c. The Pythagoreans further constructed the heavenly bodies of the visible universe by means of numbers, and here we see at once the barrenness and abstraction present in the determination of numbers. Aristotle says (Met. I. 5), “Because they defined numbers to be the principles of all nature, they brought under numbers and their relationships all determinations and all sections, both of the heavens and of all nature; and where anything did not altogether conform, they sought to supply the deficiency in order to bring about a harmony. For instance, as the Ten or dekad appeared to them to be the perfect number, or that which embraces the whole essence of numbers, they said that the spheres moving in the heavens must be ten; but as only nine of these are visible, they made out a tenth, the Antichthone (ἀντίχθονα).” These nine are, first the milky way, or the fixed stars, and after that the seven stars which were then all held to be planets: Saturn, Jupiter, Mars, Venus, Mercury, the Sun, Moon, and in the last and ninth place, the Earth. The tenth is thus the Antichthone, and in regard to this it must remain uncertain whether the Pythagoreans considered it to be the side of the Earth which is turned away, or as quite another body.
Aristotle says, in reference to the specially physical character of these spheres (De cœlo II. 13 and 9), “Fire was by the Pythagoreans placed in the middle, but the Earth was made a star that moved around this central body in a circle.” This circle is, then, a sphere, which, as the most perfect of figures, corresponds to the dekad. We here find a certain similarity to our ideas of the solar system, but the Pythagoreans did not believe the fire to be the sun. “They thus,” says Aristotle, “rely, not on sensuous appearance, but on reasons,” just as we form conclusions in accordance with reasons as opposed to sensuous appearances; and indeed this comes to us still as the first example of things being in themselves different from what they appear. “This fire, that which is in the centre, they called Jupiter’s place of watch. Now these ten spheres make, like all that is in motion, a tone; but each makes a different one, according to the difference in its size and velocity. This is determined by means of the different distances, which bear an harmonious relationship to one another, in accordance with musical intervals; by this means an harmonious sound arises in the moving spheres”—a universal chorus.
We must acknowledge the grandeur of this idea of determining everything in the system of the heavenly spheres through number-relations which have a necessary connection amongst themselves, and have to be conceived of as thus necessarily related; it is a system of relations which must also form the basis and essence of what can be heard, or music. We have, comprehended here in thought, a system of the universe; the solar system is alone rational to us, for the other stars are devoid of interest. To say that there is music in the spheres, and that these movements are tones, may seem just as comprehensible to us as to say that the sun is still and the earth moves, although both are opposed to the dictates of sense. For, seeing that we do not see the movement, it may be that we do not hear the notes. And there is little difficulty in imagining a universal silence in these vast spheres, since we do not hear the chorus, but it is more difficult to give a reason for not hearing this music. The Pythagoreans say, according to the last quoted passage of Aristotle, that we do not hear it because we live in it, like the smith who gets accustomed to the blows of his hammer. Since it belongs to our substance and is identical with ourselves, nothing else, such as silence, by which we might know the other, comes into relationship with us, for we are conceived of as entirely within the movement. But the movement does not become a tone, in the first place, because pure space and time, the elements in movement, can only raise themselves into a proper voice, unstimulated from without, in an animate body, and movement first reaches this definite, characteristic individuality in the animal proper; and, in the next place, because the heavenly bodies are not related to one another as bodies whose sound requires for its production, contact, friction, or shock, in response to which, and as the negation of its particularity its own momentary individuality resounds in elasticity; for heavenly bodies are independent of one another, and have only a general, non-individual, free motion.
We may thus set aside sound; the music of the spheres is indeed a wonderful conception, but it is devoid of any real interest for us. If we retain the conception that motion, as measure, is a necessarily connected system of numbers, as the only rational part of the theory, we must maintain that nothing further has transpired to the present day. In a certain way, indeed, we have made an advance upon Pythagoras. We have learned from Kepler about laws, about eccentricity, and the relation of distances to the times of revolution, but no amount of mathematics has as yet been able to give us the laws of progression in the harmony through which the distances are determined. We know empirical numbers well enough, but everything has the semblance of accident and not of necessity. We are acquainted with an approximate rule of distances, and thus have correctly foretold the existence of planets where Ceres, Vesta, Pallas, &c., were afterwards discovered—that is, between Mars and Jupiter. But astronomy has not as yet found in it a consistent sequence in which there is rationality; on the other hand, it even looks with disdain on the appearance of regularity presented by this sequence, which is, however, on its own account, a most important matter, and one which should not be forgotten.
d. The Pythagoreans also applied their principle to the Soul, and thus determined what is spiritual as number. Aristotle (De anim. I. 2) goes on to tell that they thought that solar corpuscles are soul, others, that it is what moves them; they adopted this idea because the corpuscles are ever moving, even in perfect stillness, and hence they must have motion of their own. This does not signify much, but it is evident from it that the determination of self-movement was sought for in the soul. The Pythagoreans made a further application of number-conceptions to the soul after another form, which Aristotle describes in the same place as follows:—“Thought is the one, knowledge or science is the two, for it comes alone out of the one. The number of the plane is popular idea, opinion; the number of the corporeal is sensuous feeling. Everything is judged of either by thought, or science, or opinion, or feeling.” In these ideas, which we must, however, ascribe to later Pythagoreans, we may undoubtedly find some adequacy, for while thought is pure universality, knowledge deals with something “other,” since it gives itself a determination and a content; but feeling is the most developed in its determinateness. “Now because the soul moves itself, it is the self-moving number,” yet we never find it said that it is connected with the monad.
