The advance made by the determination of the principle as infinite in comprehensiveness rests in the fact that absolute essence no longer is a simple universal, but one which negates the finite. At the same time, viewed from the material side, Anaximander removes the individuality of the element of water; his objective principle does not appear to be material, and it may be understood as Thought. But it is clear that he did not mean anything else than matter generally, universal matter.[26] Plutarch reproaches Anaximander “for not saying what (_τι_) his infinite is, whether air, water or earth.” But a definite quality such as one of these is transient; matter determined as infinitude means the motion of positing definite forms, and again abolishing the separation. True and infinite Being is to be shown in this and not in negative absence of limit. This universality and negation of the finite is, however, our operation only: in describing matter as infinite, Anaximander does not seem to have said that this is its infinitude.
He has said further (and in this, according to Theophrastus, he agrees with Anaxagoras), “In the infinite the like separates itself from the unlike and allies itself to the like; thus what in the whole was gold becomes gold, what was earth, earth, &c., so that properly nothing originates, seeing that it was already there.”[27] These, however, are poor determinations, which only show the necessity of the transition from the undetermined to the determined; for this still takes place here in an unsatisfying way. As to the further question of how the infinite determines the opposite in its separation, it seems that the theory of the quantitative distinction of condensation and rarefaction was held by Anaximander as well as by Thales. Those who come later designate the process of separation from the Infinite as development. Anaximander supposes man to develop from a fish, which abandoned water for the land.[28] Development comes also into prominence in recent times, but as a mere succession in time—a formula in the use of which men often imagine that they are saying something brilliant; but there is no real necessity, no thought, and above all, no Notion contained in it.
But in later records the idea of warmth, as being the disintegration of form, and that of cold, is ascribed to Anaximander by Stobæus (Eclog. Phys. c. 24, p. 500); this Aristotle (Metaphys. I. 5) first ascribed to Parmenides. Eusebius (De præp. Evang. I. 8), out of a lost work of Plutarch, gives us something from Anaximander’s Cosmogony which is dark, and which, indeed, Eusebius himself did not rightly understand. Its sense is approximately this: “Out of the Infinite, infinite heavenly spheres and infinite worlds have been set apart; but they carry within them their own destruction, because they only are through constant dividing off.” That is, since the Infinite is the principle, separation is the positing of a difference, i.e. of a determination or something finite. “The earth has the form of a cylinder, the height of which is the third part of the breadth. Both of the eternally productive principles of warmth and cold separate themselves in the creation of this earth, and a fiery sphere is formed round the air encircling the earth, like the bark around a tree. As this broke up, and the pieces were compressed into circles, sun, moon, and stars were formed.” Hence Anaximander, according to Stobæus (Ecl. Phys. 25, p. 510), likewise called the stars “wheel-shaped with fire-filled wrappings of air.” This Cosmogony is as good as the geological hypothesis of the earth-crust which burst open, or as Buffon’s explosion of the sun, which beginning, on the other hand, with the sun, makes the planets to be stones projected from it. While the ancients confined the stars to our atmosphere, and made the sun first proceed from the earth, we make the sun to be the substance and birthplace of the earth, and separate the stars entirely from any further connection with us, because for us, like the gods worshipped by the Epicureans, they are at rest. In the process of origination, the sun, indeed, descends as the universal, but in nature it is that which comes later; thus in truth the earth is the totality, and the sun but an abstract moment.
3. _Anaximenes._ Anaximenes still remains as having made his appearance between the 55th and 58th Olympiads (560-548 B.C.). He was likewise of Miletus, a contemporary and friend of Anaximander; he has little to distinguish him, and very little is known about him. Diogenes Laertius says neither with consideration nor consistency (II. 3): “He was born, according to Apollodorus in the 63rd Olympiad, and died in the year Sardis was conquered” (by Cyrus, Olympiad 58th).
In place of the undetermined matter of Anaximander, he brings forward a definite natural element; hence the absolute is in a real form, but instead of the water of Thales, that form is air. He found that for matter a sensuous being was indeed essential, and air has the additional advantage of being more devoid of form; it is less corporeal than water, for we do not see it, but feel it first in movement. Plutarch (De plac. phil. I. 3) says: “Out of it everything comes forth, and into it everything is again resolved.” According to Cicero (De Nat. Deor. I. 10), “he defined it as immeasurable, infinite, and in constant motion.” Diogenes Laertius expresses this in the passage already quoted: “The principle is air and the infinite” (_οὖτος ἀρχὴν ἀέρα εἶπε καὶ τὸ ἄπειρον_) as if there were two principles; however, _ἀρχὴν καὶ ἄπειρον_ may be taken together as subject, and _ἀέρα_ regarded as the predicate in the statement. For Simplicius, in dealing with the Physics of Aristotle, expressly says (p. 6, a) “that the first principle was to him one and infinite in nature as it was to Anaximander, but it was not indefinite as with the latter, but determined, that is, it was air,” which, however, he seems to have understood as endowed with soul.
