Lecture 9 — Two other arguments, proving no irregularity in the motion of the heaven

283 For if irregularity occurs, there must be change either in the movement as a whole, from fast to slow and slow to fast, or in its parts. That there is no irregularity in the parts is obvious, since, if there were, some divergence of the stars would have taken place before now in the infinity of time, as one moved slower and another faster: but no alteration of their intervals is ever observed. Nor again is a change in the movement as a whole admissible. Retardation is always due to incapacity, and incapacity is unnatural. The incapacities of animals, age, decay, and the like, are all unnatural, due, it seems, to the fact that the whole animal complex is made up of materials which differ in respect of their proper places, and no single part occupies its own place. If therefore that which is primary contains nothing unnatural, being simple and unmixed and in its proper place and having no contrary, then it has no place for incapacity, nor, consequently, for retardation or (since acceleration involves retardation) for acceleration.

284 Again, it is inconceivable that the mover should first show incapacity for an infinite time, and capacity afterwards for another infinity. For clearly nothing which, like incapacity, unnatural ever continues for an infinity of time; nor does the unnatural endure as long as the natural, or any form of incapacity as long as the capacity. But if the movement is retarded it must necessarily be retarded for an infinite time.

285 Equally impossible is perpetual acceleration or perpetual retardation. For such movement would be infinite and indefinite, but every movement, in our view, proceeds from one point to another and is definite in character.

286 Again, suppose one assumes a minimum time in less than which the heaven could not complete its movement. For, as a given walk or a given exercise on the harp cannot take any and every time, but every performance has its definite minimum time which is unsurpassable, so, one might suppose, the movement of the heaven could not be completed in any and every time. But in that case perpetual acceleration is impossible (and, equally, perpetual retardation: for the argument holds of both and each), if we may take acceleration to proceed by identical or increasing additions of speed and for an infinite time.

287 The remaining alternative is to say that the movement exhibits an alternation of slower and faster: but this is a mere fiction and quite inconceivable. Further, irregularity of this kind would be particularly unlikely to pass unobserved, since contrast makes observation easy.

288 That there is one heaven, then, only, and that it is ungenerated and eternal, and further that its movement is regular, has now been sufficiently explained.

374. Here [the Philosopher] gives the third argument which is taken solely from the viewpoint of the mobile (288b7). And he says that if the motion of the heaven were executed irregularly this would be either in such a way that the entire change of the heaven would vary in such a way as to be now slower, now swifter, or else parts of it would vary. The phrase entire change refers to the motion of the whole highest sphere, while parts of the change refers to the motions of the parts of the heaven. But that the parts of the supreme sphere are not moved irregularly so that one part of the heaven moves now swifter and now slower, he shows on the supposition that the sphere of the fixed stars is the supreme sphere. For in his [Aristotle's] time it had not yet been discovered that the fixed stars, in addition to the diurnal motion of the heaven, had a motion of their own [the precession of the equinox]. And therefore he attributes the first motion, namely, the diurnal motion, to the sphere of the fixed stars, as though proper to it. Later astronomers, however, assert the sphere of the fixed stars to have a certain proper motion, above which they place another sphere to which they attribute the first motion. On the supposition, therefore, that the sphere of the fixed stars is the supreme [outermost] sphere, he proves that its parts are not moved irregularly. For if its individual parts were moved now slower, now faster, then over a long period of time the fixed stars would have come to have different distances between themselves than previously as a result of one star moving faster and another slower. But the contrary of this appears. For they are found to retain the same configuration, and to be at the same distance from one another, now as when these were established by the earliest observers. Therefore there is no irregularity in the motion of the first heaven so far as its parts are concerned.

375. But if we pass [from the parts] to the whole "change" of the first heaven, there is no variation in velocity to a remission of velocity either. For it is plain that the slowing down of a mobile's motion is due to lack of power, just as, when the bodies of animals become tired, their motion slows down. But all impotency and defect is against nature, as is plain in animals, in which old age and decrease and other things of the sort are against nature. This of course is to be understood with respect to the particular nature, which preserves the individual as far as it can; hence it is against its intent that it be deficient in conserving. But it is not against universal nature, which is the cause not only of generation but also of corruption and, consequently, of the other defects that lead to corruption in the lower bodies. By universal nature is meant the active power present in a universal cause, for example, in the heavenly body. Now the reason why defects beyond the particular nature can occur in animals is that the whole substance of an animal is a resultant of bodies that are outside their appropriate places. For the body of an animal is composed of the four elements, none of which is in its own proper place. And because those things which are "outside nature" cannot last forever, as is evident from what has been stated above, necessarily corruption and defect will occur at some time to animals. But in the first bodies, namely, the heavenly bodies, nothing "outside nature" can happen, for they are simple things and not mixtures of various elements; moreover, they are in their appropriate place and there is nothing contrary to them, as is plain from what was said in Book I. Hence no impotency can be found in them. Therefore, too, there cannot be in them any remission, i.e., decrease of velocity, and consequently any intension, i.e., increase of velocity, because these two follow upon each other—for just as a motion, when it is intensified, proceeds from "remiss" to "intense," so when it diminishes, it goes from "intense" to "remiss."

