Chapter I: Period I.—division I.—thales to Anaxagoras (3)

It is at first in opposition to common reality that this idea of reality as the manifold of simple essence, has in itself its opposition and the subsistence of the same; this essential, simple Notion of reality is elevation into thought, but it is not flight from what is real, but the expression of the real itself in its essence. We here find the Reason which expresses its essence; and absolute reality is unity immediately in itself. Thus it is pre-eminently in relation to this reality that the difficulties of those who do not think speculatively have become so intense. What is its relation to common reality? What has taken place is just what happens with the Platonic Ideas, which approximate very closely to these numbers, or rather to pure Notions. That is to say, the first question is, “Numbers, where are they? Dispersed through space, dwelling in independence in the heaven of ideas? They are not things immediately in themselves, for a thing, a substance, is something quite other than a number: a body bears no similarity to it.” To this we may answer that the Pythagoreans did not signify anything like that which we understand by prototypes—as if ideas, as the laws and relations of things, were present in a creative consciousness as thoughts in the divine understanding, separated from things as are the thoughts of an artist from his work. Still less did they mean only subjective thoughts in our consciousness, for we use the absolute antithesis as the explanation of the existence of qualities in things, but what determines is the real substance of what exists, so that each thing is essentially just its having in it unity, duality, as also their antithesis and connection. Aristotle (Met. I. 5, 6) puts it clearly thus: “It is characteristic of the Pythagoreans that they did not maintain the finite and the infinite and the One, to be, like fire, earth, &c., different natures or to have another reality than things; for the Infinite and the abstract One are to them, the substance of the things of which they are predicated. Hence too, they said, Number is the essence of all things. Thus they do not separate numbers from things, but consider them to be things themselves. Number to them is the principle and matter of things, as also their qualities and forces;” hence it is thought as substance, or the thing as it is in the reality of thought.

These abstract determinations then became more concretely determined, especially by the later philosophers, in their speculations regarding God. We may instance Iamblichus, for example, in the work _θεολογούμενα ἀριθμητικῆς_, ascribed to him by Porphyry and Nicomachus. Those philosophers sought to raise the character of popular religion, for they inserted such thought-determinations as these into religious conceptions. By Monas they understood nothing other than God; they also call it Mind, the Hermaphrodite (which contains both determinations, odd as well as even), and likewise substance, reason, chaos (because it is undetermined), Tartarus, Jupiter, and Form. They called the duad by similar names, such as matter, and then the principle of the unlike, strife, that which begets, Isis, &c.

c. The triad (_τριάς_) has now become a most important number, seeing that in it the monad has reached reality and perfection. The monad proceeds through the duad, and again brought into unity with this undetermined manifold, it is the triad. Unity and multiplicity are present in the triad in the worst possible way—as an external combination; but however abstractly this is understood, the triad is still a profound form. The triad then is held to be the first perfect form in the universal. Aristotle (De Cœlo I. 1) puts this very clearly: “The corporeal has no dimension outside of the Three; hence the Pythagoreans also say that the all and everything is determined through triplicity,” that is, it has absolute form. “For the number of the whole has end, middle, and beginning; and this is the triad.” Nevertheless there is something superficial in the wish to bring everything under it, as is done in the systematization of the more modern natural philosophy. “Therefore we, too, taking this determination from nature, make use of it in the worship of the gods, so that we believe them to have been properly apostrophized only when we have called upon them three times in prayer. Two we call both, but not all; we speak first of three as all. What is determined through three is the first totality (_πᾶν_); what is in triple form is perfectly divided. Some is merely in one, other is only in two, but this is All.” What is perfect, or has reality, is its identity, opposition and unity, like number generally; but in triplicity this is actual, because it has beginning, middle, and end. Each thing is simple as beginning; it is other or manifold as middle, and its end is the return of its other nature into unity or mind; if we take this triplicity from a thing, we negate it and make of it an abstract construction of thought.