Plutarch characterizes Anaximenes’ mode of representation which makes everything proceed from air—later on it was called ether—and resolve itself therein, better thus: “As our soul, which is air, holds us together (_συγρατεῖ_), one spirit (_πνεῦμα_) and air together likewise hold (_περιέχει_) the whole world together; spirit and air are synonymous.” Anaximenes shows very clearly the nature of his essence in the soul, and he thus points out what may be called the transition of natural philosophy into the philosophy of consciousness, or the surrender of the objective form of principle. The nature of this principle has hitherto been determined in a manner which is foreign and negative to consciousness; both its reality, water or air, and the infinite are a “beyond” to consciousness. But soul is the universal medium; it is a collection of conceptions which pass away and come forth, while the unity and continuity never cease. It is active as well as passive, from its unity severing asunder the conceptions and sublating them, and it is present to itself in its infinitude, so that negative signification and positive come into unison. Speaking more precisely, this idea of the nature of the origin of things is that of Anaxagoras, the pupil of Anaximenes.
Pherecydes has also to be mentioned as the teacher of Pythagoras; he is of Syros, one of the Cyclades islands. He is said to have drawn water from a spring, and to have learned therefrom that an earthquake would take place in three days; he is also said to have predicted of a ship in full sail that it would go down, and it sank in a moment. Theopompus in Diogenes Laertius (I. 116), relates of this Pherecydes that “he first wrote to the Greeks about Nature and the gods” (which was before said of Anaximander). His writings are said to have been in prose, and from what is related of them it is clear that it must have been a theogony of which he wrote. The first words, still preserved to us, are: “Jupiter and Time and what is terrestrial (_χθών_) were from eternity (_εἰς ἀεί_); the name of earthly (_χθονίῃ_) was given to the terrestrial sphere when Zeus granted to it gifts.”[29] How it goes on is not known, but this cannot be deemed a great loss. Hermias tells us only this besides:[30] “He maintained Zeus or Fire (_αἰθέρα_), Earth and Chronos or Time as principles—fire as active, earth as passive, and time as that in which everything originates.” Diogenes of Apollonia, Hippasus, and Archelaus are also called Ionic philosophers, but we know nothing more of them than their names, and that they gave their adherence to one principle or the other.
We shall leave these now and go on to Pythagoras, who was a contemporary of Anaximander; but the continuity of the development of the principle of physical philosophy necessitated our taking Anaximenes with him. We see that, as Aristotle said, they placed the first principle in a form of matter—in air and water first, and then, if we may so define Anaximander’s matter, in an essence finer than water and coarser than air. Heraclitus, of whom we have soon to speak, first called it fire. “But no one,” as Aristotle (Metaph. I. 8) remarks, “called earth the principle, because it appears to be the most complex element” (_διὰ τὴν μεγαλομέρειαν_); for it seems to be an aggregate of many units. Water, on the contrary, is the one, and it is transparent; it manifests in sensuous guise the form of unity with itself, and this is also so with air, fire, matter, &c. The principle has to be one, and hence must have inherent unity with itself; if it shows a manifold nature as does the earth, it is not one with itself, but manifold. This is what we have to say about the early Ionic Philosophy. The importance of these poor abstract thoughts lies (_a_) in the comprehension of a universal substance in everything, and (_b_) in the fact that it is formless, and not encumbered by sensuous ideas.
No one recognized better the deficiencies in this philosophy than did Aristotle in the work already quoted. Two points appear in his criticism of these three modes of determining the absolute: “Those who maintain the original principle to be matter fall short in many ways. In the first place, they merely give the corporeal element and not the incorporeal, for there also is such.” In treating of nature in order to show its essence, it is necessary to deal with it in its entirety, and everything found in it must be considered. That is certainly but an empirical instance. Aristotle maintains the incorporeal to be a form of things opposed to the material, and indicates that the absolute must not be determined in a one-sided manner; because the principle of these philosophers is material only, they do not manifest the incorporeal side, nor is the object shown to be Notion. Matter is indeed itself immaterial as this reflection into consciousness; but such philosophers do not know that what they express is an existence of consciousness. Thus the first great defect here rests in the fact that the universal is expressed in a particular form.
