions only, in such a way, namely, that some things are always at rest and others always in motion, and there is not a third class of things that are sometimes in motion and sometimes at rest. He rejects this in two ways.

He does this first (783) in the same way that he rejected the two previous positions, namely, on the ground that they are contrary to sense observation. For we see by the senses not only that some things are in motion (which destroys the first position, namelyt of those who posit all things to be always at rest), and that some are at rest (by which is destroyed the second position, of those who maintain that all things are always in motion); but we also see that the aforementioned changes or variations from motion to rest, and from rest to motion, occur in the same things. This shows that there are some things which are sometimes moved and sometimes at rest.

1015. In a second way at (784) he rejects the same opinion on the ground that the one who would engender this doubt would be contrary to what is evident in nature. In the first place it would deny the motion of growth, for we see that growth takes place in things that are not always growing, because, were they always growing, they would be tending not to a definite quantity but to the infinite.

In the second place it would deny compulsory local motion, for a motion is not compulsory, unless something is moved not in keeping with its nature when previously it was naturally at rest; for a forced motion is nothing more than a departure from natural rest. If therefore nothing at rest can be moved, it will follow that what is naturally at rest cannot later be moved by compulsion.

In the third place generation and ceasing-to-be would be excluded by this opinion. For the former is a change from non-being to being, and the latter from being to non-being. Therefore, in order that a thing cease to be, it ought previously to have been existing for a time, and in order that a thing be generated, it ought previously not to have been existing for a time. But whatever is a being or a non-being for some time is at rest (where rest is taken in a very general sense), If, therefore, nothing at rest can be moved, it follows that nothing which is for some time a non-existent can be generated, and that nothing which exists for a time can cease to be.

In the fourth place this position destroys all motion universally, because every motion involves generation and ceasing-to-be either absolutely or in a qualified sense. For what is being moved toward something as toward a terminus is being made such-and-such, so far as alteration and growth are concerned, or being made to be in such-and-such, so far as local motion is concerned; for example, what is being changed from black to white, or from small to large, becomes white or large, but whatever is being moved to a place comes to exist in that place. But from the fact that something is changed from its terminus a quo, a “such and such” ceased to be, when it is a case of alteration and growth, and a “there” ceased to be, if it is a case of local motion. Therefore, because in every motion there is generation and ceasing-to-be, it consequently rejects all motion.

Because such things are impossible, it becomes clear that some things are being moved, but not always; and that some things are at rest, not always, but sometimes.

1016. Then at (785) he studies the other two members of his division.

First he reveals his intention;

Secondly, he pursues it, (L. 7).

About the first he does three things:

First he shows to which opinion the fourth member pertains;

Secondly, he summarizes what has been said in this chaptert at 1017;

Thirdly, he states what remains to be said, at 1020.

He says therefore first (785) that to posit that all things are sometimes at rest and sometimes in motion pertains to the ancient arguments which we touched upon in discussing the eternity of motion. For Empedocles seems to be the chief protagonist of this opinion that all things are at some time moved by friendship and by discord and in the meantime are at rest.

1017. Then at (786) he sums up what has been said in this chapter.

First he recalls the divisions previously made;

Secondly, he recalls the rejection of the first member which posited all things at rest, at 1018;

Thirdly, the rejection of the other two members, at 1019.

He says therefore first (786) that in order to make clearer the intention of what follows, we must begin with what has just been determined and use the same principle as before, namely, that beings must maintain themselves in one of three dispositions, i.e., either that all are at rest or all in motion or some at rest and some in motion. And this third is again divided into three members, for if all things are such that some are at rest and others in motion, then necessarily all must be at one time at rest and at another in motion, or some are always at rest and others always in motion, or to these two a third member may be added, namely, that there are others of which some are at rest not always but sometimes, while the others are in motion sometimes but not always.

l018. Then at (787) he rejects the first member and says that it was said above that it is not possible for all things to be always at rest; but something else must now be added. And he says two things against this position.

First, some motion must be posited at least in the soul. For should anyone want to say that according to truth it is a fact that nothing is being moved (as the followers of Melissus did, who posited that being is infinite and immobile), yet it is also a fact that this does not appear to be so according to sense, for many things appear to the senses to be moving.

If, therefore, anyone declares as false the opinion by which we believe that some things are in motion, it still follows that motion exists. For if there is false opinion, there is motion; and universally if there is opinion, there is motion and, likewise, if there is imagining, there is motion. The reason is that imagining is a motion of the sensitive part and is produced by the sense in act. Opinion also is a certain motion of the reason and proceeds from several acts of reasoning. But it follows even more strongly that there is motion in opinion and imagining, if things appear to be this at one time and that at another. This happens when things at one time seem to us to be at rest and at another time not to rest. Thus, it entirely follows that motion exists.

He says, secondly, against the opinion at issue, that to have the intention of destroying this opiniong and to look for an argument to prove those things that we ought to hold in a respect surpassing the need for proof, since they are accepted as self-evident. To do this, I say, is no different from judging poorly between what is better and what is worse in morals, and between what is credible and incredible in logical matters, and between a principle and a non-principle in matters of demonstration.

For whoever looks for arguments to prove things which are self-evident and, consequently, held as principles, does not recognize them for principles so long as he intends to prove them through other principles. Likewise, it seems that he does not recognize what is credible and what is incredible, because he is trying to prove what is per se credible through something else, as though it were not per se credible. Nor does he seem capable of distinguishing between the better and the worse who tries to prove the more evident by means of the less evident. But it is self-evident that some things are in motion. Therefore, we should not address ourselves to trying to prove this by arguments.

1019. Then at (788) he rejects two more members of his original division. And he says that just as it is impossible for all things to be always at rest, so too is it impossible that all things be always in motion, or that some things are always in motion and some always at rest, so as to leave nothing which is sometimes in motion and sometimes at rest. Against all this, sufficient credence arises from one medium, namely, the fact that we see that some things are sometimes in motion and sometimes at rest. Hence, it is clear that it is impossible to say that all things are continually at rest—which was the first member—and that all things are continually in motion—which was the second member—or that some are always in motion and the remainder always at rest without any mediate possibility.

1020. Then at (789) he shows what is left to be said, and he concludes from the foregoing that since three members of the division cannot stand, what remains is to consider which of the other two is the truer, whether, namely, all things are capable of both motion and rest, or whether some are capable of both motion and rest while still others are always at rest and others always in motion. This last is what we intend to demonstrate. In this way it will be shown that the first motion is eternal, and the first mover immobile.

Lecture 7

Universally, whatever is moved is moved by another

1021. After revealing his aim, the Philosopher now begins to execute it, namely, to establish that not all things are sometimes in motion and sometimes at rest, but that something is entirely immobile, and something always in motion. The treatment is divided into two parts.

In the first he shows that the first mover is immobile;

In the second that the first mobile is always being moved, (L. 13).

The first part is divided into two sections:

In the first he shows the immobility of the first mover from the order of movers and mobiles;

In the second, from the eternity of motion, (L. 13).

The first is divided into two parts:

In the first he shows that the first mover is immobile;

In the second that the first mover is eternal, (L. 12).

About the first he does two things:

First he shows that to prove what follows depends on showing that whatever is moved is moved by another;

Secondly, he shows the proposition, (L. 9).

He had indeed showed above, in the beginning of Book VII, that whatever is moved is moved by another, by a generic argument based on motion itself, but because he has now begun to apply motion to mobile things, he here shows that what was previously proved in a universal way is verified universally in all mobiles and movers. Hence the first part is divided into two parts:

In the first he gives a division of movers and mobiles;

In the second he explains his proposition in individual cases, at 1024.

About the first he does two things:

First he divides movers and mobiles;

Secondly, he explains the division, at 1023.

1022. He gives therefore first (790) three divisions of movers and mobiles. The first of these is that among movers and mobiles some move or are moved per accidens, and some per se. And he takes “per accidens” in a wide sense include what moves or is moved with respect to a part. Hence in explaining what he means by “per accidens, he adds that things cause motion or are moved per accidens in two ways. (1) Whatever things are said to cause motion by virtue of being present in things which move are said to cause it per accidens, as when it is said that a musician causes health, because a knowledge of music is present in the one who heals; and likewise things are said to be moved per accidens either on account of existing in what is being moved in the way that an object in place exists in a place, e.g., when we say that a man is being moved, because the ship on which he is is being moved, or on account of being an accident in a subjects as when we say that the white is being moved, because a body is being moved. (2) In another way, things are said to move or to be moved per accidens, because they move or are moved with respect to a part, as a man is said to strike or be struck, because his hand strikes or is struck.

But when these two per accidens ways of causing motion or being moved are eliminated, things are said to move or to be moved per se, i.e., when they are not said to cause motion or be moved by virtue of being in the cause of motion or in what is being moved, or because some part of them causes motion or is moved.

Therefore, leaving out what causes motion or is moved per accidens, he subdivides things that are moved per se into those which are moved by themselves, as are animals, and those moved by others, as are the non-living.

He gives a third division, namely, that some things are moved according to nature and some not according to nature.

1023. Then at (791) he explains how to discern what is according to nature and what is not according to nature, both in things that are moved by themselves and in things that are moved by something else.

First, with respect to things that are moved by themselves—such as are animals, which move themselves—he says that they are moved according to nature. And he proves this on the ground that they are moved by an intrinsic principle, and since things whose principle of motion is within are said to be moved by nature, it follows that an animal’s motion, by which it moves itself, if it is compared to the whole animal, is natural, because that motion proceeds from the soul which is the nature and form of the animal. But if it be compared to the body, an animal’s motion may be both natural and not according to nature. The difference depends on the type of motion and on the element of which the animal is composed. For if an animal consists of a predominant heavy element, as does the human body, and it is moved upwards, such a movement would be compulsory with respect to the body; but if it is moved downward, it will be a movement that is natural to the body. However, if there were animals whose bodies were composed of air, as Platonists held, then the contrary would be true.

Secondly, he explains how to discern compulsory and natural motions in things that are moved by another. Of these, some, he says, are moved according to nature, as fire upward and earth downward; others are moved outside their nature, as earth upward and fire downward, which is a compulsory motion.

Thirdly, he mentions another type of unnatural motion in animals, namelyt those in which the parts of animals are moved in an unnatural way, their positions and the character of the motion being abnormal. For example, a man’s arms bend (at the elbow) facing forward, while his legs bend (at the knee) facing backward; but dogs and horses and the like, bend the forelegs facing backward and the hind legs facing forward. If motions contrary to these are made, they will be compulsory and not according to nature.

1024. Then at (792) he proves that everything that is moved is moved by another.

First he manifests it in cases that are evident;

Secondly, in cases about which there is doubt, at 1025.

Leaving aside things that are moved per accidens, because such things are not moved but are merely said to be moved when other things are moved, and confining ourselves to those which are moved per se, it is clear, especially in things moved by compulsion and outside their nature, that what is moved is moved by another.

For in the case of things moved by compulsion, it is clear from the very definition of compulsion that they are moved by another. For compulsion, as is said in Ethics III, is that whose principle is from without, with the thing suffering it contributing nothing.

After things that are moved by compulsion, it is clear that what is moved is moved by another if we consider things moved by themselves according to nature, as animals are said to move themselves. For in animals it is clear that something is being moved by something else—but there might yet be a question as to how to distinguish in them the mover and what is being moved. For at first glance it appears to many that what is true with respect to ships and other artifacts which do not exist according to nature, namely, that the part which causes motion is diverse from the part which is moved, applies to animals, for it seems that the soul which causes motion is related to its body which is moved, as the mariner is related to the ship, as is said in On the Soul II. In this way it seems that the whole animal moves itself insofar as one part moves another. But whether the soul is related to the body as a mariner to a ship he leaves to be investigated in his treatise On the Soul. However, the fact that a thing is said to move itself, insofar as one part thereof moves and another is moved, will be shown later.

1025. Then at (793) he explains his proposition in regard to things in which it is more doubtful. About this he does three things.

First he sets down those things in which it is more doubtful that whatever is moved is moved by another, namely, in the heavy and the light, when they are moved according to nature.

Secondly, he shows that they do not move themselves, at 1026;

Thirdly, he shows by what they are moved, (L. 8).

He says therefore first (793) that, since it is in things moved by compulsion, and after them in things which move themselves, that it is especially evident that whatever is being moved is moved by another, the greatest doubt appears to be in the remaining member of the last division, namely, in things that do not move themselves, but yet are moved naturally.

The “last” division to which he refers is that in which he divided things that are moved not by themselves but by another into those that are moved contrary to nature, and those that are moved according to nature. In these latter there is doubt as to what moves them: for example, heavy and light objects are moved to their proper places according to nature—i.e., the light upwards and the heavy downwards—and into contrary places by compulsion; but the source of their motion when they are moved according to nature is not clear, as it is when they are moved contrary to nature.

1026. Then at (794) he proves with four arguments that these things do not move themselves. The first of which is that to move itself pertains to the notion of life and is peculiar to living things; for it is through motions and sensations that we distinguish the animate from the inanimate, as is said in On the Soul I. But it is manifest that the heavy and light as such are not alive, or animate. Therefore, they do not move themselves.

1027. The second argument is given at (795); Things that move themselves can cause themselves to stop, as we see that animals are moved and stop by reason of their appetite, Therefore, if heavy and light things moved themselves with a natural motion, they could cause themselves to stop, in the way that a person who is the cause of his walking is so also of his ceasing to walk. But we see that this is false, because the heavy and the light do not stop outside their proper places, unless some external cause intervenes to halt their motion. Therefore, they do not move themselves.

But because someone could say that although such things are not the cause of their own stopping outside their proper places, yet they are the cause of stopping in their proper places, he adds a third argument at (796): it is unreasonable to say that things which move themselves are so moved according to one motion alone and not by many, because what moves itself does not have its motion determined by another but determines its own motion for itself, so that at one time it determines this motion and at another time that one. Hence it is in the power of what moves itself to determine for itself this or that motion. Therefore, if heavy and light things moved themselves, it would follow that if it were in the power of fire to be moved upward, it would also be in its power to be moved downward, which is something we never see occurring, unless from an extrinsic cause. Therefore, they do not move themselves.

It should be recognized that these two arguments are probable in respect to what appears in things among us that move themselves, which are found at one time to be moved with this motion and at another time with that motion, and at another time to be at rest. Hence he does not say, “It is impossible,” but “It is unreasonable,” which is his manner of speaking when he talks of what is probable. For he will show later that if something is moving itself and it is an entirely immobile mover, that it is always being moved and with one motion. Yet that could not be said in regard to heavy and light things, in which there is nothing that is not moved either per se or per accidens, and they are also generated and cease to be.

1028. He gives the fourth argument at (797): No continuum moves itself. But heavy and light bodies are continua. Therefore neither of these moves itself.

That no continuum moves itself he proves in the following manner: The mover is related to the moved as agent to patient. But since the agent is contrary to the patient, that which is apt to act must be divided from what is apt to be acted upon, Now, to the extent that things are not in mutual contact but are completely one and continuous in quantity and form, to that extent they can not be acted upon by one another, In this way, therefore, it follows that no continuum moves itself, but the mover must be divided from what is moved, as is evident when non-living things are moved by living things, as is a stone by the hand, Hence, too, in animals that move themselves, there is rather a connection of parts than a perfect continuity (for which reason one part can be moved by another), a situation that is not verified in the light and the heavy.

Lecture 8

What moves the heavy and light. Everything moved, moved by another.

1029. After showing that the heavy and the light do not move themselves, he shows.by what they are moved.

First he shows by what they are moved;

Secondly, he concludes to his main intention, at 1036.

About the first he does two things:

First he shows that they are naturally moved by something;

Secondly, he investigates by what they are moved, at 1030.

He says therefore first (798) that although the heavy and the light do not move themselves, they are nevertheless moved by something. And this can be made clear if we distinguish moving causes. For just as in things that are moved, we must take it that (1) some things are moved according to nature and some not, so also in movers, some move not according to nature, e.g., a stick, which is not naturally capable of moving a heavy body such as a stone; and that (2) some things move according to nature, as what is actually hot naturally moves what is according to its nature potentially hot, and similarly in other cases. And just as what is in act causes motion naturally, so what is in potency is naturally moved, with respect either to quantity or quality or where.

And because in Book II he had said that those things are moved naturally whose principle of motion exists in them per se and not by virtue of some concomitant attribute, which might lead one to suppose that what is only potentially hot is, when it becomes hot, not moved naturally in that it is being moved by an external active principle of its motion, he now adds, as though to preclude this objection, “since it has a principle of this kind in itself and not accidentally,” as if to say that in order that a motion be natural, it is enough that a principle of this kind, i.e., the potency, about which he made mention, exist in that which is moved per se and not per accidens, as a bench is potentially combustible, not precisely as bench but as wood.

Hence in explaining the expression “per accidens,” he adds that the same subject can be quantified and qualified, but one of these is related to the other per accidens; what is potentially of such and such a quality is also potentially quantified, but per accidens.

Therefore, because what is in potency is naturally moved by something else in act, and nothing is in potency and in act with respect to the same, it follows that neither fire nor earth nor anything else is moved by itself but by another. Fire and water are moved by another, but by compulsion, when their motion is outside their natural potency; but they are moved naturally when they are moved to their proper acts, to which they are in potency according to their nature.

1030. Then at (799) he shows by what they are moved. And because what is in potency is moved by something in act,

First he distinguishes potency;

Secondly, from this he shows by what such things are moved, at 1035.

About the first he does three things:

First he shows that it is necessary to know the ways in which something is said to be in potency;

Secondly, he explains this at 1031;

            Thirdly, with this he solves a question, at 1033.

He says therefore that the reason why it is not evident by what heavy and light things are moved with respect to their natural motion (as fire upward and earth downward) is that the expression “being in potency” has many senses.

1031. Then at (800) he distinguishes “being in potency”:

First in the understanding;

Secondly, in quality, at 1032;

Thirdly, in local motion, at 1033.

He says therefore first that one who is learning and does not yet have the habit of science is not in potency to science in the same way as one who already has the science but is not using it by considering.

But something is reduced from the first potency to the second, when the active principle is united with the patient; and then the patient through the presence of the active principle comes to be with respect to such an act, but after that the patient is yet in potency: for example, a learner is through the action of the teacher reduced from potency to act, but when he is in this state of act, there is yet another potency present. Consequently, the thing existing in first potency comes to be in another state of potency; because one having science, and not considering, is in a sense in potency to an act of science, but not in the same way as he was before he learned. Therefore, from first potency he is reduced to an act to which is united a second potency, by some agent, namely, the teacher.

But when he is in the state of possessing the habit of science, it is not necessary that he be reduced to second act by some agent; rather he operates immediately by himself, just by considering, i.e., unless he is prevented by other occupations or by sickness or by his will. On the other hand, if he were not impeded and still could not consider, then he would not be in the habit of science but in its contrary, namely, ignorance.

1032. Then at (801) he manifests the same thing in qualities. And he says that what was said with respect to the potency of anything in the mind applies also to natural bodies. For when a body is actually cold, it is potentially hot, just as an ignorant person is potentially a knower. But when this body has been so modified that it has the form of fire, then it is now actually fire and has the power to burn; and it acts at once and burns, unless it is prevented by something acting to the contrary or somehow preventing its acting, as by removing the combustible material. This is similar to what was said above, that when someone after learning becomes a knower, he at once considers, unless prevented by something.

1033. Then at (802) he manifests the same thing in the local motion of the heavy and the light. And he says that a light thing comes to be from a heavy, as a hot thing comes to be from the cold, as, for example, when air which is light comes to be from water which is heavy. Therefore, this water is first potentially light and later becomes actually light, and then it has its own activity at once, unless something prevents. But now being light, it is related to a place as potency to act—for the act of the light as light is to be in some definite place, namely, above; but it is prevented from being up by the fact of being in a contrary place, namely, down, because it cannot be in two places at the same time. Hence, that which keeps a light thing down prevents it from being up. And what has been said of local motion is true also of motion with respect to quantity or quality.

1034. Then at (803) he uses the foregoing to answer a question. For although the act of the light is to be above, yet some ask why the heavy and the light are moved to their appropriate places. But the cause of this is that they have a natural aptitude for such places. For to be light is to have an aptitude for being above, and the nature of the heavy is to have an aptitude to be down. Hence, to ask why a heavy thing is moved downward is exactly the same as to ask why it is heavy. Accordingly, the very same thing that makes it heavy makes it be moved downward.

1035. Then at (804) he uses the foregoing to show what moves the heavy and the light. And he says that since what is in potency is moved by what is in act (as has been said), it must be considered that something is said in many senses to be potentially light or heavy.

For in one way, when something is yet water, it is in potency to lightness; in another way, when from the water air has now been made, it is still in potency to the act of what is light, which is to be above in the same way that one having the habit of science and not considering is said still to be in potency—for what is light can possibly be prevented from being up.

If, therefore, that obstacle be removed, it immediately acts for the purpose of being up by ascending, as it was said with respect to quality that when a thing is actually of such and such a quality, it immediately tends to its act, as a knower immediately considers, unless he be prevented. And the same is true with respect to the motion to quantity, for from the fact that an addition of quantity has been made to a quantitative thing, extension immediately follows in an increasable body, unless something prevents.

Accordingly, it is clear that what moves, i.e., what removes the obstacle preventing and sustaining does in some sense cause motion and in other senses does not; for example, if a pillar supports something heavy and thus keeps it from descending, the one who casts down the pillar is said somehow to move the heavy object that was supported by the pillar. In like manner, one who removes a stopper that was preventing water from flowing out of a container is said in some sense to move the water; for he is said to move per accidens and not per se. Also when a ball rebounds from a wall, it is moved per accidens by the wall but per se by the one who first threw it. For it was not the wall but the thrower that gave it the impetus for motion; but it was per accidens that, being prevented by the wall from continuing according to its impetus, it rebounded into a contrary motion, the original impetus remaining. In like manner, the one who casts down the pillar did not give the heavy object resting upon it the impetus or inclination to be downward, for it had that from the first generator, which gave it the form upon which that inclination follows. Consequently, the generator is the per se mover of the light and the heavy, whereas the remover of obstacles is a per accidens mover.