376. The fourth argument, at again, it is inconceivable (288b22) is considered from the standpoint of the mover, and proceeds from a certain division. For if there is intensity and remission in the motion of the heaven, this can take place in only three ways: In one way, it might be always growing in intensity or always becoming remiss; in another way, it could at one time be getting intense and at another time be getting remiss, and this in two ways—in one way, such that the whole intensity and the whole remission would occur at once, on which follows (supposing, according to his opinion, that the heaven is moved for infinite time), that for an infinite time its motion first becomes intense and later becomes remiss, or conversely; in another way so that it alternates between successive states of intensity and remission. But each one of these is impossible. Therefore, it is impossible for remission and intensity to occur in the motion of the heaven.

First, therefore he shows that it is impossible for that motion to become intense for an infinite time and later become remiss for an infinite time, or conversely;

secondly, he shows that it is impossible for it to be always becoming intense or always becoming remiss, at equally impossible (288b27; [378]);

thirdly, he shows that it cannot be alternately becoming intense and remiss, at the remaining alternative (289a4; [381]).

377. He says therefore first (288b22) that it is unreasonable to suppose that the mover of the heaven for an infinite time is in power and moves swiftly, and then for another infinite time is weak and moves slowly (for remission of motion is due to lack of power, whereas intensity is due to power). The same conclusion that this is unreasonable, he now proves through two middles.

First, because nothing contrary to nature is seen to exist for an infinite time—for things according to nature exist always or for the most part. Now lack of power is contrary to nature, as was had. Therefore, it is impossible for anything to be deficient in power for an infinite time.

Secondly, because the time is not equal in the case of that which is according to nature and in the case of that which is not according to nature—for that which is not according to nature occurs in a few cases only, whereas what is according to nature happens for the most part or always. But the power of a thing is according to nature, whereas defeat of strength is "outside" nature. Therefore, it is impossible for anything for an equal period of time, namely, for an infinite time, to be in power and powerless. Consequently, it is also impossible for motion to become intense for an infinite time and then to become remiss for an infinite time.

But if the motion of the heaven becomes remiss in the manner described, it must become so for an infinite time. Now some, not understanding Aristotle's intention, take this as stated absolutely on the ground that there is no reason why it should become remiss at one time rather than another. But this is not according to his intention.

378. Then, a equally impossible (288b27), he shows that it is impossible for the motion of the heaven to become always more intense or to become always more remiss. He shows this with two arguments.

The first of these is that the intensity and remission of any irregular motion cease near some terminus of the motion, just as a natural motion becomes intense up to a certain terminal point and as a violent motion becomes remiss up to a certain terminal point. If, therefore, the intensity or remission of the motion of the heaven should be never terminated but proceed ad infinitum, it would follow that the motion of the heaven would be infinite and undeterminate, Now this is plainly false, for it has been proved in Physics VI that, since every motion proceeds from something to something, it must necessarily be determinate. For this reason even a single revolution of the heaven is determinate. It is only according to the various revolutions that succeed one another that the motion of the heaven is said to be infinite.

379. The second argument on this point he gives, at again, suppose one (288b30). And he says, that this is impossible is also evident if you grant that there is a minimum time, in less than which the heaven cannot be moved. For every motion or action involves a determinate time that it cannot ignore. Thus, although time is divisible ad infinitum, yet it is not possible to play the harp or walk in just any time whatever; rather, every action requires a minimum of time which it cannot exceed by speed, in such a way as for it to be performed in less time. For this reason it is not possible for the heaven to be moved in just any period of time, but rather it has some definite minimum time. From this it is clear that the speed of its motion is not forever being increased, because then its speed would exceed any minimum time whatever, Now if the speed of the heavenly motion cannot be always increasing, then for the same reason it cannot be always decreasing, because the same argument applies to both—for just as there is a minimum time required for an action, so too there is a maximum in which it takes place.

380. But someone could object to this argument and say that the velocity of the heavenly motion can be always increasing, without, nevertheless, some minimum given time ever being transgressed, so long as any addition of speed is not equal or greater but is always smaller and smaller. For it is said in Physics III that if a line be divided according to the same proportion, for example, by taking 1/3 from the whole line and then 1/3 from the remainder, and again 1/3 from that remainder, the process could go on ad infinitum; and if the segments removed subsequently be added to what was removed earlier, the process of adding will continue forever without ever arriving at the quantity of the whole line, because there will always be some part left of the line which is being divided. However, if one always takes a part of equal or greater quantity, and it is added to what was taken previously, one will necessarily exceed any predetermined quantity. And he says that we should understand this case similarly in the sense of every minimum given time's being surpassed, which is to exceed every greatness of velocity, by the addition, over an infinite time, of equal or greater speed. For if a great velocity were first added, and then a lesser one, and so on, as was said in the division and addition of a line, not every velocity or every minimum time would be transcended, since there would not be a pure intensification, but an intensification combined with remission, because the mover would not be able always to make equal additions to the velocity.

381. Then, at the remaining alternative (289a4), he shows that it is impossible for the motion of the heaven to be alternately intensified and remitted, and this for two reasons.

First, such a thing is seen to be utterly unreasonable, and like something imaginary—since no reason for this alternation can be assigned.

Secondly, such diversity in the motion of the heaven would not escape observation—for when two opposites are juxtaposed, their differences become more striking. Yet we perceive no such variations. Hence, it remains that there is no irregularity in the motion of the heaven.

Finally, (289a8), because he here puts an end to his consideration of the whole heaven, he states in summary that so far it has been said that there is one single heaven, and that it is ungenerated and eternal, and it is moved with a regular motion.