Lecture 17 — Two difficulties proposed in connection with what has been determined about the stars

318 There are two difficulties, which may very reasonably here be raised, of which we must now attempt to state the probable solution: for we regard the zeal of one whose thirst after philosophy leads him to accept even slight indications where it is very difficult to see one's way, as a proof rather of modesty than of overconfidence.

319 Of many such problems one of the strangest is the problem why we find the greatest number of movements in the intermediate bodies, and not, rather, in each successive body a variety of movement proportionate to its distance from the primary motion. For we should expect, since the primary body shows one motion only, that the body which is nearest to it should move with the fewest movements, say two, and the one next after that with three, or some similar arrangement. But the opposite is the case. The movements of the sun and moon are fewer than those of some of the planets. Yet these planets are farther from the center and thus nearer to the primary body than they,

320 as observation has itself revealed. For we have seen the moon, half-full, pass beneath the planet Mars, which vanished on its shadow side and came forth by the bright and shining part.

321 Similar accounts of other stars are given by the Egyptians and Babylonians, whose observations have been kept for very many years past, and from whom much of our evidence about particular stars is derived.

322 A second difficulty which may with equal justice be raised is this. Why is it that the primary motion includes such a multitude of stars that their whole array seems to defy counting, while of the other stars each one is separated off, and in no case do we find two or more attached to the same motion?

323 On these questions, I say, it is well that we should seek to increase our understanding, though we have but little to go upon, and are placed at so great a distance from the facts in question. Nevertheless there are certain principles on which if we base our consideration we shall not find this difficulty by any means insoluble.

450. Having determined the question of the stars and shown their nature, motion, order and figure, the Philosopher here solves certain difficulties with respect to what has been said. Concerning this he does two things:

first he presents the questions;

secondly, he resolves them, at we may object that we have been thinking (L. 18; 292a18).

As to the first he does three things:

First he excuses himself from presumption in dealing with these difficult questions;

secondly, he states the questions, at of many such problems (291b28; [451]);

thirdly, he points out the difficulty of the questions, at on these questions, I say (292a14; [457]).

He says therefore first (291b24) that since there are two doubts which anyone could reasonably raise with respect to the stars, we should try to state what we think about them. In so doing we deem it proper that a person's readiness to consider questions of this kind should be attributed rather to respect [shame], i.e., to seemliness or modesty, than to boldness, i.e., presumption, if the one who tackles these doubts welcomes even small sufficiencies, i.e., reasons that are only slightly sufficient, to discover the truth about these matters concerning which we have very great difficulties, and does this because of what he desires in philosophy, namely, that its principle may stand, i.e., abide firmly.

451. Then, at of many such problems (291b28), he presents the two difficulties:

the second of which begins at a second difficulty (292a10; [456]).

With regard to the first he does two things:

first, he raises the question;

secondly, he proves something he had presupposed, at as observation has itself revealed (292a3; [455]).

With respect to the first (291b28) there are three things to be considered for the understanding of this difficulty.

The first of these is that Aristotle is seen to assign to the planets an order different from that of the astronomers of our time. For the earliest astronomers took Saturn as the outermost planet and after it Jupiter; Mars they put third, the Sun fourth, Venus fifth, Mercury sixth, and the Moon seventh. But the astronomers of Plato's and Aristotle's time changed this order as to the Sun, by putting it immediately above the Moon and under Venus and Mercury, which positing Aristotle follows here. Later on, Ptolemy corrected this order of the planets by showing that what the earlier astronomers said was truer, and this is the opinion held by current astronomers.

Secondly, we must keep in mind that certain anomalies, i.e., irregularities, appear with respect to the motions of the planets. For the planets seem to be now swifter, now slower, now stationary, now retrogressing. Now this does not seem to be appropriate to heavenly motions, as is evident from what has been said above. Therefore, Plato first proposed this problem to an astronomer of his time, named Eudoxus, who tried to reduce these irregularities to a right order by assigning diverse motions to the planets; a project also undertaken by later astronomers in various ways. Yet it is not necessary that the various suppositions which they hit upon be true—for although these suppositions save the appearances, we are nevertheless not obliged to say that these suppositions are true, because perhaps there is some other way men have not yet grasped by which the things which appear as to the stars are saved. Aristotle nevertheless uses suppositions of this kind, in what regards the quality of the motions, as true.