He concludes, thereforel that it is clear from the foregoing that none of these, i.e., of the heavy and the light, moves itself; yet their motion is natural, because they have in themselves the principle of their motion, not indeed a moving or active principle but a passive one, which is a potency to such-and-such an act.

From this it is evidently contrary to the intention of the Philosopher that in matter there be an active principle, which some declare is necessary for a natural motion; for a passive principle is sufficient, since it is a natural potency for act.

1036. Then at (805) he concludes to the conclusion chiefly intended in the whole chapter. And he says that if it is true that all things which are per se moved are moved either according to nature, or outside their nature and by compulsion, and if of those which are moved by compulsion it is true that all are moved not only by a mover but even by an external mover that is other; and, again, if among things that are moved according to nature, some are moved by themselves—in which things it is clear that they are moved by something not extrinsic but intrinsic—while others, such as heavy and light things are moved according to nature not by themselves but by some mover) as has been explained—for they are moved either per se by the generator which makes them be heavy and light, or they are moved per accidens by whatever removes what impedes or removes their natural motion—it is accordingly clear that all things which are moved are moved by something, i.e., either by an intrinsic or an extrinsic mover; which is to be moved by something other.

Lecture 9

No process to infinity in movers. Not every mover need be moved.

1037. After showing that whatever is moved is moved by another, the Philosopher now begins to show that it is necessary to reach a first immobile mover. And his treatment is divided into two parts.

In the first he shows that it is necessary to reach a first that is either immobile or moves itself;

In the second he shows that even if a first that moves itself is reached, it is further necessary to reach a first mover that is immobile, (L.10).

About the first he does two things:

First he shows that it is not possible that things be moved by another ad infinitum;

Secondly, he shows that not every mover need be moved, at 1042.

About the first he does two things:

First he explains the proposition by ascending in the order of mobiles and movers;

Secondly, by descending, at 1041.

About the first he does two things:

First he premisses things needed for manifesting his proposition;

Secondly, he gives an argument that shows the proposition, 1040.

1038. Now he premisses two things, of which the first (806) is a division of movers. For since it has been said that whatever is moved is moved by something, a thing might be a mover in two senses. In one sense, when it moves not on its own account, i.e., not by its own power, but because it has been moved by some other mover. This is a second mover. In another sense, something moves on its own account, i.e., by its own power and not because it has been moved by another. Now, such a mover can cause motion in two ways: First, in such a way that the first mover moves the one next to the last, i.e., the one which is nearest to it after the second mover; this happens when the first mover moves a mobile through just one intermediate. Secondly, in such a way that the mover moves a mobile through a number of intermediates, as when a stick moves a stone and the stick is moved by a hand, which is moved by a man who does not move as being moved by something else. In this way the man is a first mover on his own account and he moves the stone through a number of intermediates; however, if he moved the stone with his hand, he would be moving the tone through one intermediate only.

1039. Secondly, at (807) he compares the first mover with the second. For since both the first mover and the ultimate are said to cause motion, we say that the first mover is more a mover than the ultimate mover. This is clear for two reasons: first, because the first mover moves the second

mover but not vice versa; secondly, because the second mover cannot cause motion independently of the first, but the first can cause it independently of the second. For example, the stick cannot move the stone unless it is moved by the man, but the man can move the stone without using the stick.

1040. Then at (808) he proves his proposition in the light of the foregoing. For it has been shown that whatever is being moved is being moved by another. But that by which it is moved is itself either moved or not moved; and if it is moved, it is either moved by another or not. Now these two, namely, being moved by another or not being moved by another, are such that if one is posited the other must be and not vice versa: that is, if there is something which is moved by another, it is necessary to come to a first that is not moved by another; but if such a first is posited, namely, a first that is not moved by another, it is not necessary further to posit another, namely, one that is moved by another.

This, indeed, is self-evidentt but there could be some doubt about the first one, namely, that if there be found something moved by another, there be found a first that is not moved by another. For this reason, he proves this in the following manner.

If something is moved by another and this in turn by another, and if something not moved by another is never reached, it follows that there is a process to infinity in movers and moved things. But this is impossible, as was proved in Book VII. However, he here proves it in a more certain way, from the fact that there is no first in an infinite series. Therefore, if movers and moved things go on ad infinitum, there will be no first mover. But it has already been said that if the first mover does not act, the last mover does not act and, consequently, there will be no mover, which is evidently false. Therefore, the process of something being moved by another cannot go on ad infinitum. If, therefore, it be conceded that whatever is being moved is being moved by another, as has been proved, and again, if it be supposed that the first mover is itself being moved but not by something else, it is necessarily being moved by itself.

It should be noted that this argument is not proving that the first mover is being moved, but he is supposing this according to the common opinion of the Platonists. As to the force of the argument, it does not conclude more that the first mover moves itself than that it is immobile. Hence he later presents this same conclusion under a disjunction, as will be clear below.

1041. Then at (809) he proves his proposition by descending. And it is the same argument as the preceding so far as its illative value is concerned, but differs with respect to the order of the process; he repeats it, however, for the sake of greater clarity.

He says therefore that the previous argument might be presented in another way. And he premisses propositions that have the same truth value as the previous ones, but in a different order. For above he had premissed that whatever is being moved is being moved by another and that that by which it is moved acts either on its own account or on account of something else previously moving it; and this was an ascending process.

But now he uses a descending process, saying that every mover moves something and moves by means of something, i.e., either by itself or by means of some lesser mover, as a man moves a stone either by himself or by means of a stick and the wind casts something to the earth either by its own impulse or by means of a stone which it moves.

Again, he had premised above that the last mover does not cause motion independently of the first mover, but vice versa. In place of that he here says that what a mover uses as an instrument in causing motion cannot itself cause motion without a principal mover moving it, as a stick cannot cause motion independently of the hand; but if something moves by itself as a principal mover, the addition of an instrument is not required. And this is more evident in instruments than in an ordered array of mobiles, although the same truth is present in both cases, because not every one would consider the second mover an instrument of the first. But as he deduced above that, if there is something that is being moved by another, there must be something that is not being moved, but not vice versa, so here in a descending process he says that if that by which the mover causes motion is another thing, as an instrument, there has to be something which causes motion not by an instrument but by itself. Otherwise, there is an infinite process with respect to instruments, which is the same as proceeding to infinity with respect to movers, and that is impossible, as has been proved above.

If, therefore, there exists a mover of that which is being moved, a halt must be made and the process cannot go to infinity. For if the stick causes motion because it is moved by the hand, it follows that the hand moves the stick; if, however, something else is moving the hand, it also follows conversely that a mover is moving the hand. Consequently, the same process that was valid with respect to moved instruments is valid for movers of instruments. But with respect to movers, as was shown, an infinite process must be avoided; therefore, it must be avoided with respect to instruments. Thereforet since it is always so that a thing being moved is moved by another which moves, and an infinite process must be avoided, it is necessary that there be a first mover that moves by itself and not through an instrument.

If, therefore, it be granted that this first which moves itself is indeed moved but there is no other moving it (because then it would be an instrument), it follows of necessity that it is moving itself—following the supposition of the Platonists that every mover is moved.

Hence also according to this argument, either what is being moved will be immediately moved by a mover that moves itself, or at some time such a mover that moves itself must be reached.

1042. Then at (810) he shows that not every mover is being moved, as was supposed in the preceding arguments. About this he does two things:

First he proves that not every mover is being moved;

Secondly, from this and from the previous arguments he concludes to his main proposition, at 1049.

He says therefore first that to the above-mentioned things may be added the following in order to show our proposition. About this he does three things:

First he premises a division;

Secondly, he rejects one member$ at 1043;

Thirdly, he rejects another, at 1046.

He says therefore first (830) that if whatever is being moved is being moved by another, which is tantamount to saying that every mover is moved, this can be in two ways: in one way, that it is per accidens in things that a mover is moved, i.e., the mover does not act in virtue of being moved (as if we should say that a musician is a builder not because he is a musician, but this is per accidens); or in a second way, that it is not per accidens but per se that a mover is moved.

1043. Then at (811) he rejects the first member in three ways. First, with this argument: Nothing per accidens is necessary, for what is in a thing per accidens is not present of necessity, but may happen not to be present, as musician in a builder. If, therefore, it is per accidens that movers are moved, it follows that it can happen that they not be moved. But once you posit that every mover is moved, it is a consequence, if movers are not moved, that they do not cause motion. It follows, therefore, that at some time, nothing is being moved. But this is impossible, for it has been proved above that it is necessary that motion always exist. This impossibility, however, does not follow from the supposition that movers are not moved; because if it is per accidens that a mover is moved, it will be possible for movers not to be moved, and if a possibility is posited, no impossibility follows. It remains, therefore, that the other statement from which it (the cessation of motion) followed is impossible, namely, the statement that every mover is moved.

1044. Secondly, at (812) he proves the same with another probable argument, which is this: Three things are found in motion: one is the mobile that is being moved; another is the mover, and the third is the instrument by which the mover causes motion. Now among these three, it is clear that the thing which is moved has to be moved, but it does not have to cause motion. The instrument, however, by which the mover causes motiont must both move and be moved—it is moved by the principal mover and it moves the last thing moved. For this reason, whatever “moves and is moved” has the character of an instrument.

Now, the reason why the instrument by which the mover causes motion both is moved and moves is that it partakes of both and exists in a sort of identity to what is moved. This is especially evident in local motion, for it is necessary that from the first mover to the last thing moved, all must touch one another. Accordingly, it is evident that an intermediate instrument is through contact the same as the mobile and is moved at once with it, insofar as it is in union with it. But it is also in union with the mover, because it is a mover—although under its aspect as the instrument by which the mover causes motion, it is not immobile.

Accordingly, thereforeo it appears from the premisses that the last thing moved is, indeed, being moved but it does not have in itself a principle for moving either itself or anything else, and it is moved indeed by something else and not by itself. Hence, it seems to be reasonable, i.e., probable (and in the present case we do not care to say that it is necessary) that there be a third thing which causes motion but is immobile.

For it is probable that if two things are joined per accidens, and one is found without the other, then the other might be found without it (but that it may be found without the other is necessary, because things joined per accidens may happen to be not joined); for example, if white and sweet are joined per accidens in sugar, and if white is found without sweet, as in snow, it is probable that sweet be found in some thing without white, as in cheese. If, therefore, it is per accidens that a mover be moved and something is found to be moved without moving something else, as happens in the last thing moved, it is probable that one may find moving without being moved, so that there would be a mover that is not moved.

From this it is evident that this argument does not have force in substance and accident, and in matter and form, and in like things, of which one is found without the other but not vice versa; for accident per se exists in a substance, and to matter it belongs per se to have existence through form.

1045, Thirdly, at (813) he proves the same point on the testimony of Anaxagoras. For since it may be that a mover be found that is not moved, Anaxagoras spoke aright when he said that Mind is impassible and unmingled. He said this because he posited Mind as the first principle of motion, and the only way it could cause motion and command, without itself being moved, was that it be unmingled—for what is mingled with something else is in a certain way moved when that something else is moved.

1046. Then at (814) he concentrates on the other part of the division, namely, that whatever is moved, is being moved by another which is moved per se and not according to an accident.

And he disproves this with two arguments, the first of which is: If it is not according to an accident but of necessity that a mover be moved and if it can never cause motion unless it is movedt this must happen in two ways: one of which is that the mover is moved according to the same species of motion as that which it causes; the other is that the mover moves according to one species of motion, and is moved according to another. He subsequently explains the first way at (815): We say that a mover is being moved according to the same species of motion if, for example, the thing that causes heating is heated, and the healer is healed, and something carrying locally is itself being carried locally.

He explains the second way when he says: “Or else the healer is carried along, or the thing carrying along is growing.” These are examples of “moving and being moved” according to different species of motion.

Then he shows the impossibility of the first way, at (816). For it is clearly impossible that a mover be moved according to the same species of motion. For it is not sufficient to stop at some subalternate species, but one Must divide until he reaches the “individuals,” i.e., the most special species. For example, if someone is teaching, it is not enough for him simply to be taught at the same time, but he must be teaching and being taught the same; e.g., if he is teaching geometry he must be at the same time being taught it; or if he is the cause of a local motion called throwing, he must himself be moved according to the same motion of throwing. This is clearly false.

Then he dismisses the second ways namely, that the mover not be moved according to the same species of motion, but that it move according to one species and be moved according to another; for example, if it moves with a local motion, and is being moved with respect to growth; and if what causes the growth is being moved by some thing else according to alteration; and if this mover in turn is being moved with respect to some other motion.

Now it is clear that motions are not infinite either in genus or species. For it was held in Book V that motions differ in genus and species according to the differences of the species in which motion occurs. But the genera and species of things are not infinite, as we proved elsewhere; accordingly, neither are the genera and species of motion. If, therefore, a mover is necessarily being moved according to some other genus or species of motion, one will not be able to proceed to infinity and there will be some first immobile mover.

1047. But because someone could say that when all the species of motion are exhausted, a return will be made to the first species, in such a way that if the first thing taken as moved was moved locally, and we distributed all the genera and species of motion to different movers until these genera and species were exhausted, the remaining mover will then be moved according to local motion, in order to exclude this he subsequently says that such a return is tantamount to saying that the cause of alteration is being moved locally (he uses this explanation because above in his example he mentioned local motion first and alteration last), the same, I say, as supposing from the very beginning that the mover according to local motion is being moved, and that the teacher is being taught not only generically but in the specific sense.

And that this means nothing more, he proves consequently. For whatever is being moved is moved more by the higher mover than by the lower one, and, consequently, much more so by the first mover. If, therefore, the thing posited as being moved locally is being moved by a neighboring mover that is being increased, and it by a mover that is being altered, and it further by one that is being moved according to place, what is being moved according to place will be more moved by the first one moved according to place than by the second one which is being altered or by the third one which is being increased.

Therefore it will be true to say that the mover according to place is being moved according to place, and the same for every sphere of motion. Now this is not only false, because it is seen to be belied in many cases, but it is also impossible. For it would follow that the teacher is learning while he is teaching—which is impossible. For this involves a contradiction, since it is the property of a teacher that he have science, and of a learner that he not have it. Accordingly, it is clear that it is not necessary for a mover to be moved.

1048. He gives a second argument at (817) which does not differ from the preceding one except in that the first leads to certain particular inconsistencies, for example, that a thrower would be thrown or that a teacher would be being taught. But this one leads to inconsistencies in general.

Hence he says that although it is inconsistent that a teacher be learning, there is something still more unreasonable, for it turns out that every mover is mobile, if nothing is moved except by what is being moved. For it will thus follow that every mover is mobile, if, for example, one says that whatever has thepower to heal, or is actually causing health, is healable, and that whatever has the power to build is buildable—which is more unreasonable than that a teacher be learning, for a teacher could have been learning before, but a builder was never built.

Now this follows in two ways. For if it be conceded that every mover is being moved with respect to the same species of motion, it follows that a builder is being built immediately (i.e., without intermediary) and that a healer is being healed immediately. But if it be conceded that the mover is not being moved according to the same species of motion, it follows that we shall finally come to this after passing through a number of intermediates. And he explains this: If every mover is being moved by another but not being moved immediately with respect to the same species in which he is causing motion but according to some other species—for example, if a healer is not at once being healed but is being moved according to the motion of discipline by learning—yet, since the species of motion are not infinite, by thus ascending from mobile to mover one will at length reach the same species of motion, as was explained above.

Therefore, of these two, one appears plainly impossible, e.g., that the builder be immediately being built, while the other is seen as a fancy, namely, that one come to the same thing through a number of intermediates. For it is unacceptable that what is apt to cause alteration is of necessity apt to be increased in size.

1049. Accordingly, (818) having considered the foregoing arguments, the first of which concluded that this process—that whatever is being moved is being moved by another—must not go on ad infinitum, and the second of which concluded that not every mover is being moved, we can conclude from all the foregoing arguments that it is not necessary ad infinitum that what is being moved be moved by another in such a way that it is always being moved by a mover that is being moved. Therefore, it is necessary to stop at some first. However, this first must either be immobile or be moving itself.

But if we are considering which is the first cause of motion in the genus of mobiles, whether it is something that moves itself or a mobile that is moved by another, it is held as probable among all that the first mover moves itself. For a per se cause is always prior to what is a cause through another. For this reason, the Platonists held that prior to things that are moved by another there is something that moves itself.

And therefore we must consider this thing that moves itself and make of this another beginning of our consideration, namely, that we consider that if something moves itself, how is this possible.

Lecture 10

In that which moves itself, one part moves and the other is moved.

1050. After showing that in mobiles and movers there is no going on to infinity, but that a first is reached with is either immobile or selfmoving, the Philosopher now shows that even if a first that moves itself is reached, it is nevertheless necessary to come to a first which is immobile. This treatment is divided into three parts.

In the first he shows that what moves itself is divided into two parts, one of which is mover and the other moved;

In the second how these parts are mutually related, (L. 11);

In the third that it is necessary to come to a first which is immobile, (end of L, 11).

About the first he does two things:

First he shows that in a thing that moves itself, one part is mover and the other is moved, because a whole cannot move its whole self;

Secondly, he rejects other ways in which a thing that moves itself might be thought to do so, at 1054.

About the first he does three things:

First he proposes that what moves itself does not totally move itself as a whole;

Secondly, he proves the proposition, at 1052;

Thirdly, he concludes to the main conclusion intended—end of 1053.

1051. Because whole and part have no place except in things that are divisible, Aristotle, therefore, from what he had proved in Book VI, concludes first that whatever is moved is necessarily divisible into parts that are always further divisible—for this pertains to the very notion of a continuum. Now, whatever is being moved is a continuum, if it is being moved per se (for it is not impossible for an indivisible, for example, a point or whiteness, to be moved per accidens). And this was shown previously in Book VI: for all the statements made prior to Book VIII he calls universals of nature, because in Book VIII he begins to apply to things the statements he previously made about motion in common. Accordingly, since what is moved is divisible, a whole and a part can be found in everything that is being moved. If, therefore, there is anything that moves itself, we shall be able to take a whole and a part in it; but a whole cannot move its whole self, i.e., in its entirety move itself.

1052. Then at (820) he proves his proposition with two arguments, the first of which is this: The motion of a thing that moves itself at one time and in one motion is numerically one; if, therefore, a thing should move itself in such a way that the whole moves the whole, it will follow that one and the same will be mover and moved with respect to one and the same motion, whether it bel local motion or alteration. But this is seen to be impossible: for mover and moved are mutually opposite, and opposites cannot exist in the same thing with respect to the same. It is therefore not possible that some same thing be mover and moved with respect to the same motion.

For when something is at once moving and being moved, the motion according to which it moves is different from the one according to which it is being moved, as when a stick, moved by the hand, moves a stone, the motion of the stick is numerically different from the motion of the stone. Accordingly, it will follow further that someone will be both teaching and be taught at the same time with respect to one and the same knowable thing, and, similarly, that someone will heal and be healed with respect to one and the same numerical health.

1053. He gives the second argument at (821) which is this: It has been determined in Book III that what is being moved is a mobile, i.e., something existing in a state of potency, since what is being moved is being moved precisely because it is in potency and not in act, for a thing is considered to be in motion when, being in potency, it is tending toward act. Howeverf that which is being moved is not in potency in such a way that it is in no wise in act, because the very motion is a kind of act of the mobile precisely as being moved; but it is an imperfect act, being the act of the mobile inasmuch as it is still in potency.

But what causes motion is already in act, for what is in potency is not reduced to act except by something in act, namely, the mover; for example, the hot causes heat and that generates which has the form to be generated, as one who has the human form generates a man, and so on for other things. If, thereforet the whole moves its whole self, it follows that the same thing is, with respect to the same, at once hot and not hot, because, insofar as it moves, it will be hot in act; insofar as it is moved, it will be hot in potency.

The same is true in all other cases in which the mover is univocal, i.e., agreeing in name and species with the thing moved, as when the hot makes the hot and a man generates a man.

And he says this because there are some agents which are not univocal and which do not agree in name and notion with their effects, as the sun generates a man. In such agents, nevertheless, even though they do not possess the form of the effect according to the same notion, they do so in a higher and more universal sense. Consequently, it is universally true that the mover is somehow actually what the mobile is potentially. If, therefore, the whole moves its whole self, it follows that the same thing is at once in potency and in act—which is impossible.

From this he concludes (822) the main proposition that, with respect to a thing that moves itself, one part is mover and the other part moved.

1054. Then at (823) he rejects certain ways that someone might suppose to take place in the motion of a thing that moves itself.

First he shows that with respect to a thing that moves itself, both parts are not moved by each other;

Secondly, that with respect to a thing which moves itselfg one part does not move itself, at 1059.

About the first he does two things:

First he proposes what he intends;

Secondly, he proves his proposition, at 1055..

He says therefore first (823) that it is clear from what follows that a thing can not move itself in such a way that each part is moved by the other; for example, if AB moves itself, that A move B, and B move A.

1055. Then at (824) he proves the proposition with four arguments. And it should be noted that for this conclusion he re-uses the reasons previously used to show that not every mover is being moved by another. Hence from the foregoing he here collects four abridged arguments.

The first of these he takes from the first argument presented above in a double (i.e., ascending and descending) order to show that the process of something else being moved by another does not go on always, ad infinitum, because then there would be no first mover—from whose non-existence would follow the non-existence of all coming after it. Hence in this place too, the Philosopher premises the same unacceptable outcome.