Secondly, Aristotle says (Metaph. I. 3): “From this it may be seen that first cause has only been by all these expressed in the form of matter. But because they proceeded thus, the thing itself opened out their way for them, and forced them into further investigation. For whether origin and decay are derived from one or more, the question alike arises, ‘How does it happen and what is the cause of it?’ For the fundamental substance (_τὸ ὑποκείμενον_) does not make itself to change, just as neither wood nor metal are themselves the cause of change; wood neither forms a bed nor does brass a statue, but something else is the cause of the change. To investigate this, however, is to investigate the other principle, which, as we would say, is the Principle of Motion.” This criticism holds good even now, where the Absolute is represented as the one fixed substance. Aristotle says that change is not conceivable out of matter as such, or out of water not itself having motion; he reproaches the older philosophers for the fact that they have not investigated the principle of motion for which men care most. Further, object is altogether absent; there is no determination of activity. Hence Aristotle says in the former passage: “In that they undertake to give the cause of origin and decay, they in fact remove the cause of movement. Because they make the principle to be a simple body (earth being excepted), they do not comprehend the mutual origination and decay whereby the one arises out of the other: I am here referring to water, air, fire, and earth. This origination is to be shown as separation or as union, and hence the contradiction comes about that one in time comes earlier than the other. That is, because this kind of origination is the method which they have adopted, the way taken is from the simple universal, through the particular, to the individual as what comes latest. Water, air, and fire are, however, universal. Fire seems to be most suitable for this element, seeing that it is the most subtle. Thus those who made it to be the principle, most adequately gave expression to this method (_λόγῳ_) of origination; and others thought very similarly. For else why should no one have made the earth an element, in conformity with the popular idea? Hesiod says that it was the original body—so ancient and so common was this idea. But what in Becoming comes later, is the first in nature.” However, these philosophers did not understand this so, because they were ruled by the process of Becoming only, without again sublating it, or knowing that first formal universal as such, and manifesting the third, the totality or unity of matter and form, as essence. Here, we see, the Absolute is not yet the self-determining, the Notion turned back into itself, but only a dead abstraction; the moderns were the first, says Aristotle, (Metaph. I. 6; III. 3) to understand the fundamental principle more in the form of genus.
We are able to follow the three moments in the Ionic philosophy: (_α_) The original essence is water; (_β_) Anaximander’s infinite is descriptive of movement, simple going out of and coming back into the simple, universal aspects of form—condensation and rarefaction; (_γ_) the air is compared to the soul. It is now requisite that what is viewed as reality should be brought into the Notion; in so doing we see that the moments of division, condensation, and rarefaction are not in any way antagonistic to the Notion. This transition to Pythagoras, or the manifestation of the real side as the ideal, is Thought breaking free from what is sensuous, and, therefore, it is a separation between the intelligible and the real.
B. PYTHAGORAS AND THE PYTHAGOREANS.
The later Neo-Pythagoreans have written many extensive biographies of Pythagoras, and are especially diffuse as regards the Pythagorean brotherhood. But it must be taken into consideration that these often distorted statements must not be regarded as historical. The life of Pythagoras thus first comes to us in history through the medium of the ideas belonging to the first centuries after Christ, and more or less in the style in which the life of Christ is written, on the ground of ordinary actuality, and not in a poetic atmosphere; it appears to be the intermingling of many marvellous and extravagant tales, and to take its origin in part from eastern ideas and in part from western. In acknowledging the remarkable nature of his life and genius and of the life which he inculcated on his followers, it was added that his dealings were not with right things, and that he was a magician and one who had intercourse with higher beings. All the ideas of magic, that medley of unnatural and natural, the mysteries which pervade a clouded, miserable imagination, and the wild ideas of distorted brains, have attached themselves to him.
