Lecture 2 — Diversity of parts of the heaven as to position. Opinion of Pythagoras

224 Since there are some who say that there is a right and a left in the heaven, with those who are known as Pythagoreans—to whom indeed the view really belongs—we must consider whether, if we are to apply these principles to the body of the universe, we should follow their statement of the matter or find a better way. At the start we may say that, if right and left are applicable, there are prior principles which must first be applied.

225 These principles have been analysed in the discussion of the movements of animals, for the reason that they are proper to animal nature. For in some animals we find all such distinctions of parts as this of right and left clearly present, and in others some; but in plants we find only above and below.

226 Now if we are to apply to the heaven such a distinction of parts, we must exect, as we have said, to find in it also the distinction which in animals is found first of them all. The distinctions are three, namely, above and below, front and its opposite, right and left—all these three oppositions we expect to find in the perfect body—and each may be called a principle.

227 Above is the principle of length, right of breadth, front of depth.

228 Or again we may connect them with the various movements, taking principle to mean that part, in a thing capable of movement, from which movement first begins. Growth starts from above, locomotion from the right, sensemovement from in front (for front is simply the part to which the senses are directed).

229 Hence we must not look for above and below, right and left, front and back, in every kind of body, but only in those which, being animate, have a principle of movement within themselves. For in no inanimate thing do we observe a part from which movement originates. Some do not move at all, some move, but not indifferently in any direction; fire, for example, only upward, and earth only to the center.

230 It is true that we speak of above and below, right and left, in these bodies relatively to ourselves. The reference may be to our own right hands, as with the diviner, or to some similarity to our own members, such as the parts of a statue possess; or we may take the contrary spatial order, calling right that which is to our left, and left that which is to our right. We observe, however, in the things themselves none of these distinctions; indeed if they are turned round we proceed to speak of the opposite parts as right and left, [a boy land] below, front and back.

231 Hence it is remarkable that the Pythagoreans should have spoken of these two principles, right and left, only, to the exclusion of the other four, which have as good a title as they.

232 There is no less difference between above and below or front and back in animals generally than between right and left. The difference is sometimes only one of function, sometimes also one of shape;

233 and while the distinction of above and below is characteristic of all animate things, whether plants or animals, that of right and left is not found in plants.

234 Further, inasmuch as length is prior to breadth, if above is the principle of length, right of breadth, and if the principle of that which is prior is itself prior, then above will be prior to right, or let us say, since 'prior' is ambiguous, prior in order of generation.

235 If, in addition, above is the region from which movement originates, right the region in which it starts, front the region to which it is directed, then on this ground too above has a certain original character as compared with the other forms of position. On these two grounds, then, they may fairly be criticized, first, for omitting the more fundamental principles, and secondly, for thinking that the two they mentioned were attributable equally to everything.

300. After settling the question of the perpetuity of the heavens, the Philosopher here determines the question of the variety of its parts.

First he determines the question of the diversity of parts considered from the viewpoint of their respective position in the same heaven;

secondly, as considered from the relationship of the various heavenly bodies one to the other, at since circular motion is not the contrary (L. 4; 286a3).

As to the first he does two things:

first he determines concerning the diversity of the positional parts of the heaven according to the opinions of others;

secondly, according to his own opinion, at since we have already determined (L. 3; 285a27).

As to the first he does two things:

first he states his intention;

secondly, he manifests his proposition, at these principles have been analysed (284b13; [301]).

He says therefore first (284b6) that because some assert that one part of the heaven is on the right and another on the left, namely, the Pythagoreans, who put a right and a left in all things, it seems necessary to inquire whether things are as they assert or whether one should not rather attribute such things in a way different from theirs—if indeed it be necessary to apply these principles, i.e., right and left, to the body of the entire world by virtue of their being found in the heavenly body, which encompasses the whole world. The reason why this matter should be considered is that it immediately occurs to a man that if there is a right and a left in the heaven, then there is even a greater reason and a prior one for thinking the prior principles are in the heaven, namely, up and down, before and behind.

301. Then, at these principles have been analysed (284b13), he manifests this proposition.

First, he explains the condition of these principles as found in other things;

secondly, that they are not found in all bodies, at hence we must not look for (284b30; [305]).

As to the first he does two things:

first he shows that not all the aforesaid principles are found in all things;

secondly, he explains in what order they are mutually related, at above is the principle (284b24; [303]).

As to the first he does two things:

first he shows that all these principles are not found in everything, but in some things some only and not all;

secondly, that it would be entirely unfitting that some, but not all, be attributed to the heaven, at now if we are to apply to the heaven (284b18; [302]).

He says therefore first (284b13) that these principles, which are called differences of position, have been dealt with in the book De Processu Animalium, since they are peculiar to such natures, namely, those of animals. For these differences of position are clearly found in animals according to definite parts. For some animals, namely, the perfect, which not only sense but move with local motion, possess all these parts, namely, right and left, before and behind, above and below; other animals, namely, the imperfect and stationary, possess some of them, namely, above and below, before and behind; while plants have only above and below.