It is now comprehensible that Christians sought and found the Trinity in this threefold nature. It has often been made a superficial reason for objecting to them; sometimes the idea of the Trinity as it was present to the ancients, was considered as above reason, as a secret, and hence, too high; sometimes it was deemed too absurd. But from the one cause or from the other, they did not wish to bring it into closer relation to reason. If there is a meaning in this Trinity, we must try to understand it. It would be an anomalous thing if there were nothing in what has for two thousand years been the holiest Christian idea; if it were too holy to be brought down to the level of reason, or were something now quite obsolete, so that it would be contrary to good taste and sense to try to find a meaning in it. It is the Notion of the Trinity alone of which we can speak, and not of the idea of Father and Son, for we am not dealing with these natural relationships.

d. The Four (_τετράς_) is the triad but more developed, and hence with the Pythagoreans it held a high position. That the tetrad should be considered to be thus complete, reminds one of the four elements, the physical and the chemical, the four continents, &c. In nature four is found to be present everywhere, and hence this number is even now equally esteemed in natural philosophy. As the square of two, the fourfold is the perfection of the two-fold in as far as it—only having itself as determination, i.e. being multiplied with itself—returns into identity with itself. But in the triad the tetrad is in so far contained, as that the former is the unity, the other-being, and the union of both these moments, and thus, since the difference, as posited, is a double, if we count it, four moments result. To make this clearer, the tetrad is comprehended as the _τετρακτύς_, the efficient, active four (from _τέτταρα_ and _ἄγω_); and afterwards this is by the Pythagoreans made the most notable number. In the fragments of a poem of Empedocles, who originally was a Pythagorean, it is shown in what high regard this tetraktus, as represented by Pythagoras, was held:

“If thou dost this,
It will lead thee in the path of holy piety. I swear it
By the one who to our spirit has given the Tetraktus,
Which has in it eternal nature’s source and root.”[43]

e. From this the Pythagoreans proceed to the ten, another form of this tetrad. As the four is the perfect form of three, this fourfold, thus perfected and developed so that all its moments shall be accepted as real differences, is the number ten (_δεκάς_), the real tetrad. Sextus (adv. Math. IV. 3; VII. 94, 95) says: “Tetraktus means the number which, comprising within itself the four first numbers, forms the most perfect number, that is the number ten; for one and two and three and four make ten. When we come to ten, we again consider it as a unity and begin once more from the beginning. The tetraktus, it is said, has the source and root of eternal nature within itself, because it is the Logos of the universe, of the spiritual and of the corporeal.” It is an important work of thought to show the moments not merely to be four units, but complete numbers; but the reality in which the determinations are laid hold of, is here, however, only the external and superficial one of number; there is no Notion present although the tetraktus does not mean number so much as idea. One of the later philosophers, Proclus, (in Timæum, p. 269) says, in a Pythagorean hymn:—

“The divine number goes on,”...
“Till from the still unprofaned sanctuary of the Monad
It reaches to the holy Tetrad, which creates the mother of all that
is;
Which received all within itself, or formed the ancient bounds of all,
Incapable of turning or of wearying; men call it the holy Dekad.”

What we find about the progression of the other numbers is more indefinite and unsatisfying, and the Notion loses itself in them. Up to five there may certainly be a kind of thought in numbers, but from six onwards they are merely arbitrary determinations.

2. _Application of the System to the Universe_. This simple idea and the simple reality contained therein, must now, however, be further developed in order to come to reality as it is when put together and expanded. The question now meets us as to how, in this relation, the Pythagoreans passed from abstract logical determinations to forms which indicate the concrete use of numbers. In what pertains to space or music, determinations of objects formed by the Pythagoreans through numbers, still bear a somewhat closer relation to the thing, but when they enter the region of the concrete in nature and in mind, numbers become purely formal and empty.

