CHAPTER I

PERIOD I.—DIVISION I.—THALES TO ANAXAGORAS

SINCE we possess only traditions and fragments of this epoch, we may speak here of the sources of these.

1. The first source is found in Plato, who makes copious reference to the older philosophers. For the reason that he makes the earlier and apparently independent philosophies, which are not so far apart when once their Notion is definitely grasped, into concrete moments of one Idea, Plato’s philosophy often seems to be merely a clearer statement of the doctrines of the older philosophers, and hence it draws upon itself the reproach of plagiarism. Plato was willing to spend much money in procuring the writings of the older philosophers, and, from his profound study of these, his conclusions have much weight. But because in his writings he never himself appeared as teacher, but always represented other people in his dialogues as the philosophers, a distinction never has been made between what really belonged to them in history and what was added by him through the further development which he effected in their thoughts. In the Parmenides, for instance, we have the Eleatic philosophy, and yet the working out of this doctrine belongs peculiarly to Plato.

2. Aristotle is our most abundant authority; he studied the older philosophers expressly and most thoroughly, and he has, in the beginning of his Metaphysics especially, and also to a large extent elsewhere, dealt with them, in historical order: he is as philosophic as erudite, and we may rely upon him. We can do no better in Greek philosophy than study the first book of his Metaphysics. When the would-be-wise man depreciates Aristotle, and asserts that he has not correctly apprehended Plato, it may be retorted that as he associated with Plato himself, with his deep and comprehensive mind, perhaps no one knew him better.

3. Cicero’s name may also occur to us here—although he certainly is but a troubled spring—since he undoubtedly gives us much information; yet because he was lacking in philosophic spirit, he understood Philosophy rather as if it were a matter of history merely. He does not seem to have himself studied its first sources, and even avows that, for instance, he never understood Heraclitus; and because this old and deep philosophy did not interest him, he did not give himself the trouble to study it. His information bears principally on later philosophers—the Stoics, Epicureans, the new Academy, and the Peripatetics. He saw what was ancient through their medium, and, generally speaking, through a medium of reasoning and not of speculation.

4. Sextus Empiricus, a later sceptic, has importance through his writings, _Hypotyposes Pyrrhonicæ_ and _adversus Mathematicos_. Because, as a sceptic, he both combated the dogmatic philosophy and also adduced other philosophers as testifying to scepticism (so that the greater part of his writings is filled with the tenets of other philosophers), he is the most abundant source we have for the history of ancient philosophy, and he has retained for our use many valuable fragments.

5. The book of Diogenes Laertius (_De vitis_, &c., Philoss. lib. x., ed. Meibom. c. notis Menagii, Amstel. 1692) is an important compilation, and yet it brings forward copious evidence without much discrimination. A philosophic spirit cannot be ascribed to it; it rambles about amongst bad anecdotes extraneous to the matter in hand. For the lives of philosophers, and here and there for their tenets, it is useful.

6. Finally, we must speak of Simplicius, a later Greek, from Cilicia, living under Justinian, in the middle of the sixth century. He is the most learned and acute of the Greek commentators of Aristotle, and of his writings there is much still unpublished: to him we certainly owe our thanks.

I need give no more references, for they may be found without trouble in any compendium. In the progress of Greek philosophy men were formerly accustomed to follow the order that showed, according to ordinary ideas, an external connection, and which is found in one philosopher having had another as his teacher—this connection is one which might show him to be partly derived from Thales and partly from Pythagoras. But such a connection is in part defective in itself, and in part it is merely external. The one set of philosophic sects, or of philosophers classed together, which is considered as belonging to a system—that which proceeds from Thales—pursues its course in time and mind far separate from the other. But, in truth, no such series ever does exist in this isolation, nor would it do so even though the individuals were consecutive and had been externally connected as teacher and taught, which never is the case; mind follows quite another order. These successive series are interwoven in spirit just as much as in their particular content.

We come across Thales first amongst the Ionic people, to whom the Athenians belonged, or from whom the Ionians of Asia Minor, as a whole, derived their origin. The Ionic race appears earlier in Peloponnesus, but seems to have been removed from thence. It is, however, not known what nations belonged to it, for, according to Herodotus (I. 143), the other Ionians, and even the Athenians, laid aside the name. According to Thucydides (I. 2 and 12), the Ionic colonies in Asia Minor and the islands proceeded principally from Athens, because the Athenians, on account of the over-population of Attica, migrated there. We find the greatest activity in Greek life on the coasts of Asia Minor, in the Greek islands, and then towards the west of Magna Græcia; we see amongst these people, through their internal political activity and their intercourse with foreigners, the existence of a diversity and variety in their relations, whereby narrowness of vision is done away with, and the universal rises in its place. These two places, Ionia and Greater Greece, are thus the two localities where this first period in the history of Philosophy plays its part until the time when, that period being ended, Philosophy plants itself in Greece proper, and there makes its home. Those spots were also the seat of early commerce and of an early culture, while Greece itself, so far as these are concerned, followed later.