The third thing that must be considered is that not as many kinds of irregularities appear with respect to the sun and moon as with the other planets: for the sun and moon never appear to be stationary or to undergo retrograde movement as do the other planets, but present only swiftness and slowness. Accordingly, Eudoxus, who at Plato's request first tried to straighten out these irregularities, assigned fewer motions to the sun and moon, which he called the lowest planets, than to the higher ones. To each of these he assigned four movements, according to the four spheres that revolved the stellar body fixed in the lowest of them. Thus the first sphere moves the stellar body from east to west according to the diurnal motion; the second moves the stellar body in the opposite direction of west to east in the Zodiac—and this is called longitudinal motion; the third sphere moves a stellar body latitudinally, according to which a star is now in a more southerly, now a more northerly, position in the Zodiac. Now he placed the poles of this third sphere in the Zodiac; hence it followed that a major circle, equidistant from the poles, would go through the poles of the Zodiac. From this it seemed to follow that the planets in their latitudinal motion would sometimes reach the very poles of the Zodiac—a situation that never appears. Hence, he posited a fourth sphere that would move a star in an opposite direction to this movement and thus prevent it from ever reaching the poles of the Zodiac. He did not, however, attribute the motion of this fourth sphere to the sun and the moon, but tried to save their appearances by positing only three spheres, proportional to the first three of the other planets, but in such a way that the latitudinal motion of the moon would be greater than the sun's, as is explained in Metaphysics XII.

452. With these considerations in mind Aristotle here formulates a question. And he says that while there are many such doubtful matters about the stars, not the least to be wondered at is why the stars farther from the motion of the first sphere are not always moved with a greater number of motions, but rather the intermediate ones are moved with the most, namely, the five planets, which, according to Eudoxus' theory, are moved with four motions. For it seems to be reasonable, if the first sphere is moved with one motion alone, that the star nearest it should be moved with the fewest motions, say two, and the had, i.e., the next, with three or in some such progression. But now it is the contrary that happens according to Eudoxus' theory, which attributes fewer motions, i.e., only three, to the sun and moon than to some of the wandering stars which he posits as having four motions, although the five planets are farther from the middle [center] of the universe, i.e., from the earth, and closer to the first body, i.e., the outermost sphere, than they, i.e., than the sun and moon are, according to the opinion prevalent in Plato's and Aristotle's time.

453. One should further know that, since the suppositions of Eudoxus could not save all the appearances concerning the stars, another astronomer named Callippus, at Aristotle's behest, corrected Eudoxus' suppositions. He added to Mars and Venus and Mercury one sphere and one motion apiece, and to the Sun and Moon two apiece. Thus to Saturn and Jupiter four motions were now assigned, and to each of the lower planets five. Consequently, the problem raised here by Aristotle would no longer be a problem, because the higher planets, according to this supposition, are now moved with fewer motions than the lower ones. Moreover, to each of the planets he also assigned certain other revolving spheres, as is explained in Metaphysics XII.

454. But even this theory could not account for all the appearances about the stars, especially as to their being near and far away from us—which is grasped from the fact that under the same disposition of the air, the planets are seen at one time larger and at another time smaller. Also it seemed unacceptable that such a multitude of spheres should concur in order to move the planets. It seemed especially superfluous to assign to each planet a sphere to revolve it from east to west with its diurnal motion when this could be caused by the highest sphere revolving the entire heaven with this motion.