This is a simple relationship to number-determinations. Aristotle instances (De anim. I. 3) one more intricate from Timæus: “The soul moves itself, and hence also the body because it is bound up with body; it consists of elements and is divided according to harmonic numbers, and hence it has feeling and an immediately indwelling (σύμφυτον) harmony. In order that the whole may have an harmonious movement, Timæus has bent the straight line of harmony (εὐθυωρίαν) into a circle, and again divided off from the whole circle two circles, which are doubly connected; and the one of these circles is again divided into seven circles, so that the movements of the soul may resemble those of the heavens.” The more definite significance of these ideas Aristotle unfortunately has not given; they contain a profound knowledge of the harmony of the whole, but yet they are forms which themselves remain dark, because they are clumsy and unsuitable. There is always a forcible turning and twisting, a struggle with the material part of the representation, as there is in mythical and distorted forms: nothing has the pliability of thought but thought itself. It is remarkable that the Pythagoreans have grasped the soul as a system which is a counterpart of the system of the heavens. In Plato’s Timæus this same idea is more definitely brought forward. Plato also gives further number-relations, but not their significance as well; even to the present day no one has been able to make any particular sense out of them. An arrangement of numbers such as this is easy, but to give to it a real significance is difficult, and, when done, it always must be arbitrary.
There is still something worthy of attention in what is said by the Pythagoreans in reference to the soul, and this is their doctrine of the transmigration of souls. Cicero (Tusc. Quæst. I. 16) says: “Pherecydes, the teacher of Pythagoras, first said that the souls of men were immortal.” The doctrine of the transmigration of souls extends even to India, and, without doubt, Pythagoras took it from the Egyptians; indeed Herodotus (II. 123) expressly says so. After he speaks of the mythical ideas of the Egyptians as to the lower world, he continues: “The Egyptians were the first to say that the soul of man is immortal, and that, when the body disappears, it goes into another living being; and when it has gone through all the animals of land and sea, and likewise birds, it again takes the body of a man, the period being completed in 3000 years.” Diogenes Laertius says in this connection (VIII. 14) that the soul, according to Pythagoras, goes through a circle. “These ideas,” proceeds Herodotus, “are also found amongst the Greeks; there are some who, earlier or later, have made use of this particular doctrine, and have spoken of it as if it were their own; I know their names very well, but I will not mention them.” He undoubtedly meant Pythagoras and his followers. In the sequel, much that is given utterance to is fictitious: “Pythagoras himself is said to have stated that his former personality was known to him. Hermes granted him a knowledge of his circumstances before his birth. He lived as the son of Hermes, Æthalides, and then in the Trojan war as Euphorbus, the son of Panthous, who killed Patroclus, and was killed by Menelaus; in the third place he was Hermotimus; fourthly, Pyrrhus, a fisherman of Delos; in all he lived 207 years. Euphorbus’ shield was offered up to Apollo by Menelaus, and Pythagoras went to the temple and, from the mouldering shield, showed the existence of signs, hitherto not known of, by which it was recognized.”[46] We shall not treat further of these very various and foolish stories.
As in the case of the brotherhood copied from the Egyptian priesthood, so must we here set aside this oriental and un-Greek idea of the transmigration of souls. Both were too far removed from the Greek spirit to have had a place and a development there. With the Greeks, the consciousness of a higher, freer individuality has become too strong to allow any permanence to the idea of metempsychosis, according to which, man, this independent and self-sufficing Being, takes the form of a beast. They have, indeed, the conception of men as becoming springs of water, trees, animals, &c., but the idea of degradation which comes as a consequence of sin, lies at its root. Aristotle (De anim. I. 3) shortly and in his own manner deals with and annihilates this idea of the Pythagoreans. “They do not say for what reason soul dwells in body, nor how the latter is related to it. For owing to their unity of nature when one acts the other suffers: one moves and the other is moved, but none of this happens in what is mutually contingent. According to the Pythagorean myths any soul takes to any body, which is much like making architects take to flutes. For crafts must necessarily have tools and soul body; but each tool must have its proper form and kind.” It is implied in the transmigration of souls that the organization of the body is something accidental to the human soul; this refutation by Aristotle is complete. The eternal idea of metempsychosis had philosophic interest only as the inner Notion permeating all these forms, the oriental unity which appears in everything; we have not got this signification here, or at best we have but a glimmering of it. If we say that the particular soul is, as a definite thing, to wander about throughout all, we find firstly, that the soul is not a thing such as Leibnitz’ Monad, which, like a bubble in the cup of coffee, is possibly a sentient, thinking soul; in the second place an empty identity of the soul-thing such as this has no interest in relation to immortality.
3. Practical Philosophy. As regards the practical philosophy of Pythagoras, which is closely connected with what has gone before, there is but little that is philosophic known to us. Aristotle (Magn. Moral. I. 1) says of him that “he first sought to speak of virtue, but not in the right way, for, because he deduced the virtues from numbers, he could not form of them any proper theory.” The Pythagoreans adopted ten virtues as well as ten heavenly spheres. Justice, amongst others, is described as the number which is like itself in like manner (ἴσακις ἴσος); it is an even number, which remains even when multiplied with itself. Justice is pre-eminently what remains like itself; but this is an altogether abstract determination, which applies to much that is, and which does not exhaust the concrete, thus remaining quite indeterminate.
Under the name of the “Golden words,” we have a collection of hexameters which are a succession of moral reflections, but which are rightly ascribed to later Pythagoreans. They are old, well-known, moral maxims, which are expressed in a simple and dignified way, but which do not contain anything remarkable. They begin with the direction “to honour the immortal gods as they are by law established,” and further, “Honour the oath and then the illustrious heroes;” elsewhere they go on to direct “honour to be paid to parents and to relatives,” &c.[47] Such matter does not deserve to be regarded as philosophy, although it is of importance in the process of development.