302. Then, at now if we are to apply to the heaven (284b18), he shows that if any of them are assigned to the heaven, then all must be. And he explains that if we must assign any to the heaven, namely, either right or left, it is reasonable to suppose that that would be found which is found first in perfect animals; or it is reasonable that the heaven should possess that which is first in animals, because if we posit what is subsequent, we must posit what is prior. Now since there are three oppositions or dimensions, each of them, namely, above, before and right is a certain principle of its opposite or dimension. He subsequently expounds the three he has stated to be: one of these is the opposition or dimension between up and down, in which "up" is the principle; another is between before and its opposite, which is called "behind," where what is before is the principle; yet another is between right and left, in which "right" is the principle. Now, since the perfect is that which is composed of all its parts or principles, it is reasonable that all these oppositions or dimensions should be found in perfect bodies, i.e., in perfect animals. Hence, since the heaven is perfect above all, it is reasonable that if it be capable of any of these parts, it should have them all and not just some.

303. Then at above is the principle (284b24) he explains in two ways the order of the aforesaid principles.

First, from the viewpoint of the dimensions themselves. For "up" is the principle of length: in man who is the most perfect animal, his length, as though his greatest dimension, is said from the head, which is his "up," to the feet, which are his "down." "Right" is the principle of width, for the width of a man is reckoned according to the distance between his right and his left. "Before" is the principle of depth: for the depth or thickness of a man is reckoned according to the distance between before and behind. The same holds respectively in other animals. But length is prior to width, and width to depth, just as line is to plane, and plane to body. Therefore, "above" is prior to "right," and "right" is prior to "before."

304. Secondly, he proves the same thing, at or again we may connect them (284b25) from the viewpoint of motions. He does this because the things we have been discussing are certain principles from which motion first begins in animals that possess such parts or principles. For the motion of growth begins from above. This is evident in man, for the head, which is the "up" of man, is also up according to the position of the universe. Now the motion of growth begins from the head, because food is taken into the opening of the mouth, which is in the head, and food is the matter of growth. In plants, however, it is the root which is "up," and this is parallel to the head in animals, as far as the taking in of food is concerned. However, the "up" of a plant is opposite as to position to what is "up" for the universe. The other animals are midway between man and plants. Now motion with respect to place begins from the right, for animals move the right part before the left, as in walking they move the right foot. But in the motion by which the senses are altered, "before" is the principle, for that is said to be the forepart of the animal where the senses exist. Therefore, since the motion of growth is prior to the motion of sensation, which in turn is prior to local motion in animals, it follows that "above" is prior to "before," and "before" prior to "right."

305. Then, at hence we must not look for (284b30), he shows that these principles are not present in all bodies.

First he concludes from the foregoing that, strictly speaking, these principles do not exist in non-living bodies;

secondly, he explains how we come to speak of them as being therein, at it is true that we speak of above (285a1; [306]).

He says therefore first (284b30) that since the foregoing are principles of certain motions, we should not look for above and below, right and left, before and behind, in all bodies, but only in animate bodies having a principle of motion in themselves. Now we do not find in any non-living body any originative source of motion. This can be understood in two ways. First, in the sense that there is in living things an active principle of motion, namely, the soul, while in non-living bodies there is no such active principle of motion which could move, but such things are moved by an external mover, which is the generator or that which removes what prevents motion. Yet they do have a passive principle of motion within, by which they are apt to be moved, for example, heaviness or lightness, as is plain in Physics VIII. Or it can mean that in living bodies there is a definite part from which the motion begins, as has been said. But such a part is not found in non-living bodies. For, as he further says, some non-living bodies are not in motion at all, for example, those that already exist in their own place (or rather he says this with respect to artificial bodies which, as such, have no motion of themselves). Others are in motion, for example, the ones that are outside their own appropriate place, yet each such body is moved to its place in a similar way for each part. For example, fire is moved only upwards and earth only to the center of the world. In these cases no other difference of position is considered, either on the part of the body which is moved, so that one part would begin to be moved before another, or even on the part of the place, so that a natural thing would be moved to its own place from one position in space and not from another.

306. Then, at it is true that we speak of above (285a1) he shows how these positions are sometimes said to exist in non-living bodies. And he says that in such bodies we speak of above and below, right and left, before and behind, only in comparison to ourselves. And this can take place in three ways. In one way, as we call that the right which is opposite to our right, as diviners, e.g., augurs, refer to a bird on our right, as the right bird and one on our left as the left bird. The second way is based on a likeness to our parts, as we call the right of a statue that which is similar to the right of man and the left that which is similar to our left. The third way is by a contrary position, as when we call the left what is opposite to our right, and what is opposite to our left we call right, as is plain in the case of an image in a mirror. The same explanations apply to the other positions. But in non-living things considered in themselves, there is no such variation of parts. And this is evident from the fact that if we turn them toward us, the designations will be the opposite of what they were previously: what was right is now called left and vice-versa, and the same goes for the other positions. But in living things, no matter how they are turned about, these parts remain always the same.