For he says that if, in the first thing moved which is supposed as moving itself, both parts are reciprocally being moved by each other, it will follow that there is no first mover. This follows because, as was said above, the prior mover is more the cause of motion, and moves more, than the subsequent mover. And this was proved above on the ground that something causes motion in two ways. In one wayf something moves by being moved by another, as a stick moves a stone, because it is being moved by the hand, and this is a second mover. In another way, something moves by being moved of itself, as a man moves, and this is a condition of a first mover. Now what causes motion independently of being moved by another is farther removed from the last thing moved, and nearer to the first mover, than an intermediate which causes motion as being moved by another.

This argument should be formulated in the following way: If both parts of a thing that moves itself move each other reciprocally, one is no more the cause of motion than the other. But the first mover is more a cause of motion than a second mover; therefore, neither of the parts will be a first mover. Now this is unacceptable, since it would then follow that what is moved of itself would be no nearer to the first principle of motion (whose existence would thereby be rejected) than what is moved by another, whereas it was proved above that a mover that moves itself is first in the genus of mobiles. Therefore, it is not true that both parts of a thing that moves itself are moved by each other.

1056. Then at (825) he presents two arguments for the same taken from one he used above when he showed that not every mover is being moved, in the sense that being moved is found per accidens in the mover. In this argument he drew two conclusions above, namely, first, that a mover can happen not to be moved, and secondly, that motion is not eternal. In the light of these two conclusions he now forms two arguments.

For he says first of all “it is not necessary for a mover to be moved except by itself according to accident,” the sense of this being that unless the first mover be taken as being moved by itself, it will not also be necessary that the first mover be moved according to an accidents as some posited that every mover is being moved but that its being moved is in it ptr accidens.

When therefore it is supposed that of a thing which moves itself, the part causing motion is equally being moved by the other, this will be only per accidens. But as we conceded above, whatever is per accidens is able not to be; therefore, it is possible for the part which causes motion, not to be moved. Thus, therefore, it remains that of a thing that moves itself one part is moved, and the other causes motion and is not moved.

1057. Then at (826) he gives another argument corresponding to the second conclusion that he inferred above, namely, that it follows that motion does not always exist, Here, however, he argues in reverse order. If it is necessary that motion always exist, it is not necessary that a mover, when it causes motion, be moved, but it is necessary that the mover be either immobile or that it be moved by itself.

The reason for this conditional is apparent from an argument given above. For if a mover does not cause motion unless it is being moved, and if being moved is only in it per accidens, it follows that it can happen not to be moved. Consequently, it can happen also not to cause motion, and as a result, there will be no motion. But motion was proved to be eternal. Therefore, it is not necessary for a mover to be moved, when it is causing motion, Consequently, it is not true that each part of a thing that moves itself is moved by the other.

1058. Then at (827) he presents the fourth argument, which is taken from the argument previously given to prove that it is not essential to a mover that it be moved, because it would follow that we must come to this, that a mover would be being moved by the same motion which it is causing, as explained above.

And now abridging this argument he says that, if each part is being moved by the other, it will follow that it causes motion and is being moved with respect to the same motion. Hence, it follows that the heater is heated—which is impossible.

Now, the reason why it follows that the same thing is causing motion and being moved with respect to the same motion, when it is posited that each part of a thing which moves itself is moved by the other is that there is in the thing that moves itself just one motion, and it is according to that motion that the part causing motion will itself have to be moved.

1059. Then at (828) he excludes another way, namely, the supposition that the part of a thing which moves itself does not move itself.

First he proposes what he intends;

Secondly, he proves his proposition, at 1060.

He says therefore first that if something that is first moving itself be assumed, it cannot be said either that one part of it moves itself or that a number of parts do so, in such a way that each of them moves itself.

1060. Then at (829) he proves this with two arguments, the first of which is that if the whole is being moved by itself, this belongs to it either by reason of a part that isbeing moved by itself or by reason of the whole.

If it belongs to it by reason of its part, then that part will be a first mover that moves itself, because that part separated from the whole will move itself, but then the whole will no longer be a first mover of itself, as was supposed.

But if it be said that the whole moves itself by reason of the whole, then it will be only per accidens that some parts move themselves. But what is per accidens is not necessary. Therefore in the mover that first moves itself, it is most important to presume that the parts are not moved by themselves, Therefore, one part of the first mover that moves itself will cause motion, since it is immobile, and the other will be moved. For those are the only two ways in which it is possible that a part which causes motion could be moved, namely, either because that part would be moved by another part which it moves, or because that part would move itself.

Hence it should be noticed that Aristotle in excluding these two ways intends to conclude that in a thing which moves itself, the part which causes motion is immobile, but not that what moves itself is divided into two parts, one of which causes motion and the other is moved; for this had been sufficiently concluded, when he first proved that the whole does not move itself as a whole.

Accordingly, it is clear that it was not necessary that Aristotle introduce a division of five members, as some claimed: one member of which is that the whole moves the whole; the second that the whole moves a part; the third that a part moves the whole; the fourth that two parts mutually move one another; the fifth that one part is a mover and the other moved. For if the whole does not move the whole, it follows for the same reason that the whole does not move the part, nor the part the.whole; because in either case it would follows that a moved part would be moving itself. Hence the fact that the whole does not move the whole suffices for concluding that one part is a mover and the other is moved. But in order to conclude that the part which causes motion is not moved, he proves two other things, namely, that the part causing motion is not moved by a moved part, and that it is not moved by itself.

1061. And to prove this last point he presents a second argument (830): If it be granted that the motion-causing part of a thing that moves itself moves itself as a whole, it follows through what was proved above that a part of that part causes motion and the other part is moved. For it has been already proved above that a whole does not move itself in any other way than by one of its parts causing motion and the other being moved, So, let AB be the motion-causing part of a thing that moves itself; then by the previous argument it follows that one part of it is a mover, namely A, and the other part, namely B, is moved. Therefore, if AB as a whole moves itself as a whole, as you say, it follows that the same thing would be moved by two movers, namely, by the whole AB and by the part A—which is impossible. It remains, therefore, that the motion-causing part of a thing which moves itself is entirely immobile,

Lecture 11

How the parts of something moving itself are related.

1062. After showing that a thing which moves itself is divided into two parts, one of which causes motion and is not moved, and the other of which is moved, the Philosopher now shows how such parts are mutually related. About this he does three things:

First he proposes what he intends;

Secondly, he shows his proposition, at 1063;

Thirdly, he reaches the conclusion chiefly intended by all the foregoing, at 1068.

He says therefore first (831) that since a mover is divided into two elements, one of which is also moved by something else, and the other of which is immobile, and again, since a mobile is divided into two, there being a mobile which also causes motion, and another which does not move anything, one must say that what moves itself is composed of two parts, one of which is such a mover as to be immobile, and the other of which is so moved as not to move anything else.

And when he says that the latter does not move anything “of necessity,” it can mean two things: If it is understood as though the moved part of a self-mover does not move anything that is part of the self-mover, the word “necessity” should be interpreted in an affirmative sense, referring to his calling it “non-moving,” as meaning that of necessity it does not move anything else. For he at once proves that it is impossible for a thing that moves itself to have a third part which is moved by the moved part. But if the words are interpreted as meaning that the moved part does not move anything extrinsic, then the phrase, “of necessity,” must be given a negative meaning; for it is not necessary in a thing which moves itself that its moved part move something extrinsicq but neither is it impossible.

1063. How this happens he shows at (832). About this he does two things:

First he explains his proposition;

Secondly, he solves a doubt, at 1066.

About the first he does two things:

First he shows how the parts of a thing that moves itself are related;

Secondly, how with respect to them a whole is said to move itself,1065.

About the first he does two things:

First he shows that in a thing which moves itself there are just two parts, one of which causes motion and is not moved, and the other of which is moved and does not cause any motion;

Secondly, how these two parts are joined to one another, at 1064.

He explains the first part in this way (832): If it be said that the moved part of a thing that moves itself does in turn move something else which is part of the very thing that moves itself, then let A be the first immobile part of this self-moving thing. Let B be the second part and let it be both the one moved by A and the mover of a third part C. which is so moved by B as to move nothing else that is a part of this self-moving thing. For it cannot be said that there is an infinite descent in the parts of a thing which moves itself, such that a moved part in turn moves anothert for then it would be moving itself ad infinitum, which is impossible, as was shown above. There will be, therefore, in that self-moving thing a part which is moved but is not a mover, i.e., the part C. And although it might be that it is through many intermediate moved movers that the last moved part C is reached, we can accept B as the one intermediate taken in place of all these intermediates. Thus, therefore, does this whole, which is ABC, move itself. If from this whole there be taken away the part C, AB will still move itself, because one of its parts is a mover, namely A, and the other moved, namely B, which was required for a thing to be able to move itself, as was shown above. But C will not move itself, or move any other part, as we have assumed.

Likewise, even BC does not move itself without A, because B does not cause motion except inasmuch as it is moved by something else, which is A, which is not a part of BC. It remains, therefore, that only AB moves itself first and per se. Hence a thing which moves itself must have two parts, one of which is an immobile mover, and the other of which is moved and necessarily does not move anything that is part of the whole thing that moves itself, for this was concluded by the foregoing argument.

Or else it “moves nothing of necessity”—since it is not a necessity of a self-mover that the moved part move anything else, even anything extrinsic.

1064. Then at (833) he shows how these two parts are mutually related.

Here it must be considered that Aristotle has not yet proved that the first mover has no magnitude, as will be proved later. But some of the earlier philosophers posited that no substance can exist without magnitude. Hence Aristotle is keeping with his custom when he leaves this matter doubtful until it is proved; and he says that the two parts of a self-mover, of which one is a mover and the other moved, must be somehow conjoined if they are to be parts of one whole. But not by continuation, because above he has said that a self-mover and a moved thing cannot form a continuum but are necessarily divided. Hence it remains that these two parts must be joined by contact: either by both parts touching one another, if they have magnitude; or by just one of the parts touching the other and not vice versa, which will be the case if the mover has no magnitude. For what is incorporeal can indeed touch a body by means of its power and so move it, but it is not touched in turn by the body; two bodies, however, touch each other.

1065. Then at (834) he shows by what reason a whole is said to move itself with one part causing motion and the other part being moved.

And let us suppose at first that each part is continuous, i.e., having a magnitude, because in Book VI it has been proved of anything that is moved that it is a continuum, and let the same thing be supposed at the present time for the mover, before the truth is proved.

Therefore, using this supposition, three things are attributed to this whole composed of two parts: it is moved, it causes motion, and it moves itself. But self-movement is attributed to it not because a part moves itself but because the entire whole move itself, while to cause motion, and to be moved, are attributed to the whole by reason of the part. For the whole neither moves nor is moved, but one part A moves, and the other part B is moved only; and it has already been shown that there is no third part C which is moved by B. For this is impossible, if we are dealing with a thing that moves itself primarily, as has been shown above.

1066. Then at (835) he raises a doubt about the foregoing.

First he raises it;

Secondly, he solves it, at 1067.

This doubt springs from what he had previously proved, namely, that in a thing that moves itself in a primary sense, there are but two partat of which one moves and the other is moved, on the ground that, if there were a third, even if this third were removed, the composite of the first two would still move itself, and thus the latter is the primary self-mover.

From this, therefore, the following doubt follows (835). Let us suppose that the immobile but motion-causing part A of a self-moving whole is a continuum. Now it is clear that its part B, which is the moved part, is a continuum, according to what has been previously proved. But every continuum is divisible. Therefore the doubt is this: If through division a part be removed from A or R, would the remaining part be a mover or a moved part? Because if it is either, the part of AB that remains will move itself andq accordingly, AB will not be some-thing that moves itself in a primary sense. Thus it further follows that nothing will be a self-mover in a primary sense.

1067. Then at (836) he resolves this doubt.

Now it should be remembered here that in Book VI Aristotle has proved that there is no first in motion, either on the part of the mobile, or of the time or of the sphere of motion, and that this is especially true in growth and local motion: the reason being that he was then speaking of motion in common and of the mobile as it is a certain continuum, without yet making application to particular natures. And according to this, it would follow that there would not be anything that is first moved and, consequently, no first mover, if the mover were a continuum. Likewise, there would also not be anything that is a first mover.

But now Aristotle is speaking of motion and applying his doctrine to definite natures and for that reason he posits that there is a first mover of self.

And he resolves the doubt in the following manner, stating, namely, that there is nothing to prevent the mover and moved from being divisible in potency, due to the fact that they are continua, i.e., if both are continua, or at least one of them, namely, the one that is moved, which necessarily is a continuum. But yet it is possible that some continuum, whether it be a mover or something moved, have such a nature that it cannot be actually divided, as is evident of the body of the Sun. And if it happens that some continuum is divided, it will not retain the same potency for causing motion or being moved as it had before—because such a potency follows upon the form, and a natural form requires a determinate quantity. Hence, if it is an incorruptible body, it cannot be actually divided. But if it is a corruptible one, then if it be divided, it will not retain the same potency, as is evident with respect to the heart. Hence, there is nothing to prevent, in things potentially divisible, there being one first.

1068, Then at (837) he infers the conclusion mainly intended from all this. And he says that from the foregoing it is clear that it is necessary to posit a first mover that is immobile. For since there is not an infinite process in movers and moved things, but a halt must be made at a first which is immobile or self-moving, then, whether the movers and moved stop at some first immobile or at some first that moves itself, in either case it turns out that the first mover is immobile, because one part even of a thing that moves itself is an immobile mover, as has just been proved.

Lecture 12

The first mover is not moved, but is one and perpetual.

1069. Having shown that in things moved by another there is not a process to infinity but a first must be reached which is either immobile or a mover of self, and having shown that, of a thing that moves itself, one part is an immobile mover, and that, consequently, in either case there is a first mover that is immobile, now, because among self-movers which exist among us, namely, perishable animals, it happens that the motion-causing part in the thing which moves itself is perishable and moved per accidens, namely, the soul, the Philosopher wishes to show here that the first mover is imperishable and is not moved either per ae or per accidens. About this he does two things:

First he proposes what he intends;

Secondly, he proves it, at 1072.

About the first he does three things:

First he reviews what has been previously manifested;

Secondly, he omits something that seemed useful for his proposition, at 1070;

Thirdly, he explains his proposition, at 1071,

He says therefore first (838) that it was shown above that motion always exists and never fails. And since all motion is from a mover, and in movers there is not a process to infinity, it is necessary that there be a first mover. And since it has not yet been proved that the first mover is one, he accordingly lets it remain doubtful whether it is one or many. Further, it has been shown that the first mover is immobile, whether by ascending from moved to movers one imediately reaches a first immobile mover, or whether what is reached is a first mover that moves itself, one part of which is an immobile mover.

1070. Some have opined that all moving principles in things that move themselves are imperishable, for Plato posited all the souls of animals to be perpetual. And if this opinion were true, Aristotle would have his proposition clinched at once, so far as the first mover’s being eternal is concerned. But the opinion of Aristotle is that among the parts of the soul, only the intellect is imperishable, even though other parts of the soul are movers.

Consequently he omits this at (839) where he says that as far as the present argument is concerned it is of no moment whether each of the principles that move themselves and are immobile is imperishable, even though some have posited this by positing that all souls are imperishable. And he says that this does not affect the present argument, because he will prove his proposition without using this supposition.

1071. Then at (840) he explains what he intends to prove. And he says that by considering the thitgs that follow, it can be plain that even though not every immobile mover is imperishable, there must,be something immobile in such a way that it is no way moved from without, either absolutely or per accidens, and yet is a mover of something else.

When he says “immobile with respect to any change from without,” he does not mean to exclude a motion, i.e., an operation, which is in the one operating in the sense that to understand is called a “motion,” and in the sense that the appetite is moved by the desirable object. A motion of this sort is not excluded from the first mover which Aristotle is discussing.

1072. Then at (841) he proves what he had said, namely, that there exists a first mover that is eternal and entirely immobile.

First he proves this through self-movers that at one time exist and at another time do not;

Secondly, through moving principles which sometimes are causing motion and sometimes not, (L. 13).

About the first he does three things:

First he shows that there must be a first mover that is eternal;

Secondly, that such a mover should be one rather than many, at 1075;

Thirdly, he shows both at once, i.e., that there is one first mover and that it is eternal, at 1076.

About the first he does two things:

First he rejects an argument by which some could try to prove this proposition;

Secondly, he goes on to explain his proposition, at 1074.

1073. Now, someone could proceed as follows (841): Whatever cannot at one time be and at another not be is eternal; but the first mover, since it is immobile, as has been shown above, cannot be at one time and not be at another time, for whatever is such is generated and ceases to be, which involves its being moved. Therefore, the first mover is eternal.

But Aristotle does not have any use for this argument, because someone could say, if he wants, that in some things it happens that at one time they exist and at another time they do not, without their being generated or ceasing to be, speaking per se, and consequently without their being moved per se. For if something not divisible into parts, which is, namely, not composed of matter and form, is at one time in a certain way, and at another time is not, then necessarily every such thing—without any self-change—does at one time exist and at another time not exist, as may be said of a point, and of whiteness, and of anything of this sort, for it has been shown in Book VI that whatever is moved can be divided into parts, and in Metaphysics VII that whatever is generated is composed of matter and form. Such non-divisible things, therefore, are neither generated nor changed per se, but per accidens, when other things are generated or changed.

From this it is also plain that if something is moved neither per se nor ar accidens, it is eternal; and that if it is eternal, it is moved neither per se nor per accidens, insofar as it is eternal. If, therefore, it is conceded to be contingent for something to exist at one time and not at another without its being generated or ceasing to be, then let it also be conceded to be contingent that certain immobile moving principles, which are yet mobile per accidens, exist at one time and do not exist at another. Nevertheless it is not at all possible that all such principles which are movers and immobile be such that they exist at one time and not exist at another.

1074. Then at (842) he proves his proposition. And he says that if some things which move themselves exist at one time and not at another, then there must be a cause of their generation and ceasing-to-be, by virtue of which they exist at one time and do not exist at another, because whatever is moved has a cause of its motion. But what exists at one time and not at another, if it is a composite, is generated and ceases-to-be. Now, a thing that moves itself must possess magnitude, since it is moved, and it has been shown in Book VI that nothing indivisible into parts is moved.

But from the foregoing it cannot be held that it is necessary for the mover to have magnitude, and thus it is not moved per se, if it exists at one time and does not exist at another. But if there is a cause of the generation and perishing of things that move themselves, then there must also be a cause to account for their generation and perishing being continued forever.

But it cannot be said that the cause of this continuity is one of those immobiles that do not always exist, nor can it be said that the cause of the eternal generation and perishing of some things that move themselves are certain immobile movers which do not always exist, and of that of others, certain others. And he explains this when he says that not one, nor all of them, can be the cause of this continuous and eternal generation.

That one of them cannot be the cause he thus proves: What does not exist forever cannot be the cause of what is forever perpetual and necessary. That all cannot be the cause he proves for the reason that all such perishable principles, if generation is perpetual, are infinite and do not all exist at once. But it is impossible for one effect to depend on an infinitude of causess

And again, things that do not exist at once cannot be the cause of one thing, although it could be said that when things do not exist all at once, some dispose and some cause, as is plain with respect to drops that fall successively and wear away a stone. But if a number of things are a direct cause of anything, they must exist all together.

Accordingly, therefore, it is manifest that if there are a million principles that are movers and immobile, and if there are many things that move themselves, of which some perish and others come to be, and among these, some are mobile and some movers, nevertheless there must be something above all of them that by its power contains all the things which are generated and perish in the above-mentioned way and which would be the cause of the continual change affecting them by which they sometimes are and sometimes are not and through which these latter are the cause of coming-to-be and of motion for others, and these for yet others. For every generator is a cause of generation to the thing generated, but it is from some imperishable first principle that perishable generators possess the characteristic of being causes of generation. If, therefore, the motion through which some things at one time exist and at another do not is perpetual, as has been shown above, and a perpetual effect cannot exist except from a perpetual cause, then, necessarily, the first mover is perpetual, if it is one; and if there are more than one first mover, they too are perpetual.

1075. Then at (843) he shows that one perpetual principle ought to be posited rather than many. And he says that just as finite principles ought to be preferred to infinite, so one first principle rather than many. For if the same effects happen or follow from positing finite principles as from positing infinite principles, one should assume that the principles are finite rather than infinite, because in things that are according to nature, the preference must be given to what is better, if it is possible, because things that are according to nature are disposed the best. Now, a finite principle is better than an infinite one, and one better than many. But one first immobile principle, if it is perpetual, is sufficient for causing the perpetuity of motion. Therefore, many first principles should not be posited.

1076. Then at (844) he concludes from the foregoing that it is necessary that there be one first mover which is imperishable.

And although this seems to be sufficiently proved from the foregoing, yet someone could cavil that the cause of the continuity of generation is a perpetual first mover of self, but the mover of that is not perpetual and one but moved by diverse movers, of which some cease to be and some come to be.

But this he intends to dismiss, because if motion is perpetual, as he had proved above, then necessarily the motion of the first mover of self, which is posited as the cause of the entire perpetuity of motion, is eternal and continuousq for if it were not continuous, it would not be eternal. However, what is successive is not continuous, whereas in order that a motion be continuous it must be one; and in order to be one, it must be from one mover and in one mobile. But if the mover is other and other, the motion will not be a whole continuous motion, but a successive one.

Therefore, it is absolutely necessary that the first mover be one and perpetual. But an immobile mover that is moved pjr accidens is not perpetual, as has been said above. It remains, therefore, that the first mover is utterly immobile, both per se and per accidens.

Lecture 13

The first mover perpetual and wholly unmoved, as shown from moving principles

1077. After showing that the first mover is perpetual and utterly immobile on account of the perpetuity of the generation and perishing of animals, which move themselvesl.the Philosopher now intends to prove the same with an argument based on the moving principles. About this he does three things:

First he reviews things said from the beginning of this treatise;

Secondly, from these he forms an argument for his proposition, at 1081;

Thirdly, he finishes the solution of a doubt mentioned above, at 1085.