a. To show how the Pythagoreans constructed out of numbers the system of the world, Sextus instances (adv. Math. X. 277-283), space relations, and undoubtedly we have in them to do with such ideal principles, for numbers are, in fact, perfect determinations of abstract space. That is to say, if we begin with the point, the first negation of vacuity, “the point corresponds to unity; it is indivisible and the principle of lines, as the unity is that of numbers. While the point exists as the monad or One, the line expresses the duad or Two, for both become comprehensible through transition; the line is the pure relationship of two points and is without breadth. Surface results from the threefold; but the solid figure or body belongs to the fourfold, and in it there are three dimensions present. Others say that body consists of one point” (_i.e._ its essence is one point), “for the flowing point makes the line, the flowing line, however, makes surface, and this surface makes body. They distinguish themselves from the first mentioned, in that the former make numbers primarily proceed from the monad and the undetermined duad, and then points and lines, plane surfaces and solid figures, from numbers, while they construct all from one point.” To the first, distinction is opposition or form set forth as duality; the others have form as activity. “Thus what is corporeal is formed under the directing influence of numbers, but from them also proceed the definite bodies, water, air, fire, and the whole universe generally, which they declare to be harmonious. This harmony is one which again consists of numeral relations only, which constitute the various concords of the absolute harmony.”

We must here remark that the progression from the point to actual space also has the signification of occupation of space, for “according to their fundamental tenets and teaching,” says Aristotle (Metaph. I. 8), “they speak of sensuously perceptible bodies in nowise differently from those which are mathematical.” Since lines and surfaces are only abstract moments in space, external construction likewise proceeds from here very well. On the other hand, the transition from the occupation of space generally to what is determined, to water, earth, &c., is quite another thing and is more difficult; or rather the Pythagoreans have not taken this step, for the universe itself has, with them, the speculative, simple form, which is found in the fact of being represented as a system of number-relations. But with all this, the physical is not yet determined.

b. Another application or exhibition of the essential nature of the determination of numbers is to be found in the relations of music, and it is more especially in their case that number constitutes the determining factor. The differences here show themselves as various relations of numbers, and this mode of determining what is musical is the only one. The relation borne by tones to one another is founded on quantitative differences whereby harmonies may be formed, in distinction to others by which discords are constituted. The Pythagoreans, according to Porphyry (De vita Pyth. 30), treated music as something soul-instructing and scholastic [Psychagogisches und Pädagogisches]. Pythagoras was the first to discern that musical relations, these audible differences, are mathematically determinable, that what we hear as consonance and dissonance is a mathematical arrangement. The subjective, and, in the case of hearing, simple feeling which, however, exists inherently in relation, Pythagoras has justified to the understanding, and he attained his object by means of fixed determinations. For to him the discovery of the fundamental tones of harmony are ascribed, and these rest on the most simple number-relations. Iamblichus (De vita Pyth. XXVI. 115) says that Pythagoras, in passing by the workshop of a smith, observed the strokes that gave forth a particular chord; he then took into consideration the weight of the hammer giving forth a certain harmony, and from that determined mathematically the tone as related thereto.[44] And finally he applied the same, and experimented in strings, by which means there were three different relations presented to him—Diapason, Diapente, and Diatessaron. It is known that the tone of a string, or, in the wind instrument, of its equivalent, the column of air in a reed, depends on three conditions; on its length, on its thickness, and on the amount of tension. Now if we have two strings of equal thickness and length, a difference in tension brings about a difference in sound. If we want to know what tone any string has, we have only to consider its tension, and this may be measured by the weight depending from the string, by means of which it is extended. Pythagoras here found that if one string were weighted with twelve pounds, and another with six (_λόγος διπλάσιος_, 1 : 2) it would produce the musical chord of the octave (_διὰ πασῶν_); the proportion of 8 : 12, or of 2 : 3 (_λόγος ἡμιόλιος_) would give the chord of the fifth (_διὰ πέντε_); the proportion of 9 : 12, or 3 : 4 (_λόγος ἐπίτριτος_), the fourth (_διὰ τεσσάρων_).[45] A different number of vibrations in like times determines the height and depth of the tone, and this number is likewise proportionate to the weight, if thickness and length are equal. In the first case, the more distended string makes as many vibrations again as the other; in the second case, it makes three vibrations for the other’s two, and so it goes on. Here number is the real factor which determines the difference, for tone, as the vibration of a body, is only a quantitatively determined quiver or movement, that is, a determination made through space and time. For there can be no determination for the difference excepting that of number or the amount of vibrations in one time; and hence a determination made through numbers is nowhere more in place than here. There certainly are also qualitative differences, such as those existing between the tones of metals and catgut strings, and between the human voice and wind instruments; but the peculiar musical relation borne by the tone of one instrument to another, in which harmony is to be found, is a relationship of numbers.