Therefore Hipparchus and Ptolemy posited for each planet a single sphere which however was not concentric with the supreme sphere but had a center other than the earth, [i.e., an "eccentric"], in such a way that when the planet is in that portion of the sphere that is farther from us, the body of the planet is seen as smaller and slower moving; but when it is in the opposite region, it is seen as larger and faster. In addition to this, they posited certain small circles which they call epicycles, which are in motion upon these spheres in such a way that the bodies of the planets are in motion in these epicycles, not as though fixed in such circles, but as though turning through them with a progressive motion. Thus, in addition to the diurnal motion which they attribute to the entire heaven as due to the motion of the first sphere, they attribute to four planets, namely, Saturn, Jupiter, Mars and Venus, three motions apiece: according to one, the stellar body makes the circuit of its epicycle; according to the second, the center of the epicycle circles the sphere; according to the third, the sphere itself is moved from west to east, every hundred years, the distance of one degree in relation to the motion of the fixed stars. This last motion [the precession of the equinox], is called the motion of the increase [augus], or of the apogee, i.e., of the maximum distance in the eccentric circle. Now they add to Mercury, in addition to these motions, a fourth, according to which they say that the center of its sphere is moved in a small circle about the center of the world. They also attribute these four to the Moon with the addition of a fifth. For since the circle of the lunar sphere, along which the center of its epicycle is thought to be in motion, declines from the Zodiac to the south and to the north, it is necessary for this circle to intersect the Zodiac at two points called nodes or head and tail. It is only when the moon is present at these points that eclipses of the sun and of the moon can occur; and these do not always occur at the same place on the circle. This, therefore, caused them to posit a fifth motion in the moon according to which the aforesaid nodes are moved, and this is called the movement of the head and tail. But they do not say the body of the sun to be moved in any epicycle, but in its own eccentric. Hence, they endowed the sun with just two motions: one, whereby the body of the sun is moved in the eccentric; the other is the motion of apogee which they assign to the sphere of the sun, just as they assign it to the spheres of the other planets.

Thus it is evident that the problem Aristotle raises, arises also from the above position. For according to this supposition, Mercury and the Moon, the lowest of the planets, have the most motions, whereas the sun, which they place as intermediate, has the fewest, with the remaining planets being in between.

455. Then, at as observation has itself revealed (292a3), he proves something he had supposed, namely, that the order of the planets is as he had described. First he proves it in one respect by means of something he had witnessed. And he says that the order of certain of the planets is evident even to sight. For he says that he saw the moon when it was dichotomous, i.e., with half its face illumined, move in under the star of Mars (for its motion is swifter than Mars'), and the moon according to its blackness, i.e., according to that side which was darkened, concealed Mars, and Mars came out from under the moon passing it according to the bright and shining side of the moon.

Secondly, at similar accounts (292a7) he shows other details about the order of the planets through observations which others have made. And he says that others state themselves to have witnessed similar things concerning the order of the other planets, namely, those who from much time back have observed such things for many years, i.e., the Egyptians and Babylonians, whose study was concerned most with astronomy. From what they say we have many trustworthy statements about each of the stars, based on their observations.

456. Then, at a second difficulty (292a10), he raises the second difficulty. And he says that with good reason one can wonder why it is that in the first sphere, which is moved by the first motion, there is such a great multitude of stars that their whole order appears to be of the arithmetical, i.e., of things innumerable (for their number cannot be comprehended by us), whereas in the lower orbs we find one solitary star in each so that two or more of the wandering stars are not seen fixed in one mobile sphere.

Here one should note that in Aristotle's time no motion had yet been discovered in the fixed stars, which Ptolemy posits as moved from west to east upon the poles of the Zodiac one degree every 100 years, so that they complete one full revolution in 36,000 years. Hence the ancients posited the sphere of the fixed stars as the first mobile and as endowed with but one motion, the diurnal. But if we assume a motion of the fixed stars, then this sphere must be moved by two motions: by its own motion, which is the motion of the fixed stars, and by the diurnal motion, which is the motion of the outermost sphere, which is without stars.

457. Then, at on these questions, I say (292a14), he shows the difficulty of these questions. He says that it is good to investigate these doubtful matters, and adds, for a greater understanding. This text, says Alexander, is defective, and one should understand it as meaning that whatever in these matters is too much for our intelligence one must simply accept, rather than make them a subject of further investigation by ourselves. But it is not Aristotle's custom, in spite of his laconic style, to employ defective language, as Simplicius says. Hence he explains it to the effect that, while it is good to investigate such things, it is not a task suited to just anyone but only those of wider understanding. However, Averroes in his Commentary explains it this way: namely, that we should understand that to investigate these matters is both good in itself, and also contributes to man's growth in understanding Therefore a person who exercises his mind by trying to understand difficult matters, can better understand others, as is said in On the Soul III.

Now the matters to be investigated are difficult, because we can perceive only a little about their causes; and their accidents are further removed from our ken than the bodies themselves are physically distant from us. Yet, if what we shall say enables us to contemplate the truth of these doubtful matters, then what seemed to be doubtful at the beginning of our inquiry will be seen not to be devoid of all explanation.