We must thus remark that the character of the two sides into which these philosophies divide, the philosophy of Asia Minor in the east and that of Grecian Italy in the west, partakes of the character of the geographical distinction. On the Asia Minor side, and also in the islands, we find Thales, Anaximander, Anaximenes, Heraclitus, Leucippus, Democritus, Anaxagoras, and Diogenes from Crete. On the other side are the inhabitants of Italy: Pythagoras from Samos, who lived in Italy, however; Xenophanes, Parmenides, Zeno, Empedocles; and several of the Sophists also lived in Italy. Anaxagoras was the first to come to Athens, and thus his science takes a middle place between both extremes, and Athens was made its centre. The geographical distinction makes its appearance in the manifestation of Thought, in the fact that, with the Orientals a sensuous, material side is dominant, and in the west, Thought, on the contrary, prevails, because it is constituted into the principle in the form of thought. Those philosophers who turned to the east knew the absolute in a real determination of nature, while towards Italy there is the ideal determination of the absolute. These explanations will be sufficient for us here; but Empedocles, whom we find in Sicily, is somewhat of a natural philosopher, while Gorgias, the Sicilian sophist, remains faithful to the ideal side.

We now have to consider further:—1, The Ionians, viz. Thales, Anaximander, Anaximenes; 2, Pythagoras and his followers; 3, the Eleatics, viz. Xenophanes, Parmenides, &c.; 4, Heraclitus; 5, Empedocles, Leucippus and Democritus; 6, Anaxagoras. We have to trace and point out the progression of this philosophy also. The first and altogether abstract determinations are found with Thales and the other Ionians; they grasped the universal in the form of a natural determination, as water and air. Progression must thus take place by leaving behind the merely natural determination; and we find that this is so with the Pythagoreans. They say that number is the substance or the essence of things; number is not sensuous, nor is it pure thought, but it is a non-sensuous object of sense. It was with the Eleatics that pure thought appeared, and that its forcible liberation from the sensuous form and the form of number came to pass; and thus from them proceeds the dialectic movement of thought, which negates the definite particular in order to show that it is not the many but only the one that is true. Heraclitus declares the Absolute to be this very process, which, according to the Eleatics, was still subjective; he arrived at objective consciousness, since in it the Absolute is that which moves or changes. Empedocles, Leucippus, and Democritus, on the contrary, rather go to the opposite extreme, to the simple, material, stationary principle, to the substratum which underlies the process; and thus this last, as being movement, is distinguished from it. With Anaxagoras it is the moving, self-determining thought itself that is then known as existence, and this is a great step forward.

A. THE IONIC PHILOSOPHY.

Here we have the earlier Ionic philosophy, which we desire to treat as shortly as possible; and this is so much the easier, that the thought contained in it is very abstract and barren. Other philosophers than Thales, Anaximander, and Anaximenes, only come under our consideration as names. We have no more than half a dozen passages in the whole of the early Ionic philosophy, and that makes it an easy study. Yet learning prides itself most upon the ancients, for we may be most learned about that of which we know the least.

1. _Thales._

With Thales we, properly speaking, first begin the history of Philosophy. The life of Thales occurred at the time when the Ionic towns were under the dominion of Crœsus. Through his overthrow (Ol. 58, 1; 548 B.C.), an appearance of freedom was produced, yet the most of these towns were conquered by the Persians, and Thales survived the catastrophe only a few years. He was born at Miletus; his family is, by Diogenes (I. 22, 37), stated to be the Phœnician one of Thelides, and the date of his birth, according to the best calculation, is placed in the first year of the 35th Olympiad (640 B.C.), but according to Meiners it was a couple of Olympiads later (38th Olympiad, 629 B.C.). Thales lived as a statesman partly with Crœsus and partly in Miletus. Herodotus quotes him several times, and tells (I. 75) that, according to the narratives of the Greeks, when Crœsus went to battle against Cyrus and had difficulty in passing over the river Halys, Thales, who accompanied the army, diverted the river by a trench, which he made in the form of a crescent behind the camp, so that it could then be forded. Diogenes (I. 25) says further of him as regards his relations to his country, that he restrained the men of Miletus from allying themselves with Crœsus when he went against Cyrus, and that hence, after the conquest of Crœsus, when the other Ionic States were subdued by the Persians, the inhabitants of Miletus alone remained undisturbed. Diogenes records, moreover (I. 23), that he soon withdrew his attention from the affairs of the State and devoted himself entirely to science.