From this point the Pythagoreans enter into further applications of the theory of music, in which we cannot follow them. The _à priori_ law of progression, and the necessity of movement in number-relations, is a matter which is entirely dark; minds confused may wander about at will, for everywhere ideas are hinted at, and superficial harmonies present themselves and disappear again. But in all that treats of the further construction of the universe as a numerical system, we have the whole extent of the confusion and turbidity of thought belonging to the later Pythagoreans. We cannot say how much pains they took to express philosophic thought in a system of numbers, and also to understand the expressions given utterance to by others, and to put in them all the meaning possible. When they determined the physical and the moral universe by means of numbers, everything came into indefinite and insipid relationships in which the Notion disappeared. In this matter, however, so far as the older Pythagoreans are concerned, we are acquainted with the main principles only. Plato exemplifies to us the conception of the universe as a system of numbers, but Cicero and the ancients always call these numbers the Platonic, and it does not appear that they were ascribed to the Pythagoreans. It was thus later on that this came to be said; even in Cicero’s time they had become proverbially dark, and there is but little after all that is really old.

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.

The transition from the form of outward morals to morality as existent, is more important. As in Thales’ time, law-givers and administrators of states were preeminent in possessing a physical philosophy, so we see that with Pythagoras practical philosophy is advocated as the means of constituting a moral life. There we have the speculative Idea, the absolute essence, in its reality, and in a definite, sensuous existence; and similarly the moral life is submerged in actuality as the universal spirit of a people, and as their laws and rule. In Pythagoras, on the contrary, we have the reality of absolute essence raised, in speculation, out of sensuous reality, and expressed, though still imperfectly, as the essence of thought. Morality is likewise partly raised out of actuality as ordinarily known; it is certainly a moral disposition of all actuality, but as a brotherhood, and not as the life of a people. The Pythagorean League is an arbitrary existence and not a part of the constitution recognized by public sanction; and in his person Pythagoras isolated himself as teacher, as he also did his followers. The universal consciousness, the spirit of a people, is the substance of which the accident is the individual consciousness; the speculative is thus the fact that pure, universal law is absolute, individual consciousness, so that this last, because it draws therefrom its growth and nourishment, becomes universal self-consciousness. These two sides do not, however, come to us in the form of the opposition; it is first of all in morality that there is properly this Notion of the absolute individuality of consciousness which does everything on its own account. But we see that it was really present to the mind of Pythagoras that the substance of morality is the universal, from an example in Diogenes Laertius (VIII. 16). “A Pythagorean answered to the question of a father who inquired as to the best education he could give his son, that it should be that which would make him the citizen of a well-regulated State.” This answer is great and true; to the great principle of living in the spirit of one’s people, all other circumstances are subordinate. Nowadays men try to keep education free from the spirit of the times, but they cannot withdraw themselves from this supreme power, the State, for even if they try to separate themselves, they unconsciously remain beneath this universal. The speculative meaning of the practical philosophy of Pythagoras thus is, that in this signification, the individual consciousness shall obtain a moral reality in the brotherhood. But as number is a middle thing between the sensuous and Notion, the Pythagorean brotherhood is a middle between universal, actual morality and maintaining that in true morality the individual, as an individual, is responsible for his own behaviour; this morality ceases to be universal spirit. If we wish to see practical philosophy reappear, we shall find it; but, on the whole, we shall not see it become really speculative until very recent times.