1078. About the first he reviews three things: First (845), the destruction of certain improbable positions. And he says that anyone can know that there is a first immobile. mover not only from the foregoing, but also by considering the principles of motion. And as was said above, it is evident to sense that among natural things are found some that are at one time being moved and at another time at rest.

From this it was explained above that none of these three positions is true: the position that all things are always being moved; the position that all things are always at rest; and the position that all things which rest, always rest, and those being moved, are always being moved. The truth of this matter is demonstrated by the very things found under botht namely, under motion and under rest, since they have the potency to be moved at one time, and to be at rest at another.

1079, Secondly, he recalls the process he went through when investigating the first immobile mover. And he says that because things which at one time are being moved and at another time are at rest are plain to all, lest anyone follow a fourth position that all beings are such that they are at one time being moved and at another time at rest, we want to demonstrate two differing natures by showing, namely, that there are certain things that are always immobile, and certain things again that are always being moved.

And in dealing with this matter we proposed first that whatever is being moved is being moved by something and that this thing by which something is being moved is either immobile or is itself being moved, and if it is being movedt then either by itself or by another. And since one cannot proceed to infinity in the series of “being moved by another,” we must come to this that there is some first principle of motion, such that in the genus of things that are moved there is a first principle which moves itself, and beyond that, absolutely among all, there is a first principle which is immobile. Nor ought it to be thought strange that something move itself, because we plainly see many such in the genus of living things and animals.

1080. Thirdly, at (847) he recalls an objection mentioned and solved above. For since he had proved the eternity of motiont he cited to the contrary an objection based on living things which after having been at rest begin at a certain time to be moved. And what he says here is that those living things which move themselves seem to foster the opinion that in the entire universe motion begins after previously not having been, on the ground that we see this happen in things, namely, that they at one time begin to be moved, when previously they were not being moved.

To solve this it is necessary to accept that animals move themselves with respect to one motion, namely, local motion; for only this motion, based on appetite, is found in animals. And yet animals do not properly move themselves even with respect to this motion as though another cause of this motion does not pre-exist. For no animal is of itself the first cause of being moved locally, but other motions precede—not voluntary but natural—either from within or from without, according to which the animals do not move themselves, as is plain in the motions of growth and decrease, and respiration, according to which animals are movedt although they rest with respect to local motion by which they are moved by themselves

The cause of these local motions is either an extrinsic container—namely, the heavens and air—by which the bodies of animals are changed externally, or something enters the bodies of animals, as air enters through breathing and as food enters through eating and drinking. And from such transmutations, caused either from within or from without, it happens that animals at a certain time begin to be moved, when previously they were not being moved, as is plain from the change which arises from food: for while the food is undergoing heat the animals sleep on account of the vapors being broken down, but when the food is now digested and dissolved, and the vapors are left, the animals awaken and get up and move themselves from place to place. In all this, nevertheless, the first principle of motion is something extrinsic to the nature of the animal that moves itself.

That is the reason why animals are not always moved by themselves, because with respect to any animal moving itself there is found some previous mover, which is being moved and causes motion. For if it were entirely immobile, it would always maintain itself in the same way in causing motion and, consequently, the motion also of the animal would be perpetual. But because this extrinsic mover that moves animals is itself moved, it does not always move in the same way.

Hence, neither do animals always move themselves in the same way, because in all these things the first mover which is the cause of the animal’s moving itself, such as the soul, causes motion in such a way that it is itself being moved not per se but per accidens, for the body is changed with respect to place, and when the body has been changed, that which exists in the body, namely, the soul, is also changed per accidens, And thus the whole that moves itself is changed of necessity, so that it does not maintain itself in the same disposition for causing motion.

1081. Then at (848) from the foregoing he proves his proposition.

First that the first mover is immobile;

Secondly, that the first motion is perpetual, at 1083.

About the first he does two things:

First he proves the proposition;

Secondly, he dismisses an objection, at 1082.

He says therefore first (848) that from the foregoing we can know that if some principle is an:bmobile mover nevertheless moved per accidens, it cannot cause a continuous and perpetual motion. For the reason assigned for saying that animals do not always move is that they are moved per accidens. But it has been shown above that the motion of the universe must be continuous and perpetual. Therefore, it is necessary that the first moving cause in the whole universe be immobile, in such a way as not to be moved even per accidens.

But, as was said above, in natural things a motion that is immortal and unceasing ought to be found, and the disposition of this universe should be maintained in its disposition and in the same state. For from the immobility of the principle that is set down as remaining immobile, it follows that the entire universe has an eternal permanence, insofar as it is joined to the first immobile principle and receives an influence from it.

1082. Then at (849) he excludes an objection. For he had said that if a mover is moved per accidens, it does not move with an undying motion. Now this seems to give rise to an objection, because, according to his positiont the motions of the inferior orbs, such as the sun and moon and other planets are eternal, and yet their movers seem to be moved per accidens, if we follow what he had just said. For he said that the reason why the soul of an animal is moved per accidens is that the animalts body is moved by an external principle, which is not from the soul; in like manner, it appears that the orb of the sun is moved by some other motion as though carried along by the motion of the first orb, insofar as it revolves from east to west; this is not the way it is moved by its proper movert but contrariwise, from west to east.

He dismisses this objection, saying that “being moved per accidens” can be attributed to something either with respect to itself or with respect to something else, and this is not the same. Now “being moved per accidens” can be attributed to the movers of the orbs of the planets, not in the sense that these movers are moved per accidens, but that the orbs moved by them are moved per accidens in being influenced by the motion of the superior orb. And this is what he says, that “to be moved per accidens from another,” i.e., by reason of another, is attributed to certain principles of heavenly motions, in the case of the movers of the orbs which are moved by more than one motion, namely, by their own and by that of the superior orb. But the other case, that a thing be moved per accidens with respect to itself is found only in perishable things, as in the souls of animals. The reason for this diversity is that the movers of the superior orbs are not constituted existents through being united to bodies, and their connection with the latter is unvarying; and therefore, although the bodies of the orbs are moved, the motors are not moved per accidens. But the souls which move animals depend for their existence on being united to their bodies, and they are connected in a way subject to variation, and accordingly, as the bodies are affected by change, the souls themselves are said to be changed per accidens.

1083. Then at (850) he proves that the first motion is perpetual. And he does this with two arguments, the first of which depends on the foregoing and is this: A motion which is not perpetual is found to be from a mover that is moved per se or per accidens, as is evident from above. Since, therefore, the first mover is immobile and perpetual, and is moved neither per se nor per accidens, then, necessarily, the first mobile, which is moved by this utterly immobile mover is moved with a perpetual motion.

Now, it should be noted that above he proved the immobility of the first mover by means of the perpetuity of motion, shown above. Here, on the contrary, through the immobility of the first mover he proves the perpetuity of motion, But this would be arguing in a circle, if the same motion were meant in both arguments.

Hence it must be said that above he proves the immobility of the first mover from the perpetuity of motion in general; that is why he said that among the things that exist, there is an unceasing and immortal motion. But here through the immobility of the first mover he proves the perpetuity of the first motion. From which it is plain that what the Commentator says is false, namely, that in the beginning of this Book VIII Aristotle proved that the first motion is perpetual.

1084. The second argument is given at (851) and is taken from the perpetuity of generation. And he says that the first motion is perpetual for another reason, namely, that the only way temporal generation and ceasing-tobe, and changes of this sort, can exist is that something move and be moved, for it has been proved above that every change is caused by some mover. Therefore, coming-to-be and ceasing-to-be and change of this kind ought to be from a mover, But they cannot be immediately from the immobile mover, because the immobile will always cause the same motion and in the same way, for its relation to the mobile is not variable; and, given a relation between mover and moved that remains the same, the motion remains always the same, However, coming-to-be and ceasing-to-be are not always in the same state, but at one time something is generated and at another it ceases to be. Therefore, these changes are not immediately from the immobile mover but from a mobile mover. Now, whatever is moved by a moved mover which in turn is moved by the immobile mover can retain perpetuity in spite of the alternation of diverse motions, because, since the mobile mover stands in varying relation to the things moved, it will not always cause the same motion. Rather, since it occupies differing positions (if moved with local motion), or assumes differing forms (if moved with a motion of alteration), it will produce a contrary motion in other things and will cause them to be at one time at rest and at another time in motion. He says “in contrary positions or forms,” because it has not yet been proved by what form of motion the first mobile is moved; but he will inquire into this later.

Thus, therefore, insofar as it is moved, it is a cause of the diversity of motions; but insofar as it is moved by the immobile mover, it is the cause of the perpetuity in this diversity of changes. Therefore, the very perpetuity of generation shows that the first motion is perpetual and brought about by the immobile mover.

But it should be understood that these arguments by which Aristotle tries to prove that the first motion is perpetual do not conclude of necessity, for it can happen without any change in the first mover that it not always cause motion, as was shown above in the beginning of this Book VIII.

1085. Then at (852) he draws a conclusion which he left unsettled above, namely, why some things are always in motion and some not always.

And he says that the cause of this is now plain from what has gone before: Things which are moved by an immobile and eternal mover are always in motion; things which are moved by a changed mover are not always in motion—for the immobile, as previously stated, since it remains absolutely alike and in the same state, will cause a motion that is one and simple.

Lecture 14

Many reasons why local motion is the first motion

1086. After showing that the first mover is immobile, and the first motion perpetual, the Philosopher here begins to show which motion is the first and what kind of being the first mover is. And it is divided into two parts:

In the first he shows which is the first motion;

In the second, what kind of being the first mover is, (L. 21).

About the first he does two things:

First he states his intention;

Secondly, he carries out his proposal, at l087.

He says therefore first that in order that the consideration of the foregoing be more certain, we must begin from another starting-point and consider whether there is any motion which may be infinitely continuous and, if so, which it is, and which is the first of all motions,

And lest anyone should think that the one which may be continuous and the one which is first are two different motions, in order to exclude this he adds that it is plain that since it is necessary for motion always to exist, and the first is forever continuous, for it is caused by the first immobile mover, then necessarily it is one and the same motion which is eternally continuous and which is first.

1087. Then at (854) he proves the proposition.

First with arguments;

Secondly, by referring to the sayings of the ancients, (L. 20).

About the first he does two things:

First he shows that local motion is the first;

Secondly, which local motion, (L. 15).

The first he proves in three ways:

First through the properties of motions;

Secondly, through the difference between rior and subsequent, 1090;

Thirdly, by reason of the order of mobiles, at 1096.

1088. With respect to the first he gives two arguments, in regard to the first of which he proceeds thus:

First he proposes what he intends, and says that since there are three species of motiong one with respect to quantity and called “growth and decrease,” another with respect to passible quality and called “alteration,” and a third with respect to place and called “local motion,” the last one must be the first of all.

Secondly, he proves this on the ground that it is impossible for growth to be the first motion, For growth cannot take place unless an alteration precedes it, because that by which something is increased is somehow unlike and somehow like, That it is unlike is plain, because that by which something is increased is food, which in the beginning4s contrary to what is nourished, on account of the diversity of disposition. But when it is added and causes increaset it is necessarily like. Now the transition from unlike to like does not take place except through alteration. Therefore, it is necessary that before growth, there must occur alteration through which food is changed from one contrary disposition to the other.

Thirdly, he shows that before every alteration there is a previous local motion, for if something is altered, it is necessary that there be something causing alteration, that makes the potentially hot come to be actually hot. But if this cause of alteration were always in the same way near at an equal distance to the thing altered, then it would not make it any hotter now than previously. Therefore, it is plain that the mover in alteration does not remain the same distance from what is altered, but is at one time closer and at another time farther away—and this cannot happen without a change of place. If, therefore, motion must always exist, then local motion must always exist, since it is the first of all motions. And if one local motion is prior to all other local motions, then, necessarily, if the foregoing is true, this first motion must be eternal,

1089. The second argument he gives at (855) and it is this: Alteration, as was proved in Book VII, occurs with respect to passions and passible qualities, among which, according to the opinions of the ancients, density and rarity seem to be a principle, because the heavy and the light, the soft and the hard, and the hot and the cold, seem both to result from, and to be distinguished by reason of, the dense and the rare (for among the elements the dense are found to be the heavy and the cold, and the rare the hot and the light). Now this opinion is true to a certain extent, if the passible qualities be ranged according to their proximity to the material principle, for the rare and the dense seem especially to pertain to matter, as is clear from what was said in Book IV. But density and rarity seem to be instances of commingling and separation, according to which the ancient philosophers explained the generation and ceasing-to-be of substances. This opinion Aristotle uses as probable before manifesting the truth about generation and ceasing-to-be in his book On Generation. But things commingled and separated seem by that very fact to be changed with respect to place. Hence, change of place is a principle of alteration.

It should be noted, however, that although the commingling and separation that affect bodies actually existing pertain to local motion, yet the commingling and separation according to which the same matter is contained under larger or smaller dimensions do not pertain to local motion but to the motion of alteration, And it is was in this sense that in Book IV Aristotle explained the nature of the dense and of the rare. But here he is speaking according to what is probable according to the opinion of other philosophers.

Yet, just as local motion is required for alteration, so also for growth. For it is necessary that the magnitude of what is increased or decreased be moved with respect to place, because what is increased expands into a larger place, and what decreases shrinks into a lesser place. Therefore, in this way it is plain that local motion is naturally prior to both alteration and growth.

Ane he says that from this consideration it will be clear that change of place is the first of motions, for, just as in other things, so too in motion, one thing is said to be “prior” to another in various ways. For in one way something is said to be “prior” in the sense that, if it does not exist, neither do the other thingst while it itself can exist without the others, as “one” is prior to “two,” because “two” cannot exist unless there is “one”, but “one” can exist, even if there are not two. In a second way, something is said to be “prior” in times namely, in the past, when something is more distant from the present “now,” or in the future, when something is closer to the present, as was said in Book IV. Thirdly, something is said to be “prior” according to substance, i.e., with respect to what completes a substance, as act is prior to potency, and the perfect to the imperfect.

1091. Secondly, at (857) he proves that local motion is the first among the three above-mentioned kinds of motion:

First, as to the first;

Secondly, as to the second, at 1092;

Thirdly, as to the third, at 1094.

He says therefore first (857) that since it is necessary for motion always to exist, as was proved previously, this can be understood in two ways: first, as meaning that there exists a continuous motion; secondly, as meaning that there are motions which exist one after the other, and nothing exists between them. Now, the perpetuity of motion is better saved if motion is continuous; moreover, it is a greater thing, if it be continuous rather than successive, because the former possesses more unity and perpetuity, and in nature we ought always to take what is more noble, if possible. But it is possible that there be a motion that is infinitely continuous, provided it be a local motion. (This is assumed for the presentg but later it will be proved.) From this it is plain that local motion must be taken to be the first motion.

For other motions are not required for the existence of local motion. For in order that a thing be moved with respect to place it need be neither increased nor altered, because a body that is in local motion does not have to be subject to generation and corruption, and we know that growth and alteration affect only things that are generated and cease to be. However, none of these motions can occur unless there is that eternal motion, caused by the first mover, the motion, namely, that is none other than local motion. Consequently, local motion can exist without the others but not they without it. Therefore, it is first according to the first way of being “prior.”

1092. Then at (858) he proves that it is prior in time, About this he does two things. First he shows that, absolutely speaking, it is prior in time, because what is perpetual is, absolutely speaking, prior in time to what is not perpetual. But only local motion can be perpetual, as has been said, therefore, absolutely speaking, it is first in time.

1093. Secondly, at (859) he dismisses an objection through which this seems to be made invalid. Because if we consider some one body that is newly generated, local motion seems to be the last change to affect it. For first it is generated, then it is altered and increased, and finally it undergoes local motion, when it is now perfect, as is clear in man and in many animals.

But this does not disprove the statement that, absolutely speaking, local motion is first in point of time, because before all those motions which are found in this generated thing, a local motion had to exist in some prior mobile, which is the cause of the generation for those that are generated, as the generator is the cause of what comes to be in such a way as not to be itself generated.

That the motion which precedes generation is a local motion and that, absolutely speaking, it is the first of motions, he proves on the ground that generation is seen to be the first of motions in things that are generated, because a thing must first be made before it is moved—and this is true in everything generated. But there must be something moved prior to what is generated and which is itself not generated, or if it is generated, then there was something prior to it. In this way we must go on ad infinitum, which is impossible, as was proved above, or come to some first.

But that first cannot be generation, for then it would follow that all changeable things are perishable, because everything that can be generated is able to perish. Therefore, if the first mobile is something generated, it follows that it is perishableg and as a consequence, all the subsequent mobiles. But if generation is not absolutely first, it is clear that none of the motions that follow it is absolutely first. And I say motions that follow, meaning growth, alteration, decrease and ceasing-to-be, all of which follow generation in time. If, therefore, generation is not prior to local change, it follows that none of the other changes can be absolutely prior to local change, And so, since some change must be absolutely first, it follows that local change is first.

1094. Then at (860) he proves that local motion is first in the order of perfection, And this he proves in two ways. First, in this way: Everything that is coming to be is, while it is coming to beg imperfect and tending to its principle, i.e., to a likeness to the principle that made it, and which is naturally first. From this it is clear that what is subsequent in the order of generation is prior in the order of nature. But in the process of generation, in all things generable, local change is found to be last, not only in one and the same thing, but also in the total progress of the nature of things that can be generated. Among theset some living things are completely immobile with respect to place on account of a lack of organ, as are plants, which do not have the organs required for progressive motion, and also many types of animals. But in the perfect animals local motion is found. If, therefore, local motion is present in things which comprehend nature in a higher degree, i.e., which attain to a greater perfection of nature, it follows that local motion is among all motions the first with respect to the perfection of substance.

1095. Secondly, at (861) he proves the same thing in this way; The less a motion takes away from the mobile, the more perfect is its subjeott and in this regard, a motion is somehow more perfect. But it is only according to local motion that nothing in the mobile subject is taken away: for in alteration, a transmutation with respect to a quality in the subject takes place, and in growth and decrease, a change with respect to the quantity of the subject takes place; moreover, the change involved in generation and ceasing-to-be affects the very form which constitutes the substance of the subject. But local motion is only with respect to place, which contains the subject externally. It remains, therefore, that local motion is the most perfect.

1096. Then at (862) from the side of the mobile he shows that local motion is first. For it is plain that what moves itself, most properly moves itself according to local motion. Since, therefore, it is something which moves itself that is the principle of other movers and mobiles and is consequently the first among all things that are moved, it follows that local motion, which is proper to it, is first among all motions.

In this way, therefore, he concludes from the foregoing that change of place is the first of all motions.

Lecture 15

Local motion alone can be continuous and perpetual.

1097. After proving that local motion is the first of all motions, the Philosopher now shows which local motion is the first. And becauset as he said above, the motion must be the same which is continuous and first, this treatment is divided into two parts:

First he shows which motion can be always continuous;

Secondly, he shows that such a motion is the first, (L. 19).

The first part is divided into three sections:

In the first he shows that no motion but local can be continuous;

In the second that no local motion but a circular one can be continuous, (L. 16);

In the third that a circular motion can be continuous, (L. 19).

About the first he does two things;

First he proposes what he intends;

Secondly, he proves his propositiont at 1098.

He says therefore first that since it has been shown that change of place is the first among all types of motion, we must now show which change of place is first, because there are many types of it, as was proved in Book VII,

And at the same time, according to the same method, i.e., art, i.e., according to the same technical consideration, there will be plain what we have just said and what was also previously assumed at the beginning of Book VIIII namely, that there exists a motion which is continuous and perpetual. Now the first and the continuous must be the same, as was proved above. For that reason both of them fall under the same consideration.

That no other type of motion, however, but local motion can be continuous and perpetual will be clear from what will be said.

1098. Then at (864) he proves the proposition. And about this he does two things:

First he shows that no other species of change but local can be continuous and perpetual, remaining one and the same;

Secondly, that two changes which are opposite cannot suceed one another without an interval of rest, at 1103.

About the first he does two things:

First he proves the proposition;

Secondly, he excludes some objections, at 1100.

About the first he does two things:

First he proves the proposition in motions;

Secondly, in changes, at 1099.

He proposes therefore first (864) one proposition which is true in common both for changes and motions, namely, that all changes and motions are from opposites to opposites. But local motion is in alsense excluded from this generality, as was said at the end of Book VI. For generation and ceasing-to-be, which are changes, have, for their termini, existence and non-existence; the opposite termini of alteration are contrary passions, i.e., passible qualities, such as hot and cold, black and white; and the opposite termini of growth and decrease are large and small, or perfect and imperfect in magnitude, or quantity.

But it is plain from what was said in Book V that motions toward contrary termini are contrary. Therefore, a motion to white is contrary to a motion to black. But contraries cannot be together; therefore, while something is being moved to white, it cannot at the same time be undergoing a motion to back, Hence what begins to be moved from white to black by the motion of blackening, even though it should be moved by the motion of whitening while beeoming white, it could not simultaneously be moved by the motion of blackening, But what was existing previously, if it was not always being moved by some definite motion, must be considered as having been previously resting with a rest opposite to this motion, for whatever is apt to be moved is either at rest or being moved.

Therefore, it is plain that what is being moved to a contrary was at one time resting with a rest opposite to that motion. Hence no motion to a oontrary can be continuous and perpetual.

If, therefore, to this conclusion be added what was first assumed, namely, that every motion of alteration, or growth or decrease is to a contrary, it follows that none of these motions can be continuous and perpetual.

1099. Then at (865) he proves the same thing for changes, i.e., for generation and ceasing-to-be: these, indeed, are opposed universally according to the common opposition of being and non-being, and also in the singular thing, as the generation of fire is opposed to the ceasing-to-be of fire, according to the opposition of its existence and its non-existence.

Hence, if opposite changes cannot co-exist, it will follow that no change is continuous and perpetual in the same way that it followed previously for motions, and that between two generations of the same thing, there must intervene a time in which ceasing-to-be occurred. In like manner, a time of generation interrupts instances of ceasing-to-be.

