151. The existence of the antichthon was also a hypothesis intended to account for the phenomena of eclipses. In one place, indeed, Aristotle says that the Pythagoreans invented it in order to bring the number of revolving bodies up to ten;[[830]] but that is a mere sally, and Aristotle really knew better. In his work on the Pythagoreans, we are told, he said that eclipses of the moon were caused sometimes by the intervention of the earth and sometimes by that of the antichthon; and the same statement was made by Philip of Opous, a very competent authority on the matter.[[831]] Indeed, Aristotle shows in another passage exactly how the theory originated. He tells us that some thought there might be a considerable number of bodies revolving round the centre, though invisible to us because of the intervention of the earth, and that they accounted in this way for there being more eclipses of the moon than of the sun.[[832]] This is mentioned in close connexion with the antichthon, so there is no doubt that Aristotle regarded the two hypotheses as of the same nature. The history of the theory seems to be this. Anaximenes had assumed the existence of dark planets to account for the frequency of lunar eclipses ([§ 29]), and Anaxagoras had revived that view ([§ 135]). Certain Pythagoreans[[833]] had placed these dark planets between the earth and the central fire in order to account for their invisibility, and the next stage was to reduce them to a single body. Here again we see how the Pythagoreans tried to simplify the hypotheses of their predecessors.
Planetary motions.
152. We must not assume that even the later Pythagoreans made the sun, moon, and planets, including the earth, revolve in the opposite direction to the heaven of the fixed stars. It is true that Alkmaion is said to have agreed with “some of the mathematicians”[[834]] in holding this view, but it is never ascribed to Pythagoras or even to Philolaos. The old theory was, as we have seen ([§ 54]), that all the heavenly bodies revolved in the same direction, from east to west, but that the planets revolved more slowly the further they were removed from the heavens, so that those which are nearest the earth are “overtaken” by those that are further away. This view was still maintained by Demokritos, and that it was also Pythagorean, seems to follow from what we are told about the “harmony of the spheres.” We have seen ([§ 54]) that we cannot attribute this theory in its later form to the Pythagoreans of the fifth century, but we have the express testimony of Aristotle to the fact that those Pythagoreans whose doctrine he knew believed that the heavenly bodies produced musical notes in their courses. Further, the velocities of these bodies depended on the distances between them, and these corresponded to the intervals of the octave. He distinctly implies that the heaven of the fixed stars takes part in the concert; for he mentions “the sun, the moon, and the stars, so great in magnitude and in number as they are,” a phrase which cannot refer solely or chiefly to the remaining five planets.[[835]] Further, we are told that the slower bodies give out a deep note and the swifter a high note.[[836]] Now the prevailing tradition gives the high note of the octave to the heaven of the fixed stars,[[837]] from which it follows that all the heavenly bodies revolve in the same direction, and that their velocity increases in proportion to their distance from the centre.
The theory that the proper motion of the sun, moon, and planets is from west to east, and that they also share in the motion from east to west of the heaven of the fixed stars, makes its first appearance in the Myth of Er in Plato’s Republic, and is fully worked out in the Timaeus. In the Republic it is still associated with the “harmony of the spheres,” though we are not told how it is reconciled with that theory in detail.[[838]] In the Timaeus we read that the slowest of the heavenly bodies appear the fastest and vice versa; and, as this statement is put into the mouth of a Pythagorean, we might suppose the theory of a composite movement to have been anticipated by some members at least of that school.[[839]] That is, of course, possible; for the Pythagoreans were singularly open to new ideas. At the same time, we must note that the theory is even more emphatically expressed by the Athenian Stranger in the Laws, who is in a special sense Plato himself. If we were to praise the runners who come in last in the race, we should not do what is pleasing to the competitors; and in the same way it cannot be pleasing to the gods when we suppose the slowest of the heavenly bodies to be the fastest. The passage undoubtedly conveys the impression that Plato is expounding a novel theory.[[840]]
Things likenesses of numbers.