We may satisfy ourselves with this as giving us an idea of the Pythagorean system. I will, however, shortly give the principal points of the criticism which Aristotle (Met. I. 8) makes upon the Pythagorean number-form. He says justly, in the first place: “If only the limited and the unlimited, the even and odd are made fundamental ideas, the Pythagoreans do not explain how movement arises, and how, without movement and change there can be coming into being and passing away, or the conditions and activities of heavenly objects.” This defect is significant; arithmetical numbers are dry forms and barren principles in which life and movement are deficient. Aristotle says secondly, “From number no other corporeal determinations, such as weight and lightness, are conceivable;” or number thus cannot pass into what is concrete. “They say that there is no number outside of those in the heavenly spheres.” For instance, a heavenly sphere and a virtue, or a natural manifestation in the earth, are determined as one and the same number. Each of the first numbers may be exhibited in each thing or quality; but in so far as number is made to express a further determination, this quite abstract, quantitative difference becomes altogether formal; it is as if the plant were five because it has five stamens. This is just as superficial as are determination through elements or through particular portions of the globe; it is a method as formal as that by which men now try to apply the categories of electricity, magnetism, galvanism, compression and expansion, of manly and of womanly, to everything. It is a purely empty system of determination where reality should be dealt with.

To Pythagoras and his disciples there are, moreover, many scientific conclusions and discoveries ascribed, which, however, do not concern us at all. Thus, according to Diogenes Laertius (VIII. 14, 27), he is said to have known that the morning and evening star is the same, and that the moon derives her light from the sun. We have already mentioned what he says of music. But what is best known is the Pythagorean Theorem; it really is the main proposition in geometry, and cannot be regarded like any other theorem. According to Diogenes, (VIII. 12), Pythagoras, on discovering the theorem, sacrificed a hecatomb, so important did he think it; and it may indeed seem remarkable that his joy should have gone so far as to ordain a great feast to which rich men and all the people were invited. It was worth the trouble; it was a rejoicing, a feast of spiritual cognition—at the cost of the oxen.

Other ideas which are brought forward by the Pythagoreans casually and without any connection, have no philosophic interest, and need only be mentioned. Aristotle, for instance, says (Phys. IV. 6) that “the Pythagoreans believed in an empty space which the heavens inspire, and an empty space which separates natural things and brings about the distinction between continuous and discrete; it first exists in numbers and makes them to be different.” Diogenes Laertius (VIII. 26-28) says much more, all of which is dull; this is like the later writers, who, generally speaking, take up what is external and devoid of any intellectual meaning. “The air which encircles the earth is immovable” (_ἄσειστον_, at least through itself) “and diseased, and all that is in it is mortal; but what is highest is in continual movement, pure and healthy, and in it everything is immortal—divine. Sun, moon and the other stars are gods, for in them warmth has predominance and is the cause of life. Man is related to the gods because he participates in warmth, and hence God cares for us. A ray penetrates from the sun through the thick and cold ether and gives life to everything; they call air, cold ether, the sea and moisture, thick ether. The soul is a detached portion of ether.”

C. THE ELEATIC SCHOOL.

The Pythagorean philosophy has not yet got the speculative form of expression for the Notion. Numbers are not pure Notion, but Notion in the form of ordinary idea or sensuous perception, and hence a mixture of both. This expression of absolute essence in what is a pure Notion or something thought, and the movement of the Notion or of Thought, is that which we find must come next, and this we discover in the Eleatic school. In it we see thought becoming free for itself; and in that which the Eleatics express as absolute essence, we see Thought grasp itself in purity, and the movement of Thought in Notions. In the physical philosophy we saw movement represented as an objective movement, as an origination and passing away. The Pythagoreans similarly did not reflect upon these Notions, and also treated their essence, Number, as fleeting. But since alteration is now grasped in its highest abstraction as Nothing, this objective movement changes into a subjective one, comes over to the side of consciousness, and existence becomes the unmoved. We here find the beginning of dialectic, _i.e._ simply the pure movement of thought in Notions; likewise we see the opposition of thought to outward appearance or sensuous Being, or of that which is implicit to the being-for-another of this implicitness, and in the objective existence we see the contradiction which it has in itself, or dialectic proper. When we reflect in anticipation on how the course of pure thought must be formed, we find (_α_) that pure thought (pure Being, the One) manifests itself immediately in its rigid isolation and self-identity, and everything else as null; (_β_) that the hitherto timid thought—which after it is strengthened, ascribes value to the “other” and constitutes itself therefrom—shows that it then grasps the other in its simplicity and even in so doing shows its nullity; (_γ_) finally, Thought manifests the other in the manifold nature of its determinations. We shall see this in the development and culture of the Eleatics in history. These Eleatic propositions still have interest for Philosophy, and are moments which must necessarily there appear.