1100. Then at (866) he dismisses three objections. First of all, someone could say that since changes are opposed according to the opposition of their termini, whereas the termini of generation and ceasing-to-be are not contrary but contradictory, it seems to follow that generation and ceasing-to-be are not contrary; consequently, the same argument will not apply to them and to motions that are contrary.

To this objection he replies that it makes no difference whether changes which differ according to contradictory termini are contrary or not contrary, as long as this alone is true, that it is impossible for both to be in the same thing at the same time, For to be contrary or not contrary has no bearing on the argument given.

1101. The second objection he dismisses at (867). For someone could say that it is necessary for what is not always being moved to be previously at rest, because motion is the opposite of rest. But this does not occur in generation and ceasing-to-be, to which, properly speaking, rest is not opposed, as was said in Book V.

To this objection he responds that it makes no difference to the argument given whether there is rest in either of the contradictory termini or not, or whether change is not contrary to rest (because perhaps what does not exist cannot rest, and ceasing-to-be tends to non-existence, whence it seems that rest cannot occur in the terminus of a ceasing-io-be): but the proposition is sufficiently proved if an intermediate time exists between two generations or two instances of ceasing-to-be. For the consequence will be that neither of these changes is continuous.

After this he returns once more to the first objection and says that the reason why it makes no difference whether the changes between contradictory termini are contrary or not is that in the earlier discussions about motions likewise, it was not the question of contrariety that played a part in the proofs but the fact that the two changes could not occur at one and the same time. And this is not a peculiarity of contraries, but is common to all opposites.

1102. The-third objection he dismisses at (868). For he had said previously that motions which tend to contraries are contrary. Therefore, since motion is contrary to rest, it seems to follow that one thing has two contraries—which is impossible, as is proved in Metaphysics X.

In order to exclude this he says that there is no need to be disturbed about the fact that one thing seems to be contrary to two things, i.e., a motion contrary to rest and to the motion which is to a contrary. Rather, the only thing we ought to take is that one contrary motion is in some manner opposed both to another contrary motion and to restt to another contrary motion according to direct contrariety; but to restt more according to privative opposition. Yet this latter opposition has some contrariety, inasmuch as an opposite rest is the end and complement of a contrary motion, just as “equal and commensurable” is opposed in a way to two things, namely, to the excelling and to what is excelled, i.e., to the large and the small, to which two it is opposed rather according to privation, as is plain in Metaphysics X. And once more, what is important to grasp is that opposite motions or opposite changes do not occur at one and the same time.

1103. Then at (869) he shows that there must not only be a time between two motions or changes of the same species, and that no single change which tends to one of two opposites can be perpetual and continual, but also that it is impossible for opposite motions or changes so to follow one upon the other that there is no time between them. For it seems to be utterly at odds with generation and ceasing-to-be that when something has come to be and its generation is complete, that immediately it begin to cease to be, so that there would be no period of time in which the generated thing would be permanent. For a thing would be generated in vain, if the generated thing were not to remain in existence.

Hence from these changes of generation and ceasing-to-be, we can understand the others. For the natural is what occurs in a like way in all things, since nature always acts in the same way. Therefore, just as it seems unacceptable for something to cease to be as soon as it is generated, so, toot it seems unacceptable that a thing should start becoming black as soon as it became white, and..that a thing should begin to shrink as soon as it is grown. For in all these cases, the intention of nature would be frustrated.

Lecture 16

No change of place can be continuous and perpetual except the circular

1104. After showing that no change but local can be continuous and perpetual, the Philosopher now shows that no local change can be continuous and perpetual, unless it be a circular one. About this he does two things:

First he proves his proposition by a demonstration;

Secondly, dialectically, (L. 18).

About the first he does two things:

First he proves his proposition;

            Secondly, from the proven truth he solves some doubts, (L. 17).

About the first he does three things:

First he mentions what he chiefly intends. For he intends to prove that it is possible that there be a motion which, being one, might be continued ad infinitum, and that such a motion can be none but a circular one. This is the first thing he proves.

1105. Secondly, at (871) he shows how to proceed. And he says that whatever is moved locally is moved with either a circular motion or a straight one or in a motion that combines these two, e.g., a motion through a chord and an arc. Hence it is clear that if either of the two simple motions, namely, the circular or the rectilinear, cannot be infinitely continuous, much less their combination. Therefore one must omit the latter and attend to the simple ones.

1106. Thirdly, at (872) he shows that a rectilinear motion upon a straight and finite magnitude cannot be infinitely continuous and that consequently no rectilinear motion can be infinitely continuous unless an actually infinite magnitude is assumed—and this was proved impossible in Physics III above.

He proves his point with two arguments,, of which the following is the firstt If anything be moved ad infinitum upon a finite magnitude, it has to be done by reflexion. For it has been proved in Book VI that something will traverse a finite magnitude in finite time. When, therefore, the boundary of the finite magnitude is reached, the motion will cease, unless the mobile is returned by reflexion to the beginning of the magnitude whence the motion began. But what is reflected in a rectilinear motion is being moved with contrary motions. And this he now proves;

Contrary motions are ones whose terminal points are contrary, as was proved in Book V. But the contrarieties of place are up and down, ahead and behind, right and left. Now, whatever is reflected must be reflected according to one or other of these contrarieties. Therefore, whatever is reflected is moved with contrary motions.

But it was shown in Book V which motion is one and continuous: the one, namely, which is of one subject, in one time, and in the same category that does not differ specifically. For these three elements are considered in every motion: first, there is the time; secondly, the subject being moved, such as a man or a god, according to those who call the heavenly bodies “gods”; thirdly, there is that in which the motion occurs: in local motion it is a place; in alteration it is a passion, i.e., a passible quality; in generation and ceasing-to-be it is a form; in growth and decrease it is a magnitude.

Now it is clear that contraries differ with respect to species; hence contrary motions cannot be one and continuous, But the six things listed above are differences of place and, consequently, they must be contrary, because the differences of any genus are contrary. It remains, therefore, that it is impossible for that which moves by a reflected motion to be moved by one continuous motion.

1107. And because someone could doubt whether what is reflected is being moved with contrary motions, on the ground that there does not appear a manifest and determinate contrariety in place, such as does appear in the other genera in which motion occurs, as was said in Book V, he therefore, in order to show the same point, adds a certain sign over and above the argument above, which was based on the contrariety of termini.

And he says that the sign of this is that a motion from A to B is contrary to one from B to A, as happens in a reflex motiong because such motionst if they take place simultaneously, “arrest and stop each other,” i.e., are such that one impedes the other and stops it.

And this happens not only in reflex straight motion but in reflex circular motions. For let three points A, B and C be designated on a circle. It is evident that if something begins to be moved from A to B and later is moved from A to C, there was reflexion and those two motions block one another and one arrests the other, i.e., causes the other to stop. But if something is moved without interruption from A to B and again from B to C, there is no reflexiono But the reason why reflex motions impede one anothert both in straight and in circular motions, is that it is the nature of contraries to impede and destroy one another.

Motions, however, that are diverse but not contraryt do not impede one another, as, for example, an upward motion and a motion to the side, i.e., to the right or left, do not obstruct one another; rather something can at the same time be moved upwards and to the right.

1108. Then at (873) he gives a second argument to show that reflex motions cannot be continuous ad infinitum, and it is an argument based on the pause that must intervene. He says, therefore, that it is above all the fact that what is reflected must rest between two motions which makes it clear that it is impossible for a rectilinear motion to be infinitely continuous. And this is true not only if something is moved through a straight line but also if it is carried along according to a circle.

And lest anyone suppose that being carried along “according to a circle” is the same as being carried along “circularly,” to exclude this he adds that it is not the same to be carried along circularly according to the characteristics of a circle and to be carried along a circle, i.e., to traverse a circle. For sometimes it occurs that the motion of what is moved is according to a certain continuity, as, namely, it traverses part after part according to the order of parts of the circle, and this is “to be carried along circularly.” But sometimes it occurs that what traverses a circle has not, when it returns to the point whence the motion began, travelled in an onward direction according to the order of the parts of the circle, but has returned backwards—and this is “to be reflected.” Whether, therefore, the reflexion occurs in a straight line or a circular line, a pause must intervene.

1109. Belief in this can be based not only on sense, for it is sensibly evident, but also on an argument.

The principle of this argument is that, since three things are involved in a magnitude that is traversed, namely, a beginning, a middle, and an end, the middle is both, when compared to both. For in respect to the end, the middle is a beginning, and in respect to the beginning, it is an end. Consequently, while it is one as to subject, it is two in conception. Another principle to be taken is that what is in potency is other than what is in act.

Keeping these things in mind, it should be considered, from what has been said, that each sign, i.e., each designated point between termini of a line ever which something is being moved, is potentially a middle, but it is not one unless a division with respect to the motion takes place in such a way that at a given point the thing in motion stops and then resumes its motion at that point. Now, in this way that middle will become an actual beginning and an actual end, i.e., the beginning of the subsequent (inasmuch as the mobile resumes its motion from it) and an end of the first motion (inasmuch as the first motion was terminated there by reason of rest).

For let there be a line at whose beginning is A, at whose middle is B, and at whose end is C. Then let something be moved from A to B and stop there; then let it begin to be moved from B and be carried along to C. In this example, it is plain that B is actually the end of the prior motion and the beginning of the subsequent one.

But if something be moved continuously from A to C without any interval of rest, it is not possible to say that the mobile has “come to be,” i.e., has arrived at, or has “ceased to be,” i.e., has left, either the point A or the point B. Only this can be said, namely, that it is in A or in B at a certain “now.” (But not at a certain time, unless we should perchance say that a thing is somewhere in time because it is there in some “now” of time. And so what is being moved continuously from A to C in some time will be in B at an instant which is a divider of time. In this way, it will be said to be in B in that entire time, in the sense that we speak of something being moved in a day because it is in motion in a part of that day.)

And because it seemed doubtful that what is in motion does not arrive at and leave each determinate point of a magnitude which is traversed by a continuous motion, he shows this. He says, then, that if someone grants that the mobile arrives at and then leaves some assigned point in the magnitude, it follows that it is at rest there. For it is impossible that in the same instant a mobile arrive at and leave this point B, because to arrive somewhere and to leave there are contraries, which cannot exist in the same instant.

Therefore, it must be at other and other “now’s” that the mobile arrives at and leaves a given point of the magnitude. But between any two “now’s” is an intermediate time. Therefore, it will follow that the mobile, A, rests in B. For anything that is somewhere for a time is there before and after. And the same must be said for all the other “signs” or points, because the same reasoning applies to all.

Hence it is plain that what is being carried along continuously over a magnitude is at no time arriving at, or departing from, any intermediate point. For when it is said that the mobile is “at” this point, or is “coming to be” in it or is “approaching” it, all these expressions imply that that point is a terminus of the motion. And when it is said that it “leaves” or “departs,” a beginning of motion is implied. But a designated point of a magnitude is not actually a middle or a beginning or an end, because the motion neither begins nor ends there; rather, it is these potentially only, because the motion could begin or end there. Hence the mobile neither arrives at nor leaves an intermediate point, but it is said to be there absolutely in a “now.” For the existence of a mobile at some point of the magnitude is compared to the whole motion as the “now” is compared to time.

1110. But when the mobile A uses B as an actual middle, beginning and end, then it must be at a stop there, because by moving and stopping it makes that one point to be two, namely, a beginning and an end, as happens also in understanding. For we can simultaneously understand one point as it is one in subject, but if we consider it separately as a beginning and separately as an end, this will not take place simultaneously. So too, when that which is being moved uses a point as one, it will be there only in the one “now.” But if it uses it as two, namely, as a beginning and end in act, it will be there for two “now’s,” and, consequently, for a middle time between them. And so it will be at rest. Therefore, it is plain that what is being moved continuously from A to C was neither present nor away from the intermediate B, i.e., it neither arrived at it nor departed from it; but it was away from and left, the first point A, as the actual beginning; and it was present in, or arrived at, the final point C, because there the motion is finished, and the mobile rests.

It should be remarked that in the foregoing, “A” was sometimes taken as the mobile, and sometimes as the beginning of the magnitude.

1111. From all these things it is clear that a reflected motion, whether it occurs along a circular or a straight magnitude, cannot be continuous, but a rest intervenes, because the same point is actually the end of the first motion and beginning of the reflexed one. But in a circular motion the mobile does not use any point as an actual beginning and end, but each point is used as an intermediate. Therefore, a circular motion can be continuous, but a reflexed one cannot.

Lecture 17

Certain doubts resolved.

1112. After showing that a reflex motion is neither continuous nor one, the Philosopher now settles some doubts on the basis of what has gone before. And it is divided into three parts according to the three doubts he resolves from the foregoing.

The second part begins at 1115;

The third, at 1119.

About the first he does two things:

First he sets forth the doubt;

Secondly, he solves it, at 1114.

1113. He says therefore first (874) that what was said in order to prove that a reflex motion is not continuous may be applied to solving a certain doubt, which is this: Assume two equal magnitudes, one called E, and the other Z. Let A and D be two equally swift mobiles, such that A is continuously moved from the beginning of the magnitude (E) to C, and D (along Z) to I, And let us assume that in the magnitude E there is an intermediate point B, which is as far from C as a like point Z on Z is distant from I. Let us further assume that at the same time that A in its continuous motion is approaching B, D in its continuous motion is receding from Z and going to I. Now, since these motions are regular and equally swift, it will follow that D will arrive at I before A arrives at C, because the one which starts first will first arrive to the end of an equal distance. But D left Z before A left B, because D left Z when A was arriving at B. Therefore, according to this, A did not simultaneously arrive at B and leave B, and it consequently follows that it departed after it arrived, because if it arrives and departs at the same time, it will not have begun to move later. And so it is necessary that A, while being carried along, rest in B. Therefore a continuous motion will be composed of periods of rest, as Zeno claimed in Book VI.

1114. Then at (875) he resolves this doubt in the light of the foregoing. For the objection supposed that A in its continuous motion arrives at a point B in the magnitude and that at the same time that A arrived at B, D left the point Z—which is against what was had above. For it was said above that when something is being moved continuously, it can neither arrive at, nor depart from, any intermediate point. Therefore, what the objection assumes must not be assumed, i.e., that when A was at, i.e., approached B, D was departing from Z, because if it be granted that A arrived at B, then for the same reason it should be granted that it left B, and that this did not occur simultaneously, but in two instants, so that in the intermediate time between the two instants it was at rest.

But as was said previously, when something was being continuously moved, it was neither departing fromt nor approaching, a given point, but was simply there—and this not for a time, because then it would have been resting, but in a division of time, i.e., in some “now,” which divides time.

Therefore, what the objection assumed, namely, that A arrived at and that D left some intermediate point is impossible to state in a continuous motion. But in a reflex motion this must be stated. For if a mobile I is moved to the point D and is then rebounded, it is plain that the mobile uses the ultimate, which is D, as a beginning and as an end, i.e., the point is used for two things, hence it had to be at rest there.

Nor can it be said that it simultaneously arrived at and left D, because then it would have been, and not have been, there in the same instant. For whatever has been moved exists in the terminus to which it was being moved, and whatever begins to be moved is not in the terminus from which it begins to be moved. But when we use the expression “to be at” or “to approach,” we mean that a motion is being terminated at that point, and when we say “to be away from” or “to depart,” we mean that the motion is beginning. Hence, it is necessary that whatever arrives at, or is at, a point, be in it, while what is leaving it or is departing from it, be not in it. Since, therefore, it is impossible to be and not to be in a given point at the same time, it is consequently impossible to be at once at and away from the same, as the objection more than once assumed.

It should be noted that here he uses different letters from those used above. Here I is the mobile and D the terminus; above, it was the opposite.

But the solution given for continuous motion is not to be used with respect to a reflex motion. For it cannot be said that the mobile I is in the terminus D, from which it began to be reflected, only in the division of time, i.e., only during the “now,” and that the mobile neither arrived at, nor departed from, the same, as was said with respect to a continuous motion. For in a reflex motion an end must be reached that is an actual end, and not merely a potential one, as the intermediate point in a continuous motion was only potentially a beginning and an end. Therefore, that which is an intermediate point of a continuous motion is only potentially a beginning and an end; but the point from which a reflex motion begins is actually a beginning and end. For example, it is the end of the downward motion of a stone, and the beginning of its upward motion, in the case of a stone falling to earth and bouncing upward.

Therefore, just as in the magnitude in which a motion is occuring, a point from which the motion is reflexed is both an actual beginning and end, so also in the motions themselves, there is actually an end of one and a beginning of the other. And this would not be so, unless an interval of rest occurred. Therefore, it is necessary that what is reflected in a straight line be at rest. And so it follows that on a straight magnitude there cannot be a continuous and perpetual motion, because no straight magnitude is infinite. And so there could not be perpetual continuous rectilinear motion, unless reflexion is involved.

1115. Then at (876) he presents the second doubt. About this he does three things:

First he mentions the doubt;

Secondly, he rejects a solution given in Book VI, at 1116;

Thirdly, he gives the true solution, at 1118.

He says therefore first (876) that by the same method, using the things shown above, one can block those who give the objection of Zeno and wish to argue in the following manner: Whatever is being moved must first cross what is intermediate before arriving at the end; but between any two termini there are infinite intermediates on account of a magnitude’s infinite divisibility; and so it is impossible to traverse the intermediates, because infinites cannot be traversed. Therefore, nothing can by motion arrive at any terminus.

Again, the same difficulty can be presented under another form, as some do in fact propose it: Whatever traverses a whole must previously traverse the half; and since the half is again divided in half, half of the half must be first traversed. And thus, whatever is being moved counts off every half as it reaches it. But such halves can be multiplied ad infinitum. Therefore, it follows that if anything traverses an entire magnitude, it has counted off an infinite number, which is plainly impossible.

1116. Then at (877) he rejects the solution he had presented above in Book VI.

First he cites it;

Secondly, he sets it aside, at 1117.

He says therefore first that the foregoing objection was answered in Book VI, when motion in general was being discussed, on the ground that just as a magnitude is divided infinitely, so also is time. Consequently, time possesses infinities in itself in the same way as a magnitude. And so it is not unfitting if the infinites in a magnitude be traversed in the infinites which are in time. For it is not inconsistent for an infinite magnitude to be traversed in an infinite time. But, as shown in Book VI, the infinite is found in magnitude and in time in the same way.

1117. Then at (878) he sets aside this solution, And he says that this solution is sufficient to answer the questioner who asked whether it was possible in a finite time to traverse and count off infinites. This question was retorted by saying that a finite time possesses infinities in which the magnitudinal infinites can be traversed. But that solution does not reach the truth of the matter, because if someone should omit to ask about the magnitude and whether it is possible to traverse infinities in finite time, but asked rather this same question about time, namely, whether the infinites which are in time can be traversed—since time is divided ad infinitum—then the previous solution would not answer this question. Consequently, another solution must be sought.

1118. Then at (879) he gives the true solution in the light of his premises above. And he says that the true solution of the present doubt requires us to repeat what was premised in the immediately foregoing arguments, namely, that if someone divides a continuum into two halves, he then uses the one point at which the continuum is divided as two, because.he is making it serve both as the beginning of one part and as the end of the other. He does this by numbering, and by dividing into two halves.

But when a continuum has been divided in this manner, it is no longer a continuum, whether it be a magnitude, such as a line, that is divided, or a motion, for a motion cannot be continuous unless it is the motion of something continuous, namely, as to subjects and time and magnitude traversed. Therefore, the divided in effect counts and by counting breaks the continuity.

But so long as continuity endures in a continuum, there is an infinity of intermediates not in act but in potency, for if someone should make some middle actual, it will be due to division, as has been said, insofar as it is taken as the beginning of one and the end of the other. In that case, the continuum will not remain but will “stop,” i.e., the intermediates that,are now in act will not be infinite but one will come to a stop in them. This shows up especially in the case of one who wishes to count the intermediates, because he will have to count one as two, inasmuch as it is the end of one half and the beginning of the other. And this, I say, takes place when the whole continuum is not counted as one, but two halves are counted in it, For if the whole continuum is taken as one, it has already been stated that then an intermediate point will not be taken as an actual end and beginning but potentially only.

With these facts in mind, the answer to be given to one who asks whether infinites in time or in a magnitude may be traversed is that in one sense it does happen, and in another it does not happen. For when one has infinites in act, it is impossible that they be traversed, but when they are potentially infinite, they can be traversed. And so, since the intermediates in a continuum are infinite only in potency, it does happen that infinites are traversed, because what is in continuous motion traverses per accidens what is infinite, namely, what is infinite in potency, But per se it has traversed a finite line which happens to have an infinitude of intermediates in potency. The line itself, however, in its nature and definition, is distinct from those infinite intermediates. For a line is not a composite of points, but points may be designated in a line insofar as it is divided.

1119. Then at (880) he resolves the third doubt. About this he does three things:

First he mentions the doubt and its solution;

Secondly, he explains each with an example, at 1120;

Thirdly, he draws a corollary from the foregoing, at 1122.

First therefore (880) he states the doubt that is wont to arise with respect to generation and ceasing-to-be. For what is generated ceases not to be, and begins to be. But the time assigned for the existence of a thing that is generated or has ceased to be, must be different from the one assigned to its non-existence. For example, if from air fire is generated, then in the whole time AB there was not fire but air, but in the entire time BC there is fire. Since, therefore, sign B of the whole time ABC is common to both times, it seems that in that common instant the fire both exists and does not exist.

The Philosopher therefore solves this doubtj saying that it is plain that, unless someone holds that the point of time which divides a prior time from a later one, “always belongs to the later,” i,e., that in that instant the thing is in the state which it subsequently has, it follows that the same is simultaneously being and non-beingt and that when something has been produced, it is non-being. For it is then produced when generation terminates, namely, in that “now” which divides the prior time and the later. If, therefore, in the entire prior time it was non-being, in that “now” also when it has already been generated, it is also non-being, since this “now” is the end of the prior time.