However corrupt the history of his life, his philosophy is as much so. Everything engendered by Christian melancholy and love of allegory has been identified with it. The treatment of Plato in Christian times has quite a different character. Numbers have been much used as the expression of ideas, and this on the one hand has a semblance of profundity. For the fact that another significance than that immediately presented is implied in them, is evident at once; but how much there is within them is neither known by him who speaks nor by him, who seeks to understand; it is like the witches’ rhyme (one time one) in Goethe’s “Faust.” The less clear the thoughts, the deeper they appear; what is most essential, but most difficult, the expression of oneself in definite conceptions, is omitted. Thus Pythagoras’ philosophy, since much has been added to it by those who wrote of it, may similarly appear as the mysterious product of minds as shallow and empty as they are dark. Fortunately, however, we have a special knowledge of the theoretic, speculative side of it, and that, indeed, from Aristotle and Sextus Empiricus, who have taken considerable trouble with it. Although later Pythagoreans disparage Aristotle on account of his exposition, he has a place above any such disparagement, and therefore to them no attention must be given.
In later times a quantity of writings were disseminated and foisted upon Pythagoras. Diogenes Laertius (VIII. 6, 7) mentions many which were by him, and others which were set down to him in order to obtain authority for them. But in the first place we have no writings by Pythagoras, and secondly it is doubtful whether any ever did exist. We have quotations from these in unsatisfactory fragments, not from Pythagoras, but from Pythagoreans. It cannot be decisively determined which developments and interpretations belonged to the ancients and which to the moderns; yet with Pythagoras and the ancient Pythagoreans the determinations were not worked out in so concrete a way as later.
As to the life of Pythagoras, we hear from Diogenes Laertius (VIII. 1-3, 45) that he flourished about the 60th Olympiad (540 B.C.). His birth is usually placed in the 49th or 50th Olympiad (584 B.C.); by Larcher in Tennemann (Vol. I., pp. 413, 414), much earlier—in the 43rd Olympiad (43, 1, i.e. 608 B.C.). He was thus contemporaneous with Thales and Anaximander. If Thales’ birth were in the 38th Olympiad and that of Pythagoras in the 43rd, Pythagoras was only twenty-one years younger than he; he either only differed by a couple of years from Anaximander (Ol. 42, 3) in age, or the latter was twenty-six years older. Anaximenes was from twenty to twenty-five years younger than Pythagoras. His birthplace was the Island of Samos, and hence he belonged to the Greeks of Asia Minor, which place we have hitherto found to be the seat of philosophy. Pythagoras is said by Herodotus (IV., 93 to 96) to have been the son of Mnesarchus, with whom Zalmoxis served as slave in Samos; Zalmoxis obtained freedom and riches, became ruler of the Getæ, and asserted that he and his people would not die. He built a subterranean habitation and there withdrew himself from his subjects; after four years he re-appeared;[31] hence the Getans believed in immortality. Herodotus thinks, however, that Zalmoxis was undoubtedly much older than Pythagoras.
His youth was spent at the court of Polycrates, under whose rule Samos was brought, not only to wealth, but also to the possession of culture and art. In this prosperous period, according to Herodotus (III., 39), it possessed a fleet of a hundred ships. His father was an artist or engraver, but reports vary as to this, as also as to his country, some saying that his family was of Tyrrhenian origin and did not go to Samos till after Pythagoras’ birth. That may be as it will, for his youth was spent in Samos and he must hence have been naturalized there, and to it he belongs. He soon journeyed to the main land of Asia Minor and is said there to have become acquainted with Thales. From thence he travelled to Phœnicia and Egypt, as Iamblichus (III., 13, 14) says in his biography of Pythagoras. With both countries Asia Minor had many links, commercial and political, and it is related that he was recommended by Polycrates to King Amasis, who, according to Herodotus (II. 154), attracted many Greeks to the country, and had Greek troops and colonies. The narratives of further journeys into the interior of Asia, to the Persian magicians and Indians, seem to be altogether fabulous, although travelling, then as now, was considered to be a means of culture. As Pythagoras travelled with a scientific purpose, it is said that he had himself initiated into nearly all the mysteries of Greeks and of Barbarians, and thus he obtained admission into the order or caste of the Egyptian priesthood.
These mysteries that we meet with amongst the Greeks, and which are held to be the sources of much wisdom, appear in their religion to have stood in the relationship of doctrine to worship. This last existed in offerings and solemn festivals only, but to ordinary conceptions, to a consciousness of these conceptions, there is no transition visible unless they were preserved in poems as traditions. The doctrines themselves, or the act of bringing the actual home to the conception, seems to have been confined to the mysteries; we find it to be the case, however, that it is not only the ideas as in our teaching, but also the body that is laid claim to—that there was brought home to man by sending him to wander amongst his fellow-men, both the abandonment of his sensuous consciousness and the purification and sanctification of the body. Of philosophic matter, however, there is as little openly declared as possible, and just as we know the system of freemasonry, there is no secret in those mysteries.