Xenophanes, Parmenides, Melissus and Zeno are to be reckoned as belonging to this school. Xenophanes may be regarded as the founder of it; Parmenides is supposed to have been his pupil, and Melissus, and especially Zeno, are called the pupils of Parmenides. In fact, they are to be taken together as forming the Eleatic school; later on it lost the name, being then called Sophistic, and its locality was transferred to Greece proper. What Xenophanes began, Parmenides and Melissus developed further, and similarly Zeno perfected what these two taught. Aristotle (Metaph. I. 5) characterizes the first three thus: “Parmenides seems to comprehend the one as Notion (_κατὰ τὸν λόγον_), Melissus as matter (_κατὰ τὴν ὕλην_); hence the former says that it is limited (_πεπερασμένον_) and the latter that it is unlimited (_ἄπειρον_). But Xenophanes, who was the first of them to express the theory of the One, made the matter no plainer (_διεσαφήνισεν_), nor did he deal with either of these aspects (_φύσεως_), but looking into the heavens”—as we say, into the blue—“said, God is the One. Xenophanes and Melissus are on the whole less civilized (_μικρὸν ἀγροικότεροι_); Parmenides, however, is more acute (_μᾶλλον βλέπων_).” There is less to say of Xenophanes and Melissus, and what has come to us from the latter in particular—in fragments and derived from the sayings of others—is still in a state of ferment, and in his case there is least knowledge obtainable. On the whole, philosophic utterances and Notions are still poor, and it was in Zeno that Philosophy first attained to a purer expression of itself.

1. XENOPHANES.

The period at which he lived is clear enough, and as this suffices, it is a matter of indifference that the year of his birth and of his death is unknown. According to Diogenes Laertius (IX. 18), he was contemporary with Anaximander and Pythagoras. Of his circumstances further than this, it is only known that he, for reasons which are unknown, escaped from his native town, Colophon, in Asia Minor, to Magna Græcia, and resided for the most part at Zancle, (now Messina) and Catana (still called Catania) in Sicily. I find it nowhere said by the ancients that he lived at Elea, although all recent writers on the history of Philosophy repeat it, one after the other. Tennemann, in particular, says (Vol. I. pp. 151 and 414), that about the 61st Olympiad (536 B.C.), he repaired from Colophon to Elea. Diogenes Laertius (IX. 20), however, only says that he flourished about the 60th Olympiad and that he made two thousand verses on the colonization of Elea, from which it might be easily concluded that he was also born at Elea. Strabo says this in the beginning of his sixth book—when describing Elea—of Parmenides and Zeno only, and these he called Pythagoreans; hence, according to Cicero (Acad. Quæst. IV. 42) the Eleatic school took its name from these two. Xenophanes was nearly a hundred years old, and lived to see the Median wars: it is said that he became so poor that he had not the means of having his children buried, and was obliged to do so with his own hands. Some say that he had no teacher; others name Archelaus, which is a chronological error.

He wrote a book “On Nature,” the general subject and title of Philosophy at that time; some verses have been preserved to us which so far show no powers of reasoning. Professor Brandis of Bonn collected them together, with the fragments of Parmenides and Melissus, under the title “Commentationum Eleaticarum, P. 1,” Altonæ, 1813. The older philosophers wrote in verse, for prose comes much later on; on account of the awkward and confused mode of expression in Xenophanes’ poems, Cicero calls them (Acad. Quæst. IV. 23): _minus boni versus_.

As to his philosophy, Xenophanes in the first place maintained absolute existence to be the one, and likewise called this God. “The all is One and God is implanted in all things; He is unchangeable, without beginning, middle or end.”[48] In some verses by Xenophanes found in Clemens of Alexandria (Strom. V. 14, p. 714, ed. Potter), it is said:

“One God is greatest amongst gods and men.
Neither like unto mortals in spirit or in form;”

and in Sextus Empiricus (adv. Math. IX. 144):

“He sees everywhere, thinks everywhere, and hears everywhere,”

to which words Diogenes Laertius (IX, 19) adds: “Thought and reason are everything and eternal.” By this Xenophanes denied the truth of the conceptions of origination and of passing away, of change, movement, &c., seeing that they merely belong to sensuous perception. “He found,” says Tennemann (Vol. I. p. 156) “all origination to be inconceivable:” the One as the immediate product of pure thought, is, in its immediacy, Being.