How these impossibilities do not follow he explains by adding that one and the came sign as to number, i.e., the “now” is common to both times, namely, to the prior and to the subsequent. But although it be one as to subject, it is not one in conception but two, for it is the end of the prior time and beginning of the subsequent. But if we take the “now” as it is a thing, i.e., if it be taken as it is one in reality, it always belongs with the subsequent state (passion).

Or in other words: Although the “now” is the end of the prior time and the beginning of the subsequent, and is thus common to both, yet accordingly as it belongs to the thing, i.e., insofar as it is compared to the thing which is being moved, it always belongs to the subsequent passion, because the thing being moved is in that instant being subject to the passion of the subsequent time.

1120. Having given the objection and its solution, he explains both with examples. And first the objection, at (881). He says therefore: Let ACB be the time, and D the thing that is being moved, so that, in time A, D is white, and in B it is non-white. It seems therefore to follow that in C it is white and non-white. How this follows he now explains: If it is white in the entire time A, then at any time taken in A it is white; and likewise, if it is non-white in the entire time B, it follows that at any time taken in B it is non-white. Since, therefore, C is taken in both—being both the end of the former and the beginning of the latter—it seems to follow that in C it is white and non-white.

1121. Secondly, at (882) he illustrates the solution given above. And he says that we must not concede that it is white at any point of time in A, for the ultimate “now,” which is C, must be excepted, for it is already “later,” i.e., it is the ultimate terminus of the change. For example, if the white was coming to be or ceasing to be in the entire time A, in C it is not ceasing to be or becoming white, but already become or ceased to be. But what has already been made, exists, and what has already ceased to be, does not exist. Hence it is clear that in C it is first true to say this is white, if the generation of white has terminated there, or this is not white, if the ceasing-to-be of white has terminated there. Or, if that is not stated, the above-mentioned incompatibilities follow, namely, that when something has been already generated, it is still non-existent, and when it has ceased to be it is still a being. Or, it also follows that something is at once white and non-white, and, universally, being and non-being.

1122. Then at (883) he draws a certain corollary from the foregoing, namely, that time is not divided into indivisible times, because, should one suppose this, it would be impossible to solve the doubt previously mentioned.

He says therefore that it is necessary that whatever is first a non-being, and later is a being, come to be at some time; and again, it is necessary that when something is coming to be, it is not existing. Now, if these two aeoumptions are true, it is impossible for time to be divided into times that are indivisible. For let a time be divided into indivisible times. Then let A be the first indivisible time, and B the second and subsequent time. Now D, which was previously not white and later is white, was becoming white in time A, and at that time was not white. But one must suppose that it has been made white in some indivisible time which is “had,”, i.e., subsequent, to A, namely, in time B in which it is now white. Now, if it was becoming white in A, it follows that in A it was not white; in B, however, it is white. Since, therefore, between non-existence and existence an instance of generation occurs, because nothing passes from non-existence to existence but by generation, it follows that an act of generation occurs between time A and time B. Therefore, there will be between A and B an intermediate time in which it was becoming white (since in time B, D is already generated).

And similarly, since in that intermediate indivisible time it is becoming white, it is not white: hence for the same reason it will be necessary to posit still another intermediate time and so on ad infinitum, because we cannot assume that it is becoming white and is white in the same period of time.

But the argument is not the same, if one states that the times are not divided into indivisible times. For according to this, we will say that it is one and the same time in which it was coming to be, and was produced. But it was coming to be, and was non-being, in the entire preceding time, and it was produced and a being in the final “now” of the time, which instant is not related to the preceding time as being “had” or subsequent, but as its terminus. But if one assumes indivisible times, they are necessarily (discrete and) consecutive.

But it is plain according to the foregoing that, if we do not assume indivisible times, then if something comes to be white in the entire time A, the time in which it was coming to be and was completely made, is no greater than the time in which it was coming to be alone. For it is coming to be in the entire time, but in the ultimate terminus of that time it was completely made. But time plus its terminus is not something greater than the time by itself, any more than a point adds any magnitude to a line. But if indivisible times are assumed, it is clear from the foregoing that there must be more time in coming to be and completely being, than in coming to be alone.

Finally, in summary, he concludes to his main intention, saying that the foregoing arguments, and ones like them, are the appropriate ones to convince us that a reflex motion is not continuous.

Lecture 18

Dialectical reasons to show reflex motion is not continuous

1123. After proving with proper reasons that reflex motion is not continuous, the Philosopher now proves the same with common and logical reasons. About this he does two things:

First he expresses his intention;

Secondly, he proves his proposition, at 1124.

He says therefore first that if someone wishes to prove “reasonably,” i.e., logically, the proposition in question, it will be seen from the reasons to be given that the same thing follows, namely, that reflex motion is not continuous.

1124. Then at (885) he proves the proposition.

First, for reflex local motion only;

Secondly, in common for all motions, at 1126.

The first argument is this: Everything in continuous motion has been, from the very beginning of its motion, in the process of being carried, as toward an end, to that at which it arrives according to change of place, unless there is some obstacle (because an obstacle could deflect it in another direction). He exemplifies this by saying that if something in local motion has arrived at B, it was being moved toward B not only when it was near B but at soon as it began to be moved. For there is no reason why it should be tending more toward B now than before. And the same is true in other motions.

But if a reflex motion should be continuous, it will be true to say that what is in motion from A to C, and is then reflected back to A, is in a continuous motion. Therefore, in the very first part of the motion from A to C it was being moved to its final terminus in the part A; in this way, while it is being moved from A, it is being moved toward A. It follows, therefore, that it is being simultaneously moved with contrary motions, because in the sphere of rectilinear motions, to be moved from a thing and to be moved toward the same are contrary. But in circular motions this is not contrary. Now it is impossible for something to be moved simultaneously with contrary motions. Therefore, it is impossible for a reflex motion to be continuous.

1125. Then at (886) from the same middle he leads to another impossibility. For if something, while it is being moved from A, is being moved toward A, it cannot be moved toward A except from a counter-point C, in which the mobile was not yet present when it began to be moved from A. It follows, then, that something is being moved from a terminus at which it is not present—which is impossible. For it cannot leave a place in which it is not. Thus, it is impossible for a reflex motion to be continuous. And if this is impossible, then it is necessary that at the point of reflexion the mobile be at rest, i.e., in C. From which it is plain that it is not one motion, because a motion interrupted by rest is not one.

1126. Then at (887) he proves the same thing in a more universal way for every genus of motion, with three arguments. The first of them is this: Whatever is in motion is being moved with respect to one of the species of motion listed previously. In like manner, whatever is at. rest is so with respect to a rest that is opposite to one of the aforesaid species of motion. For it was shown above in Book V that no motions other than the ones listed are possible.

Let us, therefore, take a motion that is distinct from other motions, in the sense of being specifically distinct from others, as whitening is distinct from blackening—but not distinct in the way that one part of a motion is distinct from other parts of the same motion, as one part of the motion of whitening is distinct from other parts of the same whitening. Taking, therefore, one motion in the way described, it is true to say that whatever is not forever being moved with this motion, was before of necessity at rest with an opposite rest, as whatever is not being forever whitened was at some time at rest with a rest opposite to whitening. But this proposition would not be true if some definite part of the motion should be taken, for it is not necessary that what was not forever being moved in this part of the whitening was previously at rest with an opposite rest, because before the thing was becoming white in some other part of the whitening. And because of this he states significantly: “...not some particular part of the whole.”

This proposition he now proves: When one of two things that are in privative opposition is not in its recipient, the other must be. But rest is opposed to motion privatively. Therefore, if a mobile was existing at a time when motion was not in it, it follows of necessity that rest would then have been in it.

Accordingly, since this proposition has been provedg he takes the minor from the argument already presented above and says that, if rectilinear motions from A to C and from C to A are contrary, and contrary motions cannot coexist, it is plain that when something was being moved from A to C, it was not at the same time being moved from C to A. Consequently, it was not forever being moved with respect to the motion from C to A.

Hence, according to the previous proposition, it is necessary that the mobile first rest with an opposite rest. For it has been shown in Book V that to a motion from C is opposed rest in C. Therefore, it was at rest in C, Therefore the reflex motion was not one and continuous, since it was interrupted by the interposition of rest.

1127. He presents the second argument at (888), and it is this: Non-white ceases to be and white comes to be simultaneously; similarly, white ceases to be and non-white comes to be simultaneously. But if reflex motion in every genus is continuoust it will follow that an alteration is terminated at whiteness, and begins to depart from whiteness, in such a way as to form a continuous motion, and that it does not rest there for any time; for if rest should intervene, the alteration would not be continuous. But, as has been said, when the white comes to be, the non-white ceases to be, and when departure from white occurs, non-white comes to be. Therefore, it will follow that non-white is ceasing to be and coming to be at the same timeg for these three things are present at the same time, namely, the coming-to-be of white, the ceasing-to-be of non-white and the coming-to-be of non-white—that is, if the reflex motion is continuous without any interval of rest. This, however, is plainly impossible, namely, that non-white should be coming to be, and ceasing to be, at the same time. Therefore, a reflex motion cannot be continuous.

Now, this argument is seen to refer to generation and ceasing-to-be. For this reason he says that this argument is more proper than the previous ones, because it is more apparent in contradictories that they cannot be true at the same time. And yet, what is said in generation and ceasing-to-be applies to all motions, since in every motion there is a kind of generation and ceasing-to-be. For just as in the case of alteration, white is generated, and non-white ceases to be, so too in every other motion.

1128. At (889) he gives the third argument, which is this: As was had in Book V, it is not necessary, if the time is continuous, that a motion be on that account continuous. For motions of diverse kinds, even though they succeed one another in continuous time, are not on that account continuous, but are, rather, consequent upon one another, for continua must have one common terminus. But there cannot be one common terminus in things that are contrary and specifically different, such as whiteness and blackness. Since, therefore, a motion from A to C is contrary to one from C to A in any genus of motion, as was shown in Book Vt it is impossible that those two motions be continuous one to the other—even though the time be continuous—with no intervening rest. It remains, therefore, that a reflex motion can in no way be continuous.

It should be noted that the foregoing arguments are called “logical” because they proceed from certain common things, namely, from the property of contraries.

Lecture 19

Proper reasons why circular motion can be continuous, and why it is the first

1129. After showing that no local motion but a circular one can be continuous, the Philosopher now shows that a circular motion can be continuous and first.

First of all he shows this with proper arguments;

Secondly, with logical and common arguments, (L. 20).

About the first he does two things:

First he shows that a circular motion is continuous;

Secondly, that it is the first, at 1134.

About the first he does two things:

First he gives two arguments to prove that circular motion can be continuous;

Secondly, from the same arguments he concludes that no other motion can be continuous, at 1132.

1130. But that a circular motion can be one continuous motion he proves at (890) with his first argument: That from which nothing impossible follows is said to be possible. But nothing impossible follows from the statement that a circular motion is forever continuous.

This is plain from the fact that, in a circular motion, that which is being moved from somewhere, e.g., from A, is at the same time being moved to the same point “according to the same position,” i.e., according to the same progress of the mobile, the same order of parts having been maintained. This, however, does not happen in a reflex motion, because when something turns back, it is disposed according to a contrary order of parts in its motion. For either that part of the mobile to the fore in the first motion must be at the rear in the reflexion, or that part which was facing one difference of place, for example, the right or above, in reflexion must face a contrary direction. But in a circular motion the same position is maintained, while a thing is being moved toward the point from which it departed. Consequentlyt it could be said that even from the very beginning of its motion, while it was departing from A, it was being moved toward that which it would finally reach, namely, the very same A.

Nor does this lead to the impossibility of being moved with contrary or opposite motions at one and the same time, as followed in rectilinear motion. For not every motion to some terminal is contrary or opposite to one from the same terminal, but such contrariety is present in the straight line, according to which, contrariety in place is gauged. For contrariety between two termini is not forthcoming according to a circular line, whatever part of the circumference be taken, but according to the diameter. Contraries, indeed, are things most far apart; but the greatest distance between two termini is not measured according to a circular line, but according to a straight line. For between two points an infinit,e number of curves can be described but only one straight line, But the measure in any genus is that which is one.

Consequently, it is plain that if one takes a circle, and it be divided in half, and AB be its diameter, a motion through the diameter from A to B is contrary to a motion over the same diameter from B to A. But a motion over the semicircle from A to B is not contrary to a motion from B to A over the other semicircle. But it was contrariety that prevented a reflex motion from being continuous, as appears from the reasons given above. Nothing, therefore, once contrariety has been removed, prevents a circular motion from being continuous and also not failing at any time.

And the reason for this is that a circular motion is completed by the fact that it is from the same to the same, and thus its continuity is not impaired by this. But a rectilinear motion is completed by its being from one thing to another; hence, if it returns from that other to the same from which it began, it will be not one continuous motion, but two.

1131. Then at (891) he gives the second argument, saying that a circular motion does not exist in identical things, but a rectilinear motion is very often in identical things.

Now what this means is that, if something is moved from A to B across a diameter, and again from B to A across the same diameter, it has to return across the same middles through which it previously travelled, Consequently, it is being carried over the same middle a number of times. But if something is moved through a semicircle from A to B, and again from B to A through the other semicircle—and this is motion in the circular manner—it is clear that it does not return to the same point over the same middles.

Now, it is of the nature of opposites that they be considered with relation to the same thing. And thus it is clear that to be moved from the same to the same with a circular motion is without opposition, but to be moved from the same to the same with a reflex motion is with opposition.

In this way it is plain that a circular motion which does not return to the same over the same middles, but always goes over something other, can be one and continuous, because it does not have opposition. But that motion, namely, the reflex motion, which, in returning to the same, traverses more than once the same middles, cannot be forever continuous, because that would require something being moved with contrary motions at one and the same time, as was proved above.

And from the same argument it can be concluded that a motion confined to a semicircle, or to any portion of a circle, cannot be continuous in perpetuity, because such motions require repeated traversing of the same middles and involve being moved with contrary motions, as though a return to the beginning should be made. The reason is because the end is not joined to the beginning when you are dealing with a straight line, or a semicircle, or an arc of a circle; rather the beginning and end are apart. It is only in a circle that the end is joined to the beginning.

And for this reason only a circular motion is a perfect motion, since a thing is perfect from attaining its principle.

1132. Then at (892) he proves from the same argument that in no other genus of motion can there be continuous motion.

First he proves the proposition;

Secondly, he draws a corollary from what was said, at 1133.

He says therefore first (892) that also from this distinction between circular motion and other local motions, it is plain that neither in the other genera of motion can there be any infinitely continuous motions, because in all the other genera of motion if anything is to be moved from the same to the same, it follows that the same will be repeatedly traversed. For example, in alteration the intermediate qualities must be passed through—for the passage from hot to cold is through tepid, and if a return is to be made from cold to hot, tepid must be traversed again. The same is apparent in a motion according to quantity—for if that which is moved from large to small, should return again to large, the intermediate quantity must be traversed twice. Generation and corruption present a similar situation—for if air comes to be from fire, and then again fire from air, the intermediate dispositions must be traversed twice (for a middle may be placed in generation and ceasing-to-be, insofar as taken along with the dispositional changes).

And because the intermediates are traversed in different ways in changes that are diverse, he adds that it makes no difference whether many or few intermediates are introduced through which something is moved from one extreme to the other, or whether the intermediate is taken in a positive sense, as pallid between white and black, or in a remotive sense, as, between good and evil, that which is neither good nor evil-for, be they what they may, it always happens that the same are traversed a number of times.

1133. Then at (893) he concludes from the foregoing that the early natural philosophers did not phrase the matter well when they said that all sensible things are forever in motion, because that would necessitate their being moved with respect to one of the aforesaid motions, concerning which we have shown that they cannot be forever continuous; and especially because they said that the ever-continuous motion is alteration.

For they assert that all things are always perishing and ceasing to be, and yet they say that generation and ceasing-to-be are nothing more than alteration, and so in saying that all things are forever ceasing to be, they are saying that all things are forever being altered.

But it was proved in the argument given above that nothing can be moved forever except by a circular motion. Thus it remains that neither according to alteration, nor growth, can all things be forever in motion, as they said.

Finally, he concludes by way of summary to the chief proposition, namely, that no change can be infinite and continuous except a circular one.

1134. Then at (894) he proves with two arguments that circular motion is the first of motions. The first argument is this: Every local motion, as stated above, is either circular, or straight, or a combination of the two. But circular and straight are prior to the combination. which is composed of them. But between these two, the circular isprior to the straight, for the circular is simpler and more perfect than the straight. And this he proves as follows: Straight motion cannot go on infinitely. For this would occur in two ways: First in such a way that the magnitude traversed by the straight motion would be infinite—which is impossible. But even if there were some infinite magnitude, nothing would be moved to infinity. For what is impossible to be, never comes to be or is generated; but it is impossible to traverse the infinite; therefore, nothing is moved toward the end of traversing the infinite. Therefore, there cannot be an infinite straight motion over an infinite magnitude. In a second way, an infinite straight motion can be understood as being a reflex motion over a finite magnitude. But a reflex motion is not one, as was proved above, but is a composition of two motions.

But if a reflexion does not occur upon a finite straight line, the motion will be imperfect and destroyed: imperfect, because further addition can be made to it; destroyed, because when the terminus of the magnitude is reached, the motion will cease.

From all this it is clear that a circular motion which is not composed of two, and which is not destroyed when it comes to a terminus (for its beginning and terminus are identical), is simpler and more perfect than a straight motion. Now the perfect is prior to the imperfect, and likewise the imperishable is prior to the perishable, in nature and notion and time, as was shown above when it was proved that local change is prior to other motions. Therefore, it is necessary that circular motion be prior to straight.

1135. Then at (895) he gives the second argumentt which is this; A motion which can be perpetual is prior to one that cannot be perpetual, because the perpetual is prior to the non-perpetual, both in time and in nature. But a circular motion and no other can be perpetual, for the others must be followed by rest, and where rest intervenes, motion is destroyed. What is left, therefore, is that circular motion is prior to all the other motions. (The premisses of this argument are plain from what has been said previously.)

Lecture 20

Dialectical reasons why circular motion is continuous and first.

Confirmation from the ancients

1136. After proving with proper reasons that a circular motion is continuous and first, the Philosopher now proves the same with certain logical and common reasons. And he gives three arguments.

With respect to the first (896) he says that it is reasonable that a circular motion but not a straight one be one and forever continuous. For in a straight motion there are determined a beginning, middle, and end, and all three of these can be designated in a straight line, Therefore in a straight line there exist that whence the motion begins, and where it ends, since all motion rests at its termini, namely, the terminus from which or to which (he having distinguished these two states of rest in Book V). But in a circular line the termini are not distinct, for there is no reason why in a circle some designated point should be a terminus more than another, since each and every one alike is a beginning and an intermediate and an end. Consequently, the things which are moved circularly are in a sense always in the beginning and in the endt insofar, namely, as any point at all in a circle may be taken as a beginning or end, while in another sense, they are never in the beginning or end, inasmuch as no point in the circle is a beginning or end in act.

Hence it follows that a sphere is in one sense in motion and in another sense at rest, because, as was said in Book VI, while the sphere is being moved it always keeps the same place as to subject, and in this respect it is at rest; but yet the place is always other and other in conception, and in this respect it is being moved.

Now, the reason why a beginning, intermediate and end are not distinguished in a circular line is that these three belong to the center, from which, as from a beginning, lines proceed to the circumference and at which lines drawn from the circumference end. Moreover, it is the middle of the entire magnitude by virtue of its equidistance to all the points of the circumference.

And therefore, since the beginning and end of a circular magnitude are outside its circularity—for they are in the center which is never reached by a thing moving circularly—no place can be assigned at which a thing in circular motion should be at rest, because anything in circular motion is always carried about the middle but not to what is ultimate, because it is not carried to the middle, which is the beginning and the ultimate.

On this account, a whole that is being moved in a spherical manner is in one sense always at rest and in another in continuous motion, as has been said.

From all this the following argument may be extracted: Every motion that is never in its beginning and end is continuous. But a circular motion is of this kind. Therefore, etc, And with this same middle term, it is proved that a straight motion cannot be continuous.

1137. Then at (897) he gives the second argument, saying that these two follow one another conversely, namely, that a circular motion is the measure of all motions and that it is the first of all motions—for all things are measured by what is first in their genus, as is proved in Metaphysics X. Accordingly, this is a convertible proposition: Whatever is a measure is the first in its genus; whatever is first is a measure. But circular motion is the measure of all other motions, as is clear from what was said at the end of Book IV. Therefore, circular motion is the first of motions. On the other hand, if one suppose that a circular motion is the first of motions on account of the arguments given above, it will be concluded that it is the measure of the other motions.

1138. The third argument he gives at (898), saying that only a circular motion can be regular, since things in motion in a straight line are being carried along in an irregular manner from beginning to end.

For, as was said in Book V, a motion is irregular which is not equally swift throughout, and this must occur in every straight motion, since in natural motions the further things in motion are distant from the first rest, from which the motion started, the swifter they are moved; and in a violent motion, the farther they are distant from the ultimate rest, at which the motion terminates, the swifter they travel. For every natural motion is more intense near the end, but a violent motion at the beginning.

But this has no place in a circular motion in place, because in a circle the beginning and end do not exist somewhere in the circling which occurs along the circumference, but outside it, i,e., in the center, as was explained. Hence, there is no reason why a circular motion should be intensified or weakened on account of a nearness to its beginning or end, since it is always equally approaching the center, which is the beginning and ends

Now, it is plain from what was said in Book V that a regular motion is more one motion than an irregular one. Consequently, a circular motion is naturally prior to a straight motion. For the more a thing is one, the more it is by nature prior.

1139. Then at (899) he shows through the opinions of the early philosophers that local motion is the first of motions. And he says that the statements of all the ancient philosophers who discussed motion attest to this truth, for they declare that the principles of things move with local motion.