153. We have still to consider a view, which Aristotle sometimes attributes to the Pythagoreans, that things were “like numbers.” He does not appear to regard this as inconsistent with the doctrine that things are numbers, though it is hard to see how he could reconcile the two.[[841]] There is no doubt, however, that Aristoxenos represented the Pythagoreans as teaching that things were like numbers,[[842]] and there are other traces of an attempt to make out that this was the original doctrine. A letter was produced, purporting to be by Theano, the wife of Pythagoras, in which she says that she hears many of the Hellenes think Pythagoras said things were made of number, whereas he really said they were made according to number.[[843]] It is amusing to notice that this fourth-century theory had to be explained away in its turn later on, and Iamblichos actually tells us that it was Hippasos who said number was the exemplar of things.[[844]]
When this view is uppermost in his mind, Aristotle seems to find only a verbal difference between Plato and the Pythagoreans. The metaphor of “participation” was merely substituted for that of “imitation.” This is not the place to discuss the meaning of Plato’s so-called “theory of ideas”; but it must be pointed out that Aristotle’s ascription of the doctrine of “imitation” to the Pythagoreans is abundantly justified by the Phaedo. The arguments for immortality given in the early part of that dialogue come from various sources. Those derived from the doctrine of Reminiscence, which has sometimes been supposed to be Pythagorean, are only known to the Pythagoreans by hearsay, and Simmias requires to have the whole psychology of the subject explained to him.[[845]] When, however, we come to the question what it is that our sensations remind us of, his attitude changes. The view that the equal itself is alone real, and that what we call equal things are imperfect imitations of it, is quite familiar to him.[[846]] He requires no proof of it, and is finally convinced of the immortality of the soul just because Sokrates makes him see that the theory of forms implies it.
It is also to be observed that Sokrates does not introduce the theory as a novelty. The reality of the “ideas” is the sort of reality “we are always talking about,” and they are explained in a peculiar vocabulary which is represented as that of a school. The technical terms are introduced by such formulas as “we say.”[[847]] Whose theory is it? It is usually supposed to be Plato’s own, though nowadays it is the fashion to call it his “early theory of ideas,” and to say that he modified it profoundly in later life. But there are serious difficulties in this view. Plato is very careful to tell us that he was not present at the conversation recorded in the Phaedo. Did any philosopher ever propound a new theory of his own by representing it as already familiar to a number of distinguished living contemporaries? It is not easy to believe that. It would be rash, on the other hand, to ascribe the theory to Sokrates, and there seems nothing for it but to suppose that the doctrine of “forms” (εἴδη, ἰδέαι) originally took shape in Pythagorean circles, perhaps under Sokratic influence. There is nothing startling in this. It is a historical fact that Simmias and Kebes were not only Pythagoreans but disciples of Sokrates; for, by a happy chance, the good Xenophon has included them in his list of true Sokratics.[[848]] We have also sufficient ground for believing that the Megarians had adopted a like theory under similar influences, and Plato states expressly that Eukleides and Terpsion of Megara were present at the conversation recorded in the Phaedo. There were, no doubt, more “friends of the ideas”[[849]] than we generally recognise. It is certain, in any case, that the use of the words εἴδη and ἰδέαι to express ultimate realities is pre-Platonic, and it seems most natural to regard it as of Pythagorean origin.[[850]]
We have really exceeded the limits of this work by tracing the history of Pythagoreanism down to a point where it becomes practically indistinguishable from the earliest form of Platonism; but it was necessary to do so in order to put the statements of our authorities in their true light. Aristoxenos is not likely to have been mistaken with regard to the opinions of the men he had known personally, and Aristotle’s statements must have had some foundation. We must assume, then, a later form of Pythagoreanism which was closely akin to early Platonism. That, however, is not the form of it which concerns us here, and we shall see in the next chapter that the fifth-century doctrine was of the more primitive type already described.