For us the determination of Being is already known and trivial, but if we know about Being, the One, we place this, as a particular determination, in a line with all the rest. Here, on the contrary, it signifies that all else has no reality and is only a semblance. We must forget our own ideas; we know of God as Spirit. But, because the Greeks only had before them the sensuous world, these gods of their imagination, and found in them no satisfaction, they rejected all as being untrue, and thus came to pure thought. This is a wonderful advance, and thought thus becomes for the first time free for itself in the Eleatic school. Being, the One of the Eleatic school, is just this immersion in the abyss of the abstract identity of the understanding. Just as this comes first, so it also comes last, as that to which the understanding comes back, and this is proved in recent times when God is grasped only as the highest Being. If we say of God that this the highest Being is outside of and over us, we can know nothing more of it but that it is, and thus it is the undetermined; for if we knew of determinations, this would be to possess knowledge. The truth then simply is that God is the One, not in the sense that there is one God (this is another determination), but only that He is identical with Himself; in this there is no other determination, any more than in the utterance of the Eleatic school. Modern thought has, indeed, passed through a longer path, not only through what is sensuous, but also through philosophic ideas and predicates of God, to this all negating abstraction; but the content, the result arrived at is the same.

With this the dialectic reasoning of the Eleatics is closely connected in respect that they have also proved that nothing can originate or pass away. This deduction is to be found in Aristotle’s work, De Xenophane, Zenone et Gorgia, c. 3. “It is impossible, he says,[49] that if anything is, it arises (and he even applies this to the Godhead); for it must arise either from the like or from the unlike. But both are equally impossible: for it is no more probable that the like should be engendered from the like, than that it should engender it, for the like must have determinations identical with one another.” In acknowledging similarity, the distinction between begetting and begotten falls away. “Just as little can unlike arise from unlike, for if from the weaker the stronger takes its rise; or from the smaller, the greater; or from the worse, the better: or if, conversely, the worse proceeds from the better, non-being would result from Being: this is impossible, and thus God is eternal.” The same thing has been expressed as Pantheism or Spinozaism, which rests on the proposition _ex nihilo fit nihil_. The unity of God is further proved by Xenophanes: “If God is the mightiest, He must be One; for were He two or more, He would not have dominion over the others, but, not having dominion over the others, He could not be God. Thus were there several, they would be relatively more powerful or weaker, and thus they would not be gods, for God’s nature is to have nothing mightier than He. Were they equal, God would no longer possess the quality of being the mightiest, for the like is neither worse nor better than the like”—or it does not differ therefrom. “Hence if God is, and is such as this, He is only one; He could not, were there several, do what He willed. Since He is one, He is everywhere alike. He hears, sees and has also the other senses everywhere, for were this not the case, the parts of God would be one more powerful than the other, which is impossible. Since God is everywhere alike, He has a spherical form, for He is not here thus and elsewhere different, but is everywhere the same. Since He is eternal and one and spherical in form, He is neither unlimited nor limited. To be unlimited is non-being; for that has neither middle, beginning, end, nor part; and what is unlimited corresponds to this description. But whatever non-being is, Being is not. Mutual limitation would take place if there were several, but since there is only One, it is not limited. The one does not move itself, nor is it unmoved; to be unmoved is non-being, for to it none other comes, nor does it go into another; but to be moved must mean to be several, for one must move into another. Thus the One neither rests nor is it moved, for it is neither non-being nor is it many. In all this God is thus indicated; He is eternal and One, like Himself and spherical, neither unlimited nor limited, neither at rest nor moved.” From this result, that nothing can arise from the like or from the unlike, Aristotle (De Xenophane, Zenone et Gorgia c. 4) draws this conclusion: “that either there is nothing excepting God, or all else is eternal.”