He refers first to the opinion of Empedocles, who posited friendship and strife as the first moving principles, the former gathering and the latter separating—and gathering and separating are local motions.

Secondly, he shows the same thing through the opinion of Anaxagoras, who posited Intellect as the first moving cause, whose work, according to him, is to separate what is commingled.

Thirdly, he shows the same thing through the opinion of Democritus, who did not posit a moving cause but said that all things are moved on account of the nature of the void. But a motion that is due to the void is a local motion or one similar to local motion, for void and place differ only in conception, as was said in Book IV. And so, by posi ting that things are first moved on account of the void, they posit local motion as naturally first and none of the other motions, but they believe that the other motions follow upon local motion. For those who follow Democritus declare that being increased and corrupted and altered occur by a certain assembling and separating of indivisible bodies.

Fourthly, he shows the same thing through the opinions of the ancient philosophers of nature who posited only one cause, a material cause, namely, water, or air, or fire, or some intermediate. For from that one material cause they explain the generation and ceasing-to-be of things through condensation and rarefaction, which are completed by a kind of assembling and separation.

Fifthly, he shows the same through the opinion of Plato who posited soul as the first cause of motion. For Plato posited that that which moves itself, which is the soul, is the principle of all things that are moved. But self-movement belongs to animals and all animate things, according to autokinesis with respect to place, i.e., per se local transmutation.

Sixthly, he shows the same thing through what is commonly and popularly held, For we only say that to be moved in the proper sense which is moved with respect to place. Whereas, if something is at rest in place, but is moved with the motion of growth or decrease or alteration, it is said to be moved in a certain sense but not absolutely.

1140. Then at (900) he summarizes what he had said, namely, that motion always has been and always will be, and that there is some first principle of perpetual motions and what the first motion is, and which motion happens to be perpetual, and that the first mover is immobile. For all these things have been set forth in what has preceded.

Lecture 21

Limitations of a finite mover

114l. After describing the condition of the first motion, the Philosopher here describes the condition of the first mover. And it is divided into two parts:

First he mentions his intention;

Secondly, he carries out his proposal, at 1142.

He says first (901), then, that since it was said above that the first mover is immobile, now we must assert that the first mover is indivisible and has no magnitude, as being wholly incorporeal. But before we show this, certain things necessary for this proof must be settled in advance.

1142. Then at (902) he carries out his proposal:

First he premises things required for proving the main proposition; Secondly, he proves the main proposition, at the end of L. 23.

About the first he does three things:

First he shows that an infinite motion supposes an infinite power;

Secondly, that an infinite power cannot exist in a magnitude, at 1146;

Thirdly, that the first mover must be one which causes a continuous and undying motion, (L. 22).

He says therefore first (902) that among the things to be established before the main proposition, one is that it is impossible for anything of finite power to cause motion for an infinite time. This he now proves.

There are three things in every motion: one of which is what is moved, another is the mover, and the third is the time in which the motion occurs.

But all three must be infinite, or all three finite, or some finite and some infinite, i.e., either two only or one.

Suppose, therefore, that A is the mover, B the mobile, and C the infinite time. Then let D, a part of At move E, a part of B. Under these conditions, it could be concluded that D moves E in a time not equal to time C (in which A moved B) but in less time.

For it has been proved in Book VI that the entire mobile requires more time to pass a certain point than it takes for a part of it. Therefore, since the time C is infinite, it follows that the time in which D meves E will not be infinite but finite. So let that time be Z, so that just as A moves B in the infinite time C, D moves E in the finite time Z. But since D is part of A, then if we add to D by subtracting from A, the A will eventually be entirely taken away or used up, since it is finite, and every finite is used up by subtraction, if the same quantity is continually taken away, as said in Book III.

And likewise, B will be used up, if continual subtractions are made from it and added to E, because B is also finite. But no matter how much is taken from the time C—even if the same amount is continually taken away—all of C will not be used up, because it is infinite.

From this he concludes that the entire A moves the entire B in a finite time, which is part of C. And this does indeed follow from the premisses, because additions are made to the time of the motion in the same ratio as they are made to the mobile and to the mover, Since, therefore, by subtracting from the entire mobile and mover and by adding to their parts, the whole mobile the whole mover are at length used up, so that all that was in the whole is added to the part, it will follow that by proportional additions being made to the time, there will result a finite time in which the whole mover will move the whole mobile. Thus, if the mover is finite and the mobile also finite, the time too must be finite.

According to this, therefore, it is not possible that by a finite mover anything be moved with an infinite motion, namely, according to an infinite time. And so what was first proposed is now plain, namely, that it does not happen that a finite mover should cause motion for an infinite time.

1143. But Avicenna raises a difficulty about this demonstration of Aristotle. For it seems not to be universal, since there exists a finite mover and mobile from which nothing can be subtracted or taken away, such as a heavenly body, which nevertheless was not excluded from Aristotle’s proof. Hence it seems that the proof is either particular, or it proceeds from a false assumption.

To this objection Averroes in his Commentary answers that although nothing can be subtracted from the heavenly body, yet the conditional is true, that if a part be taken away from the body, that part will move or be moved in less time than the whole body. For there is nothing to prevent a conditional from being true, even if its antecedent be impossible, as is patent from this conditional: If a man flies, he has wings. But whatever takes away the truth of a true conditional is false, even though the antecedent of the conditional be false. Now the truth of the above conditional cannot stand with the statement that the finite moves for an infinite time, as is evident through Aristotle’s deduction, Thus, therefore, from the truth of the foregoing conditional Aristotle concludes that it is impossible for a finite thing to cause motion for an infinite time.

However, it may be said more briefly that when Aristotle in his demonstrations speaks of removing or subtracting, it does not always have to be understood in the sense of destroying a thing’s continuity, which is impossible in a heavenly body; rather, substraction can be understood in the sense of designating. For example, I can without disturbing the continuity of a piece of wood designate by touch or thought a certain point as though dividing the whole, and in this way I can remove a part from the whole and say that there is less whiteness in that part than in the whole. In like.manner, it can be said that there is less power to move in a part of a heavenly body— a part removed by designating it—than in the whole.

1144. But there is another and greater difficulty. For it does not seem to be against the prerogatives of a finite mover to cause motion for an infinite time, because if that finite thing is imperishable or impassible in its nature, and never loses its nature, it will maintain itself always in the same way with respect to causing motiong for a same thing, remaining in the same state, will always do the same. Hence, there would be no reason for its not being able to get later as it did before. This is evident to sense, for we observe that the sun can in an infinite time move lower bodies.

To settle this difficulty, we must investigate the sequence of demonstration set forth by Aristotle. For it should be certain that the conclusion is to be interpreted in the sense in which it follows from the premisses.

We should consider, therefore, that the time of a motion may be taken in two senses, especially in local motion: in one sense, according to the parts of the mobile; in another sense, according to the parts of the magnitude along which the motion passes. For it is plain that one part of the mobile passes a designated point of the magnitude, before the whole does, and that the whole traverses part of the magnitude before it traverses all of it. Now, it is plainly clear from the procedure of Aristotle’s demonstration, that he is speaking of time of motion according to the parts of the mobile and not according to the parts of the magnitude. For in his demonstrations he assumes that part of the mover moves part of the mobile in less time than the whole moves the whole. But this could not be true, if we took time of motion according to the parts of the magnitude traversed by the motion; for the ratio of the part of the mover to the part of the mobile is the same as that of the whole mover to the whole mobile. Hence, a part will always move part with the same velocity as the whole moves the whole. Thus in an equal time part of the mobile moved by part of the mover will traverse some magnitude and the whole mobile moved by the whole mover will also.

Or perhaps the whole will be moved in less time than the part, because a united force is greater than a divided force, and the greater the force of the mover, the swifter the motion and the less the time. Therefore, this must be understood in the sense that the time of motion is taken according to parts of the mobile, because one part of the mobile will pass a definite point in less time than the whole will. In this sense, it is impossible for anything but an infinite mobile to be moved for an infinite time. But an infinite mobile cannot be moved by a finite mover, since the power of the mover is always greater than the power of the mobile. Hence an infinite mobile must be moved by an infinite power. Consequently, just as an impossibility follows from the assumption that a finite mover moves a finite mobile with an infinite motion according to the parts of the mobile, so, this incompatibility once removed, one must further conclude that an infinite motion belongs to an infinite mobile from an infinite mover.

1145. But against this, someone could object that Aristotle did not prove above that motion is infinite according to the parts of the mobile in the way that the motion of an infinite body is said to be infinite, for the entire corporeal universe is finite, as was proved in Book III and will be proved in On the Heavens I. Hence the demonstration of Aristotle does not seem to be verified as concluding to his proposition, namely, that the first mover, which causes an infinite motion, is infinite.

But it should be said that what is first cause of an infinite motion must be the per se cause of the infinity of the motion, because the cause which is per se is always prior to that which is so by virtue of something else, as has been said above. Now, the power of a per se cause is determined to a per se effect and not to a per accidens effect, for that is the way Aristotle taught causes are to be compared to their effects in Book II. But, because motion can be infinite in two ways, as has been said, namely, according to the parts of the mobile and according to the parts of the length along which the motion takes place, per se the infinite is in motion from the parts of the mobile, but per accidens according to the parts of the length—for the quantity of motion based on the parts of the mobile belongs to it by reason of its proper subject and so is present in it per se, whereas the quantity of motion based on the parts of the length is based on constant repetition of the mobile’s motion, in the sense that a whole mobile, having completed its entire motion upon one part of the length, now successively traverses another. The first cause, therefore, of the infinity of motion has power over the infinity of motion which is per se, in such a way, namely, as to enable it to move an infinite mobile, should there be such. Hence, it must be infinite. And even though the first mobile be finite, it has, nevertheless, a certain likeness to the infinite, as was said in Book III. But in order that something be the cause of a motion that is infinite through repetition (which is per accidens) infinite power is not required, but an immobile finite power is enough, because, so long as the power remains the same, it will be able to repeat the same effect, as the sun has a finite energy yet can move the lower elements in an infinite time, should motion be, as Aristotle posits, eternal. For it is not the first cause of the infinity of motion but is something as though moved by another to move in an infinite time, according to the position stated above.

1146. Then at (903) he shows that the power in a magnitude must be proportional to the magnitude in which it exists.

First he shows that in a finite magnitude there cannot be an infinite power—and this is what he chiefly intends;

Secondly, that on the other hand, in an infinite magnitude there cannot be a finite power, at 1156.

That an infinite power cannot exist in a finite magnitude he proves at (903), but first he mentions two assumptions. The first is that a greater power produces an equal effect in less time than a lesser power, as a greater heating force raises a thing on which it acts to an equal temperature in less time, and the same is true of a sweetener, or a hurler, or any cause of motion.

And from this assumption he concludes that since an infinite power is greater than a finite power, then, necessarily, if there is a finite magnitude possessing an infinite power, one or a number of things will in the same time undergo from such an agent a greater change than from another having finite power, or, conversely, that which undergoes an equal change will do so from it in less time. Either interpretation suits what Aristotle says here, namely, “...to a greater extent than by anything else.”

The second assumption is that, since whatever is being moved is being moved in time, as was proved in Book VI, it cannot be that something undergoing is changed in no time by an agent of infinite power. Therefore, it is changed in time.

From this he proceeds in the following manner: Let A be the time in which an infinite power causes change by heating or throwing, and let the time in which a finite power is causing change be AB, which is longer than A. Now, no matter what a finite power may be, a still greater may be taken. If, therefore, we take another finite power greater than the first and which caused change in time AB, it will act in a shorter time. Again, a third and greater power will cause the change in still less time, And thus by always taking a finite power I will at length come to a finite power that will produce the change in time A, for when an addition is continually made to a finite power, any predetermined ratio will be exceeded. But as the power is increased, the time is decreased, because a greater power can cause a change in less time.

In this way, therefore, it will follow that a finite power will produce a change in a time equal to that used by the infinite power, which was assumed as acting in time A. But this is impossible. Therefore, no finite magnitude has an infinite power.

1147. Now, there are many doubts about this argument. First, it seems not to conclude in any way. For what belongs per se to a thing cannot be taken from it by any power however great, for it is not due to any lack of power, nor does it conflict with infinity of power, if it be said that it is impossible for man not to be an animal. But to exist in time belongs per se to motion, for motion is found in the definition of time, as was had above in Book IV. Therefore, if an infinite moving power is conceded to exist, it does not follow that motion exists in non-time as Aristotle here concludes.

Likewise, if the sequence of the argument of the Philosopher is considered, it will be seen that his conclusion that motion exists in non-time is inferred from the fact that the moving power is infinite; but an infinite moving power can also not be in a body. Therefore, for the same reason, it follows that such a power, if it is infinite, will move in non-time. Hence, from the impossibility of being moved in non-time it cannot be inferred that no infinite power exists in a magnitude, but absolutely that no moving power at all is infinite.

Again, two things seem to pertain to the magnitude of a power, namely, the swiftness of motion and its diuturnity; and any superabundance in the power causes a corresponding superabundance in each of these two things. But with respect to the superabundance of an infinite power, he showed above that a perpetual motion depends on an infinite power, but not that an infinite power does not exist in a magnitude. Therefore, here too, with respect to excess of swiftness, he ought not to conclude that no infinite power exists in a magnitude, but that the power which moves in an infinite time would, on account of its infinity, also move in non-time.

Again, the conclusion seems to be false. For the greater the power of a body, the longer it can endure. If, therefore, the power of no body were infinite, no body could endure ad infinitum. Now this is plainly false, both according to his own opinion and according to the tenets of the Christian faith, which posits that the substance of the world will endure ad infinitum.

It could also be objected that the division and addition which he uses have no correspondence in reality, but since this was sufficiently discussed previously, it can be passed over at the present time.

1148. Answering, therefore, these doubts in order, it must be said with respect to the first one, that the Philosopher in this place does not intend an ostensive demonstration but one that leads to an impossibility, in which, since from something given an impossibility follows, that which was given is concluded to be impossible. For it is not true that the first supposition can possibly co-exist with the conclusion. Thus the supposition that there was some power which could remove the genus from a species, would allow us to conclude that that power could make man not be animal; but because this is impossible, the supposition too is impossible. From this, then, it cannot be concluded that it is possible for a power to exist that could make man not be animal. So, too, from the fact that an infinite power exists in a magnitude, it follows of necessity that motion exists in non-time; but since this is impossible, it is impossible for an infinite power to exist in a magnitude; nor can it be concluded from this that it is possible for an infinite power to move in non-time.

1149. To the second doubt Averroes responds in his Commentary at this place that the argument of Aristotle here proceeds from power under the aspect of its infinity. But “finite” and “infinite” belong to quantity, as was proved in Book I. Hence, finite and infinite do not properly belong to a power that is not in a magnitude.

But this answer is contrary both to the intention of Aristotle, and to the truth. It is contrary to Aristotle’s intention, because in the preceding demonstration Aristotle proved that a power which causes motion for an infinite time is infinite, and from this he later concludes that the power moving the heavens is not a power existing in a magnitude.

It is also against the truth: for since every active power is according to some form, magnitude, and consequently its finiteness and infinity, belong to a power in the way it belongs to form. But magnitude belongs to form both per se and per accidens: it belongs per se, according to the perfection of the form, as a whiteness is called “great” even in a small amount of snow, according to the perfection of its proper notion; it belongs per accidens, according to the extension that a form has in a subject, as a whiteness can be called “great” on account of the size of its surface.

Now, this second magnitude cannot belong to a power not in a magnitude, but the first magnitude most truly does, because non-material powers, the less they are restricted through union with matter, the more perfect and more universal they are.

But swiftness of motion does not follow upon a magnitude of power which is per accidens, by extension with the magnitude of the subject; rather, it follows one that is per se, according to its proper perfection, because the more perfect a thing is in act, the more vehemently is it active. Hence it cannot be said that a power which does not exist in a magnitude, because it is not infinite with the infinity of magnitude which depends on the magnitude of the subject, therefore cannot cause an increase of swiftness ad infinitum, i.e., move in non-time.

Hence the same Commentator solves this same difficulty in another way in Metaphysics XI, where he says that a heavenly body is moved by a two-fold mover, i.e., by a conjoined mover, which is the soul of the heavens, and by a separated mover, which is not moved either per se or per accidens. And because that separated mover has infinite power, the movement of the heaven acquires from it a perpetual duration; but because the conjoined mover has finite power, the movement of the heaven acquires from it a determinate swiftness.

But even this answer is not sufficient. For since both seem to follow upon an infinite power, namely, that it act for an infinite time, as the preceding demonstration concluded, and that it act in non-time, as this demonstration seems to conclude, the doubt still remains why the soul of the heaven which acts in virtue of an infinite separated mover obtains from it the ability to act for an infinite time rather than the ability to act with infinite swiftness, i.e., in non-time.

1150, In answer to this doubt it must be said that every power not in a magnitude acts through intellect, for so the Philosopher proves in Metaphysics XI that the heaven is moved by its mover. But no power in a magnitude acts as though through intellect, for it was proved in On the Soul III that the intellect is not a power of any body.

Now this is the difference between an agent that acts through intellect and a material agent: the action of the material agent is proportioned to the nature of the agent, for a heating process proceeds in proportion to the heat, but the action of an intellectual agent is not proportioned to its nature but to the form apprehended, for a builder does not build as much as he can, but as much as the notion of the conceived form requires.

Consequently, if an infinite power existed in a magnitude, it would follow that the motion produced by it would be in proportion, to it, as the present demonstration shows. But if an infinite power is not in a magnitude, a motion does not proceed from that power in proportion to its power but according to the notion of the thing apprehended, i.e., according as it fits the end and nature of the subject.

Another point that should be noted is that, as was proved in Book VII only things having magnitude are moved; wherefore, the swiftness of motion is an effect received from the mover into something having magnitude. But it is plain that nothing having magnitude can receive an effect equal proportionately to the power which is not in a magnitude, because every corporeal nature is related to the incorporeal as a certain particular to what is absolute and universal, Hencet it cannot be concluded, if an infinite power is not in a magnitude, that from it there results in a body an infinite swiftness, which is the effect proportionate to such a power, as has been said.

But there is nothing to prevent a magnitude from receiving the effect of a power existing in a magnitude, because the cause is proportioned to the effect. Hence if it were supposed that an infinite power existed in a magnitude, it would follow that a corresponding effect would exist in a magnitude, namely, an infinite swiftness. But this is impossible; therefore, the first too is impossible.

1151. From this the resolution of the third doubt is clear. For to be moved for an infinite time is not repugnant to the notion of a moved magnitude, for it befits a circular magnitude, as was shown above. But to be moved with an infinite speed, i.e,, in non-time, is contrary to the notion of a magnitude, as was proved in Book VI. Hence the first mover, possessing infinite power, is, according to Aristotle, the cause of a motion that lasts an infinite time, but not one that has infinite speed.

1152. The fourth doubt is, according to Averroes in his Commentary, answered by Alexander’s saying that a heavenly body acquires eternity from a separated mover having infinite power, as well as perpetuity of motion. Hence, just as it is not from the infinity of a heavenly body that it is perpetually moved, so, too, it is not from the infinity of the heavenly body that it endures forever. Both are from the infinity of the separated mover.

Now Averroes tries to refute this answer, both in his Commentary on this passage and in Metaphysics XI, and says that it is impossible for something to acquire perpetuity of existence from another, because it would follow that something in se perishable could be eternal. Yet something can acquire perpetuity of motion from another, for motion is an act existing in a mobile but caused by a mover. He says therefore that in a heavenly body considered in itself there is no potency to non-existence, because its substance has no contrary, but there is a potency to rest, because rest is contrary to its motion. And that is why it does not have to acquire perpetuity of existence from another, but must acquire perpetuity of motion from another.

That a heavenly body has no potency to non-existence happens, he says, because a heavenly body is not composed of matter and form as though of potency and act. Rather, says he, such a body is matter existing in act, while its form is its soul, in such a way that it is not constituted in being through the form, but only in motion. Consequently, says he, there is present in it not a potency to existence, but solely a potency to “where” (place), as the Philosopher says in Metaphysics XI.

1153. But this solution conforms neither to the truth nor to the intention of Aristotle. It is not in conformity with truth on a number of counts: First, because he says that a heavenly body is not composed of matter and form—which is utterly impossible. For it is plain that a heavenly body is something actual, otherwise it would not be in motion—something that is in potency only is not a subject of motion, as was proved in Book VI. But, whatever is actual is either a subsisting form, as are the separated substances, or has form in something else, which is related to the form as matter, and as potency to act. Now, it cannot be said that a heavenly body is a subsistent form, because then it would be understood in act and neither sensible nor existing under quantity. Therefore, it must be a composite of matter and form, and of potency and act. Consequently, there is in it in some sense a potency to non-existence.

But even if a heavenly body were not a composite of matter and form, it would still be necessary to place in it, in some sense, a potency in respect of existence. For every simple self-subsisting substance is necessarily either its own existence or it shares in existence. But a simple substance which is self-subsistent existence itself cannot be but one, just as whiteness, if whiteness were a subsistent being, could be but one. Consequently, every substance after the first simple substance participates existence. But every participant is composed of the participant and what it participates, and the participant is in potency to what it participates. Therefore, in every substance, however simple, other than the first simple substance, there is a potency to existence.

Now he was deceived by the equivocation in “potency.” For potency sometimes refers to what is open to opposites. In this sense, potency is excluded from a heavenly body and from separated simple substances, because, in Aristotle’s opinion, they have no potency to non-existence, for simple substances are forms only, and it belongs per se to a form that it exist, while the matter of a heavenly body is not in potency to another form. For just as a heavenly body is related to its figure, of which it is the subject, as potency to act, and yet cannot not have such a figure, so the matter of the heavenly body is related to its form as potency to act, and yet it is not in potency to being deprived of this form or to non-being. For not every potency is open to opposites; otherwise possibility would not follow upon necessity, as is said in Perihermeneias II.