307. Then, at hence it is remarkable that the Pythagoreans (285a10) he shows that the Pythagoreans erred in attributing these differences to the heaven, and this in three ways, which can be gathered from the above reasoning. Consequently he adduces them here as conclusions.

The first way is that, whereas there are six positions, one wonders why only two of them are attributed to the heaven, namely, the right and left, and the other four are ignored—although it is reasonable that all of them belong to the heaven, as was said above.

308. The second way is given at to the exclusion of the other four (285a10), namely, that if any are to be omitted and not attributed to the heaven, it is the less principal ones which ought to have been omitted. But that the ones omitted are not less principal than the two attributed he proves with four arguments.

The first argument is given at there is no less difference (285a13), namely, that in certain animals we do not observe that the difference between the part above and the part below, or between the part in front and the part to the rear, is less than the difference between the right side and the left side; rather, the difference is greater. For the right and left differ only in power but agree in figure (for the right hand is stronger than the left, although they are of the same shape; similarly, the right shoulder is stronger than the left as far as motions are concerned, although the left is stronger than the right for carrying a burden; in like manner, the right foot is better for motion, but the left is better for maintaining a fixed position). But it is plain that the front and rear of an animal, as well as the top and bottom, differ not only in power, but in shape as well. Now things that differ more appear to have a more principal distance.

309. The second argument is at and while the distinction of above and below (285a16), namely, that top and bottom are found in all living bodies, whether animal or plant; but right and left are not in plants but only in perfect animals. Consequently, up and down are prior, where "prior" implies a non-convertible dependence in existence [on the part of the non-prior].

310. The third argument is at further, inasmuch as length is prior to breadth (285a19), namely, that length is prior to width in the order of generation, for, according to geometers, a line in motion makes a surface. But "up" is a principle of length, and "right" a principle of width, as was explained above. Therefore, since the source of what is prior is itself prior, the consequence is that "up" is prior to "right," in the sense of something prior in the order of generation (for there are many ways in which things are said to be prior to others, as is plain in Predicaments and in Metaphysics V.

311. The fourth argument, at if, in addition, above (285a22) says that "up" is an originative source of motion, which may be understood of the motion of growth; "right" is the source of local motion; "before" is that toward which an animal moves, as though being opposite to its senses. From this it is clear that "up" has a certain chief role among all the types of position, just as the motion of growth is more essential and more intrinsic to an animal than is local motion. Nevertheless, everything stated here may be better referred to local motion, by stating that "pup," in an animal which moves according to local motion, is that whence motion proceeds, since it is in the head, namely, that sense functions and sense is the moving principle in animals, as stated in De Anima III. But "right" is that whence local motion begins, since the right part moves first, as was said, while "before" is that toward which the animal is moved. But the moving principle is that which has the primacy in the motion of an animal. In keeping with this it is evident that "up" has the primacy among the other types of position.

Thus does the Philosopher by means of these four arguments conclude his second way of disproving the assertion of the Pythagoreans. And he says it is just to rebuke them, since they ignored the more important principles and did not attribute them to the heaven.

312. He presents his third way at secondly, for thinking that the two (285a22), saying that they should be rebuked also for claiming that right and left are found similarly in all things, whereas in truth they are found only in perfect animals, as was said above.

But it should be kept in mind that it was the Pythagoreans' intent to reduce all things to good and evil as to two principles. And because they believed that all number is encompassed by 10, they posited ten things on the side of good and ten on the side of evil, as is plain in Metaphysics I. By each thing they placed in that enumeration they understood all the things to be found in its genus. Thus by "right" and "left" they understood all other positions, understanding that just as "right" is referred to good, so also "up" and "before," while "left," "down," and "behind" referred to evil. The reason why they posited right and left, rather than the other positions, was that the right is according to custom more obviously referred to the good and the left to evil — for we are accustomed to call good fortune "right" and evil "left" [i.e., "sinister"]. Consequently, they attributed right and left to all things to which they attributed good and evil. Or perhaps they mentioned only right and left, as including the others in them, because they saw that whatever possessed a right and a left possessed all the others, but not vice-versa. Likewise they perchance especially applied to the heaven a right and a left and not the others, because there is in the heaven a local motion, to which right and left belong, but no growth, or sense alteration, to which up and down, before and behind belong respectively. Or perhaps it was because up and down, before and behind, are diversified with respect to shape, whereas right and left are not—for the parts of the heaven, being circular, are uniform in shape.