His alliance with the Egyptian priesthood had a most important influence upon Pythagoras, not through the derivation of profound speculative wisdom therefrom, but by the idea obtained through it of the realization of the moral consciousness of man; the individual, he learned, must attend to himself, if inwardly and to the outer world he is to be meritorious and to bring himself, morally formed and fashioned, into actuality. This is a conception which he subsequently carried out, and it is as interesting a matter as his speculative philosophy. Just as the priests constituted a particular rank and were educated for it, they also had a special rule, which was binding throughout the whole moral life. From Egypt Pythagoras thus without doubt brought the idea of his Order, which was a regular community brought together for purposes of scientific and moral culture, which endured during the whole of life. Egypt at that time was regarded as a highly cultured country, and it was so when compared with Greece; this is shown even in the differences of caste which assumes a division amongst the great branches of life and work, such as the industrial, scientific and religious. But beyond this, we need not seek great scientific knowledge amongst the Egyptians, nor think that Pythagoras got his science there. Aristotle (Metaph. I.) only says that “in Egypt mathematical sciences first commenced, for there the nation of priests had leisure.”[32] Pythagoras stayed a long time in Egypt, and returned from thence to Samos; but he found the internal affairs of his own country in confusion, and left it soon after. According to Herodotus’ account (III. 45-47), Polycrates had—not as tyrant—banished many citizens from Samos, who sought and found support amongst the Lacedæmonians, and a civil war had broken out. The Spartans had, at an earlier period, given assistance to the others, for, as Thucydides says (I. 18), to them thanks were generally ascribed for having abolished the rule of the few, and caused a reversion to the system of giving public power to the people; later on they did the opposite, abolishing democracy and introducing aristocracy. Pythagoras’ family was necessarily involved in these unpleasant relations, and a condition of internal strife was not congenial to Pythagoras, seeing that he no longer took an interest in political life, and that he saw in it an unsuitable soil for carrying out his plans. He traversed Greece, and betook himself from thence to Italy, in the lower parts of which Greek colonies from various states and for various motives had settled, and there flourished as important trading towns, rich in people and possessions.
In Crotona he settled down, and lived in independence, neither as a statesman, warrior, nor political law-giver to the people, so far as external life was concerned, but as a public teacher, with the provision that his teaching should not be taken up with mere conviction, but should also regulate the whole moral life of the individual. Diogenes Laertius says that he first gave himself the name _φιλόσοφος_, instead of _σοφός_; and men called this modesty, as if he thereby expressed, not the possession of wisdom, but only the struggle towards it, as towards an end which cannot be attained.[33] But _σοφός_ at the same time means a wise man, who is also practical, and that not in his own interest only, for that requires no wisdom, seeing that every sincere and moral man does what is best from his own point of view. Thus _φιλόσοφος_ signifies more particularly the opposite to participation in practical matters, that is in public affairs. Philosophy is thus not the love of wisdom, as of something which one sets oneself to acquire; it is no unfulfilled desire. _Φιλόσοφος_ means a man whose relation to wisdom is that of making it his object; this relationship is contemplation, and not mere Being; but it must be consciously that men apply themselves to this. The man who likes wine (_φίλοινος_) is certainly to be distinguished from the man who is full of wine, or a drunkard. Then does _φίλοινος_ signify only a futile aspiration for wine?