His position is also contrary to the intention of Aristotle, who in On the Heavens I, in a certain demonstration, uses the fact that a heavenly body has the potency or the virtue to exist always. Therefore, he cannot avoid the incompatibility by saying that in a heavenly body there is no potency to existing: for this is evidently false and contrary to the intention of Aristotle.

1154. Therefore, let us see whether he adequately refuted the solution of Alexander who says that a heavenly body acquires its perpetuity from something else. His refutation would indeed be good, if Alexander had posited that a heavenly body had of itself a potency to existence and non-existence, and that it acquired from something else its perpetual existence. This I say while keeping in mind his intention, and not excluding the omnipotence of God, by which “this corruptible can put on incorruptibility”—to discuss which now does not pertain to the present question. Still Averroes, even supposing his intention, cannot conclude against Alexander, who did not posit that the heavenly body acquires its perpetuity from something else, as though it had a potency to existence and non-existenoe, but as though not having its existence from itself. For whatever is not its own existence participates existence from the first cause that is its own existence. Hence, he himself professes in his book, On the Substance of the Orb, that God is the cause of the heavens not only with respect to its motion, but with respect to its substance as well, which would not be true unless it has its existence from something else. But the only existence it has from another is a perpetual one; consequently, its perpetuity is from another.

And this is in agreement with the teachings of Aristotle who, in Metaphysics V and in the beginning of this Book VIII of the Physics, says that there a some necessary things that have a cause of their necessity. In the light of this, the solution according to the intention of Alexander is plain, namely, that just as a heavenly body derives its motion elsewhere, so too its existence. Hence, just as a perpetual motion demonstrates the infinite power of the mover but not of the mobile, so too its perpetual duration demonstrates the infinite power of the cause from which it derives its existence.

1155. But the potency of a heavenly body to existence is not exactly the same as its potency to perpetual motiono However, the difference is not the one he assigns, namely, that in a heavenly body there is with respect to motion a potency to opposites, these being rest and motion; rather it is to opposites which are different “where’s” (places).

But they differ in respect of something else. For motion according to itself falls under time, whereas existence according to itself does not fall under time, but only according as it is subject to motion, Therefore, if there is an existence not subject to motion, it in no wise falls under time. Hence, the potency to be moved for an infinite time regards the infinity of time directly and per se. But a potency to exist for an infinite time, if that existence is transmutable, regards a quantity of time and, therefore, a greater power is required for something to endure in transmutable existence for a longer time, But a potency in respect to intransmutable existence has no relationship to a quantity of time. Hence the magnitude or infinity of time has nothing to do with the magnitude or infinity of the power in respect to such existence. Therefore, granting the impossible assumption that a heavenly body did not derive its existence elsewhere, its perpetuity would not be grounds for concluding that an infinite power exists in it.

1156. Then at (904) he proves that in an infinite magnitude there cannot exist a finite power, And this he does with two arguments, with respect to the first of which he does three things:

First he mentions the conclusion intended, namely, that just as there cannot be an infinite power in a finite magnitude, so neither can there be a finite power in an infinite quantity taken as a whole (for if a finite part of the infinite be taken, it will have a finite power). He mentions this conclusion not as though it were needed for proving his principal conclusion but as cohering with, and akin to, the conclusion previously demonstrated.

1157. Secondly, at (905) he mentions something that could lead someone to suppose that there is a finite power in an infinite magnitude. For we see some lesser magnitude that has greater energy than a larger magnitude, as a small amount of fire has more active power than a large amount of air. But that does not permit us to conclude that an infinite quantity has a finite power, because if a still greater magnitude is taken, it will have greater power; for example, even though a greater quantity of air has less power than a small fire, yet if the quantity of air be much increased, it will have more power than the small fire.

1158. Thirdly, at (906) he presents his intended demonstration: Let AB be an infinite quantity, and BC a finite magnitude of another kind, having a finite power; let D be a mobile that is being moved by the magnitude BC in time EZ. But because BC is a finite magnitude, it is possible to take a larger magnitude; let us therefore take one which is in double proportion.

Now, the greater the power of a moving cause, the more it moves in less time, as was proved in Book VII. Therefore, the double of BC will move the same mobile, namely, D in one-half the time, namely, ZT, so that the time EZ is bisected by the point T. By continually adding to BC, the time of the motion will be decreased, yet no matter how much is added to BC, it can never traverse AB, which exceeds BC beyond any proportion, as the infinite exceeds the finite. And since AB has finite power, it moves D in a finite time. Consequently, by continually lessening the time BC consumes in moving, we shall reach a time less than the time consumed by AB in its action of moving, because every finite is surpassed by dividing. It will follow, therefore, that the lesser power will move in less time, and this is impossible. What remains, therefore, is that there was an infinite power in the infinite magnitude, for the power of the infinite magnitude exceeded every finite power.

This has been proved by subtracting time, because every finite power must have some determinate time in which it causes motion. This is clear from the following consideration: If so much power acts in so much time, a greater power will move in a time smaller but yet definite, i.e., finite, according to an inverse proportion, such that, by as much as is added to the power, by so much is the time decreased. Consequently, no matter how much is added to a finite power, so long as the power remains finite, so will the time always remain finite, for a time will be reached that will be as much less than a previously given time as the power growing by addition is greater than a power previously given.

But an infinite power in causing motion surpasses every determinate time, just as happens in all other cases involving the infinite—for every infinite, such as that of number and magnitude, exceeds everything determinate in its genus. Thus it is plain that an infinite power exceeds every finite power, because the excess of power over power corresponds to the decrease of time from time, as has been said. Hence, it is evident that the above-stated conclusion, namely, that the power of an infinite magnitude is infinite, follows of necessity from the premisses.

1159. Then at (907) he cites for the same another proof, which differs from the first merely in this, that the first proceeds on the assumption of a finite power existing in a finite magnitude of another kind; but this second proof proceeds on the assumption of a certain other finite power, in another finite magnitude of the same genus as the infinite magnitude. For example, if air is the infinite magnitude having a finite power, we will assume a finite power existing in some finite magnitude of anothef specimen of air. On these grounds, it is clear that the finite power of the finite magnitude will, if sufficiently multiplied, measure the finite power in the infinite magnitude, because a finite thing is measured or even exceeded by a smaller finite thing taken a certain number of times. Since, therefore, in a magnitude of the same kind, the greater must have more power, as a greater amount of air has more power than a smaller amount, it will be necessary that that finite magnitude which will have the same proportion to the finite magnitude previously taken, as the finite power of the infinite magnitude has to the power of the finite magnitude previously taken, have a power equal to the power of the infinite magnitude. For example, if the finite power of an infinite magnitude were to be 100 times the finite power of a given finite magnitude, then the magnitude 100 times the size of that finite magnitude has a power equal to the power of the infinite magnitude, for in a thing of the same genus the magnitude and the power increase in proportion.

However, the conclusion we have reached is impossible, because either the finite magnitude would have to be equal to an infinite ones or a smaller magnitude of the same genus would have a power equal to a larger magnitude of the same genus. Therefore, the assumption from which this conclusion followed is also impossible, namely, that an infinite magnitude may have a finite power.

In summary, therefore, he concludes to two demonstrated conclusions, namely, that in a finite magnitude there cannot be infinite power, and that in an infinite magnitude there cannot be finite power.

Lecture 22

Diversity of movers annuls continuity of motion

1160. After proving two of the things needed for demonstrating his proposition, namely, that a finite power cannot move in an infinite time, and that an infinite power cannot exist in a finite magnitude, the Philosopher now starts to prove the third, namely, the unity of the first mover. About this he does two things:

First he shows that on account of the diversity of movers, the continuity or unity of motion fails in certain mobiles that seem to be in continuous motion;

Secondly, he shows from this that the first mover is necessarily one, (L. 23).

About the first he does three things:

First he raises a doubt about projectiles;

Secondly, he resolves the doubt, at 1162;

Thirdly, from this he shows that the motion of a projectile is not continuous, at 1163.

About the first he does two things:

First he states the doubt;

Secondly, he rejects one solution, at 1161.

He proposes therefore first (909) a doubt about projectiles. It is this: It was proved above in the beginning of this Book that whatever is being moved is being moved by another, provided we are not referring to things that move themselves, such as animals, of which a projected stone is not one. Now a bodily thing causes motion through contact. Therefore there is doubt as to how projectiles remain in continuous motion even after contact with the mover ceases. For they seem to be moved without anything moving them.

1161. Then at (909) he rejects a solution attributed to Plato who said that the projector who first moves a stone moves not only the stone but something else, namely, the air, and the moved air moves the stone, even after contact by the projector.

But he rejects this solution, on the ground that it appears equally as impossible for the air to be moved when the first mover, namely, the projector, is no longer in contact with it, nor moving it, as it was for the stone. But rather it seems to be necessary that while the first mover is acting, all are being moved, and when the first mover rests,i.e., ceases to act, all rest, although also something moved by the first mover, such as the stone, may cause something to be moved, just as the original mover did.

1162. Then at (910) he gives his own solution. And he says that if the second mover causes motion insofar as it is moved by the first mover, then it is necessary to say that the first mover, namely, the thrower, gives to the second mover, namely, the air or water or any such body apt to move a thrown body, the ability both to cause motion and to be moved; for both of these are received into the air or water from the thrower, namely, to cause motion and to be moved. But since to cause motion, and to be moved, are not of necessity in the same thing—since there is found a mover that is not itself moved —the mover and moved do not pause simultaneously, i.e., the air moved by the thrower does not simultaneously cease causing motion and cease being moved, but as soon as the thrower ceases acting, the air ceases to be moved, but still moves.

And this is evident to the senses. For when a mobile has now arrived at the terminus of its motion, it is able to cause motion in the ultimate moment of its arrival, at which time it is no longer being moved but is in the state of having been moved. Now while the second mover moves, that which is “had,” i.e., which is next to it, is being moved. And the same applies to this third, for it remains a mover even when it is not being moved. And because a second mover has less power for acting than did the first, and the third less than the second, the motion called “projection” must cease, on account of the fact, namely, that the power for moving is less in the “had,” i.e., the subsequent, mover than in that in which it was first.

Thus at length, on account of the diminution of the power to move, a state is reached where that which was prior with respect to the one following will not confer upon the one following the power to cause motion but will solely cause it to be moved. And at that time it is necessary that when this last mover ceases to act upon the one following it, simultaneously that moved by it will cease being moved, Consequently, the entire motion will cease, because the last moved object is unable to cause motion in any other.

1163. Then at (911) he concludes from the foregoing that a motion of projection is not continuous.

He sayst therefore, that this motion, namely, that of projection, comes to be in bodies that are capable of being moved at one time and of resting at another time—if indeed there are bodies to which such a motion belongs. And this is evident from what was said; for the motion called “projection” ceases through a failing of the power to cause motion, as has been said.

It is also evident from the foregoing that this motion is not continuous, although it appears to be continuous. For it seems to be continuous, because there is one mobile involved; yet it is not continuous, because there are diverse movers, as has been said. For either that motion results from a series of consecutive movers or from a series of movers that are in contact—(how “consecutive” and “in contact” differ has been explained above in Books V and VI).

And it is plain to sense that in both cases the different movers can move one mobile inasmuch as they are moved by some first mover. For in things that are moved in a way that projectiles are moved, there is not just one mover but many “had” to each other (i.e., following each other), which are consecutive and in contact. And because diversity is not without division, the projection in question comes to be through a medium that is easy to divided namely, air and water, in which a diversity of movers can function on account of the easy divisibility of the medium.

This motion of projection is by some called antiperistasistasis, i.e., contra-resistance, on the ground that the surrounding air being set in motion somehow moves the projectile, as was said in Book IV. However, the problem under discussion can be solved in no other way than the way mentioned. Because, if the contra-resistance of the air is the cause of the projection, it follows that all the elements involved are moving and being moved simultaneously, i.e., that the entire air is simultaneously acting and being acted upon and, consequently, that all would cease simultaneously. But this is evidently false, For we see some one thing being moved continuously no matter what moves it. And I say this because it does not have one and the same determinate mover, but diverse movers.

Lecture 23

The first mover can have no magnitude

1164. Having resolved the doubt he raised about the motion of projectiles, from the solution of which he concluded that a motion involving a number of movers is not one continuous motion, the Philosopher now turns to his main task, namely, to prove that the first mover is one. About this he does two things:

First he states his proposition;

Secondly, he raises a doubt and solves it, at 1170.

About the first he does three things:

First he proves the unity of the first mover through the continuity of motion;

Secondly, he shows how a continuous motion comes from one mover, 1166;

Thirdly, where the principle of a continuous motion is, at 1168.

1165. That there must be one movers he proves (912) through the continuity of motion, taking what he had previously proved, namely, that some continuous motion must always exist. But a continuous motion is one, as was said in Book V. Therefore, there must always be some motion that is one. But for a motion to be one it must be of one moved magnitude (because something not able to be divided into parts cannot be moved, as was proved in Book VI) and it must be moved by one mover. For if the mobiles are diverse or the movers are diverse, a motion will not be one, and consequently, not continuous; rather, it will be one motion divided from another—on account of the division of the mobile or mover—and one will have consecutive motions. It is necessary therefore that the mover be one and that it be either a moved mover or a mover that is immovable.

1166. Then at (913) he shows how from one mover there can be a continuous motion. About this he does two things:

First he shows how from one mover there can be a motion ever continuous;

Secondly, how it is regular, at 1167.

He says therefore (913) that one motion from one mover is, as has been said, either from a moved mover or a non-moved mover. If it is the former, it follows that it is moved by something, as was proved above. But this cannot go on ad infinitum, as was proved above. Therefore, the series of movers and mobiles must stop and a first mobile moved by an immobile mover be reached, which mover does not move of necessity, because it is not moved by another. For whatever is moved by another, moves of necessity, to the extent that necessity is imposed upon it by its mover. And because it is changed from its disposition, it cannot cause motion which is always uniform, for its disposition varies.

But nothing other imposes necessity on a non-moved mover, nor does its disposition vary. Hence it does not act of necessity,” but it can move always, because to move thus, namely, without change of self, is unwearying, For fatigue occurs to some movers in moving, because they are also simultaneously moved themselves, and from fatigue it occurs that they cannot always act as movers. Hence it remains that a non-moved mover can move with a perpetual continuous motion.

1167. And because perfect continuity and unity of motion require that a motion be regular and uniform, as was had in Book V, therefore at (914) he shows that a motion from an immobile mover is regular.

And he says that either solely the motion from an immobile mover is regular, or if any others are regular also, the former is the most regular. Now he uses this disjunction, because the disposition of a moved mover sometimes remains the same for some time, without variation, at least as far as any sensible perception thereof is concerned, and accordingly, such a mover seems for a time to cause a uniform motion. But that which is always such moves above all with a uniform motion, since such a mover is subject to no change whatsoever. He says this in order to show that there are some movers that are not moved with the same kind of motion as they cause, as a heavenly body is not moved by the motion of alteration but by some other, namely, local motion. But the first mover, being utterly immobile, is moved by no change.

In order that a motion be regular and uniform, it is required that the mover be wholly immobile; besides that, in order that the motion be “similar,” i.e., uniform, it is required that what is moved not undergo any change other than that which the immobile mover causes in it, as a heavenly body is moved with local motion by an immobile mover and beyond that has no other change. For if it were altered, its disposition to the motion would not remain constant and, consequently, the motion would not be uniform.

1168. Then at (915) he shows where the beginning of the first continuous motion is. And because it was proved that the first motion is circular and belongs to a circular magnitude, the first beginning of this motion must be either in the middle, i.e., the center, or on the circle, because both are principles of a circular magnitude. For in a circular magnitude lines are extended from the center to the circumference. Hence, one of these must be taken as principle, and the other as terminus.

Then he shows, by the following argument, that the principle of the first motion is on the circle: Every motion, the closer it is to the moving principle, the swifter it is, because it receives a stronger impression from the mover. But we perceive in the motion of the whole firmament, which motion proceeds from the first immobile mover, that the closer some mobile approaches the outermost circumference, so much the swifter is its motion. Therefore, the mover is on the circle and not in the center.

The major of this argument is plain. But in order to make the minor plain, it must be considered that a twofold motion is found in heavenly bodies: one of which is the motion of the entire firmament in its daily revolution from east to west—and this is the first motion; the other is the motion by which the stars are moved contrariwise from west to east.

Now in this second motion the closer a heavenly body is to the center, the swifter its motion, as is evident from the calculations of astronomers, who assign one month for the motion of the Moon, one year for the motions of the Sun, Mercury and Venus, two years to Mars, twelve years to Jupiter, thirty to Saturn, and 36,000 years to the fixed stars [i.e., the. precession of the equinoxes, actually 26,000 years].

But with respect to the motion of the entire firmament it is the opposite. For the farther a heavenly body is from the earth, the swifter is its motion, because it traverses a larger magnitude in the same time. For the circumferences of circles are greater the farther they are from the center, and yet all the heavenly bodies are revolved with the motion of the whole in the same period of time. Consequently, the outermost bodies are swifter. Hence what remains is that the principle of the first motion is not in the center but on the circumference.

1169. But now a difficulty arises about this conclusion. For the first mover, as he will conclude below, is indivisible and has no magnitude, and its power does not exist in a magnitude. But whatever is such does not seem to have a definite position in a body. Hence it does not befit the first mover to be in one part of the first mobile more than in another.

But it should be stated that the first mover is said to be in some part of its mobile not through any determination of its substance but through its efficient causality of motion, because it begins to move at some part of the object it acts upon. And it is for that reason that the first mover is said to be in the heavens rather than in the earth, and rather in the east where the motion begins. And this is not to be understood as though the mover fixes itself to some definite part of the mobile, since there is no definite part of the mobile always in the east, but the part now in the east is later in the west. Thus it is clear that the power of the mover is said to be in the east by virtue of the inflow of motion, and not through any determination of its substance.

It should also be noted, with respect to the motion of a sphere, that simultaneously with its motion, it has a kind of immobility—for the parts are moved as to change of place both as to subject and as to conception, but the whole is moved as to change of place in conception but not as to subject, as was shown in Book VI. And these two (different) things are attributed to the two principles of the spherical magnitude he mentions here: for the principle of the motion has its seat on the circumference, while the principle of immobility derives from the fixity of the center.

1170. Then at (916) he raises a doubt about the foregoing.

First he raises it;

Secondly, he solves it, at 1171.

For he had said previously that an immobile mover can cause continuous motion and therefore here at (916) he subsequently asks whether a moved mover can cause a continuous motion, in such a way, namely, that it be truly continuous without any interruption, such as the interruption which occurs when someone pushes a body and then pushes it again. For it is clear that this motion, which is in this wise continuous from the standpoint of the mobile, is not truly continuous, because the movings are not continuous, but one follows the other; for the one pushing does not continually push but at intervals, in such a way that one push is consecutive to another.

1171. Then at (917) he resolves this difficulty and shows that no moved mover can cause a continuous motion.

For it is necessary to say that a mobile that is seemingly being moved continuously is being moved either immediately as to the whole motion by a moved mover, or else through many intermediates, one in contact with the other, as was said with respect to projection. And this division is valid whether the moved mover acts by pushing or pulling or both (as in twirling), as was explained in Book VII. Nor does it happen that a thing is moved locally by a moved mover in more than one way per so and not per accidens (for something being carried is being moved per accidens).

And because he had said that, in things that are projected, the mover is constantly other and other, and this seems to be false because the projected body seems to be continually moved by an air which remains one, he therefore, in order to refute this, adds that it is because air or water are easy to divide that, so to speak, now one, now another, mover acts, but yet it acts as if being continually moved, so long as the motion of the projectile lasts; and although the air seems one, nevertheless it is other and other through division.

But in either case, i.e., whether the moved mover acts by pushing or by pulling, the motion cannot be one but must be “had,” i.e., consecutive—for the reason given above, when the motion of projection was discussed, namely, on account of the diversity of movers.

What remains, therefore is that only the motion from an immobile mover can be forever continuous, because this mover, remains always “similar,” according to the same disposition in itself. For that reason it can maintain itself always and continuously in a similar way with respect to the mobile, so as, namely, to move it uniformly.

But it should be noted that the Philosopher here attributes eternity of continuous motion to the immobility of the mover, whereas above he attributed it to its infinite power. For eternity of continuous motion, if regarded with respect to the motion’s repetition, looks to the immobility of the mover, since, if it always remains constant with itself, it can always repeat the same motion. But the infinite power of the mover regards the motion’s whole perpetuity or infinity per se, was said above.

It should be noted, too, that because no moved mover can cause a perpetual continuous motion, he therefore, in Metaphysics XI, intends to prove a number of immobile movers according to the number of the heavenly movements, as though that consideration followed upon this.

1172. Then at (918) from the premisses already demonstrated he concludes to the main conclusion. And he says that from the foregoing it is plainly impossible for the first immobile mover to have any magnitude or to be a body or to be a power residing in a body. For if it had any magnitude, it would te either finite or infinite. But it was proved in Book III, when nature in common was discussed, that an infinite magnitude is not possible. What remains, therefore, is that, if it does have magnitude, it will have a finite magnitude. But that such is not so he proves on the ground that it is impossible for a finite magnitude to possess infinite power, such as the first immobile mover must necessarily have. Therefore, it cannot have a finite magnitude.

But that the first immobile mover must have infinite power he proves from something previously demonstrated, namely, that it is impossible for something to be moved for an infinite time by a finite power. Now, the first mover causes a motion that is perpetual and continuous, and is one and the same for infinite time, for otherwise this motion would not be continuous. Therefore, it has infinite power.

Thus it does not have a finite magnitude, and an infinite magnitude is impossible to be. It is plain, therefore, that the first mover is indivisible, both as having no part, as even a point is indivisible, and as wholly without magnitude, as though existing outside the genus of magnitude.

And thus does the Philosopher in his general consideration of natural things terminate at the first principle of the whole of nature, Who is the One above all things, the ever blessed God. Amen.