What Pythagoras contrived and effected in Italy is told us by later eulogists, rather than by historians. In the history of Pythagoras by Malchus (this was the Syrian name of Porphyry) many strange things are related, and with the Neo-Platonists the contrast between their deep insight and their belief in the miraculous is surprising. For instance, seeing that the later biographers of Pythagoras had already related a quantity of marvels, they now proceeded to add yet more to these with reference to his appearance in Italy. It appears that they were exerting themselves to place him, as they afterwards did with Apollonius of Tyana, in opposition to Christ. For the wonders which they tell of him seem partly to be an amplification of those in the New Testament, and in part they are altogether absurd. For instance, they make Pythagoras begin his career in Italy with a miracle. When he landed in the Bay of Tarentum, at Crotona, he encountered fishermen on the way to the town who had caught nothing. He called upon them to draw their nets once more, and foretold the number of fishes that would be found in them. The fishermen, marvelling at this prophecy, promised him that if it came true they would do whatever he desired. It came to pass as he said, and Pythagoras then desired them to throw the fishes alive back into the sea, for the Pythagoreans ate no flesh. And it is further related as a miracle which then took place, that none of the fishes whilst they were out of the water died during the counting. This is the kind of miracle that is recorded, and the stories with which his biographers fill his life are of the same silly nature. They then make him effect such a general impression upon the mind of Italy, that all the towns reformed upon their luxurious and depraved customs, and the tyrants partly gave up their powers voluntarily, and partly they were driven out. They thereby, however, commit such historical errors as to make Charondas and Zaleucus, who lived long before Pythagoras, his disciples; and similarly to ascribe the expulsion and death of the tyrant Phalaris to him, and to his action.[34] Apart from these fables, there remains as an historic fact, the great work which he accomplished, and this he did chiefly by establishing a school, and by the great influence of his order upon the principal part of the Greco-Italian states, or rather by means of the rule which was exercised in these states through this order, which lasted for a very long period of time. It is related of him that he was a very handsome man, and of a majestic appearance, which captivated as much as it commanded respect. With this natural dignity, nobility of manners, and the calm propriety of his demeanour, he united external peculiarities, through which he seemed a remarkable and mysterious being. He wore a white linen garment, and refrained from partaking of certain foods.[35] Particular personality, as also the externalities of dress and the like, are no longer of importance; men let themselves be guided by general custom and fashion, since it is a matter outside of and indifferent to them not to have their own will here; for we hand over the contingent to the contingent, and only follow the external rationality that consists in identity and universality. To this outward personality there was added great eloquence and profound perception; not only did he undertake to impart this to his individual friends, but he proceeded to bring a general influence to bear on public culture, both in regard to understanding and to the whole manner of life and morals. He not merely instructed his friends, but associated them in a particular life in order to constitute them into persons and make them skilful in business and eminent in morals. The Institute of Pythagoras grew into a league, which included all men and all life in its embrace; for it was an elaborately fashioned piece of work, and excellently plastic in design.
Of the regulations of Pythagoras’ league, we have descriptions from his successors, more especially from the Neo-Platonists, who are particularly diffuse as regards its laws. The league had, on the whole, the character of a voluntary priesthood, or a monastic order of modern times. Whoever wished to be received was proved in respect of his education and obedience, and information was collected about his conduct, inclinations, and occupations. The members were subject to a special training, in which a difference was made amongst those received, in that some were exoteric and some esoteric. These last were initiated into the highest branches of science, and since political operations were not excluded from the order, they were also engaged in active politics; the former had to go through a novitiate of five years. Each member must have surrendered his means to the order, but he received them again on retiring, and in the probationary period silence was enjoined (_ἐχεμυθία_).[36] This obligation to cease from idle talk may be called an essential condition for all culture and learning; with it men must begin if they wish to comprehend the thoughts of others and relinquish their own ideas. We are in the habit of saying that the understanding is cultivated through questioning, objecting and replying, &c., but, in fact, it is not thus formed, but made from without. What is inward in man is by culture got at and developed; hence though he remains silent, he is none the poorer in thought or denser of mind. He rather acquires thereby the power of apprehension, and comes to know that his ideas and objections are valueless; and as he learns that such ideas are valueless, he ceases to have them. Now the fact that in Pythagoras there is a separation between those in the course of preparation and those initiated, as also that silence is particularly enjoined, seems most certainly to indicate that in his brotherhood both were formal elements and not merely as present in the nature of things, as might occur spontaneously in the individual without any special law or the application of any particular consideration. But here it is important to remark that Pythagoras may be regarded as the first instructor in Greece who introduced the teachings of science; neither Thales, who was earlier than he, nor his contemporary Anaximander taught scientifically, but only imparted their ideas to their friends. There were, generally speaking, no sciences at that time; there was neither a science of philosophy, mathematics, jurisprudence or anything else, but merely isolated propositions and facts respecting these subjects. What was taught was the use of arms, theorems, music, the singing of Homer’s or Hesiod’s songs, tripod chants, &c., or other arts. This teaching is accomplished in quite another way. Now if we said that Pythagoras had introduced the teaching of science amongst a people who, though like the Greeks, untaught therein, were not stupid but most lively, cultured and loquacious, the external conditions of such teaching might in so far be given as follows:—(_α_) He would distinguish amongst those who as yet had no idea of the process of learning a science, so that those who first began should be excluded from that which was to be imparted to those further on; and (_β_) he would make them leave the unscientific mode of speaking of such matters, or their idle prattle, alone, and for the first time study science. But the fact that this action both appeared to be formal and likewise required to be made such, was, on account of its unwonted character, a necessary