Voyages to Phœnicia are recorded of him, which, however, rest on vague tradition; but that he was in Egypt in his old age seems undoubted.[19] There he was said to have learned geometry, but this would appear not to have been much, judging from the anecdote, which Diogenes (I. 24, 27) retails from a certain Hieronymus. It was to the effect that Thales taught the Egyptians to measure the height of their pyramids by shadow—by taking the relation borne by the height of a man to his shadow. The terms of the proportion are: as the shadow of a man is to the height of a man, so is the shadow of a pyramid to its height. If this were something new to the Egyptians, they must have been very far back in the theory of geometry. Herodotus tells (I. 74), moreover, that Thales foretold an eclipse of the sun that happened exactly on the day of the battle between the Medians and Lydians, and that he ascribed the rising of the Nile to the contrary Etesian winds, which drove back the waters.[20] We have some further isolated instances of, and anecdotes about his astronomical knowledge and works.[21] “In gazing at and making observations on the stars, he fell into a ditch, and the people mocked him as one who had knowledge of heavenly objects and yet could not see what lay at his own feet.” The people laugh at such things, and boast that philosophers cannot tell them about such matters; but they do not understand that philosophers laugh at them, for they do not fall into a ditch just because they lie in one for all time, and because they cannot see what exists above them. He also showed, according to Diogenes (I. 26), that a wise man, if he wishes, can easily acquire riches. It is more important that he fixed that the year, as solar year, should have 365 days. The anecdote of the golden tripod to be given to the wisest man, is recorded by Diogenes (I. 27-33); and it carries with it considerable weight, because he combines all the different versions of the story. The tripod was given to Thales or to Bias; Thales gave it to some one else, and thus it went through a circle until it again came to Thales; the latter, or else Solon, decided that Apollo was wisest, and sent it to Didyma or to Delphi. Thales died, according to Diogenes (I. 38), aged seventy-eight or ninety, in the 58th Olympiad; according to Tennemann (vol. i. p. 414), it was in Olympiad 59, 2 (543 B.C.), when Pythagoras came to Crotona. Diogenes relates that he died at one of the games, overcome by heat and thirst.

We have no writings by Thales, and we do not know whether he was in the habit of writing. Diogenes Laertius (I. 23, 34, 35) speaks of two hundred verses on astronomy, and some maxims, such as “It is not the many words that have most meaning.”

As to his philosophy, he is universally recognized as the first natural philosopher, but all one knows of him is little, and yet we seem to know the most of what there is. For since we find that the further philosophic progress of which his speculative idea was capable, and the understanding of his propositions, which they alone could have, make their first appearance and form particular epochs with the philosophers succeeding him, who may be recognized thereby, this development ascribed to Thales never took place with him at all. Thus if it is the case that a number of his other reflections have been lost, they cannot have had any particular speculative value; and his philosophy does not show itself to be an imperfect system from want of information about it, but because the first philosophy cannot be a system.

We must listen to Aristotle as regards these ancient philosophers, for he speaks most sympathetically of them. In the passage of most importance (Metaph. I. 3), he says: “Since it is clear that we must acquire the science of first causes (_ἐξ ἀρχῆς αἰτίν_), seeing that we say that a person knows a thing when he becomes acquainted with its cause, there are, we must recollect, four causes—Being and Form first (for the ‘why’ is finally led back to the Notion, but yet the first ‘why’ is a cause and principle); matter and substratum, second; the cause whence comes the beginning of movement, third; and fourth the cause which is opposed to this, the aim in view and the good (for that is the end of every origination). Hence we would make mention of those who have undertaken the investigation of Being before us, and have speculated regarding the Truth, for they openly advance certain principles and first causes. If we take them under our consideration, it will be of this advantage, so far as our present investigation goes, that we shall either find other kinds of causes or be enabled to have so much the more confidence in those just named. Most of the earliest philosophers have placed the principles of everything in something in the form of matter (_ἐν ὕλης εἴδει_), for, that from which everything existent comes, and out of which it takes its origin as its first source, and into which it finally sinks, as substance (_οὐσία_), ever remains the same and only changes in its particular qualities (_πάθεσι_); and this is called the element (_στοιχεῖον_) and this the principle of all that exists” (the absolute prius). “On this account they maintain that nothing arises or passes away, because the same nature always remains. For instance, we say that, absolutely speaking, Socrates neither originates if he becomes beautiful or musical, nor does he pass away if he loses these qualities, because the subject (_τὸ ὑποκείμενον_), Socrates, remains the same. And so it is with all else. For there must be one nature, or more than one, from which all else arises, because it maintains its existence” (_σωζομένης ἐκείνης_), that means that in its change there is no reality or truth. “All do not coincide as to the number of this principle or as to its description (_εἶδος_); Thales, the founder of this philosophy,” (which recognizes something material as the principle and substance of all that is), “says that it is water. Hence he likewise asserts the earth to be founded on water.” Water is thus the _ὑποκείμενον_, the first ground, and, according to Seneca’s statement (Quæst. Nat. vi. 6), it seems to him to be not so much the inside of the earth, as what encloses it which is the universal existence; for “Thales considered that the whole earth has water as its support (_subjecto humore_), and that it swims thereon.”

We might first of all expect some explanation of the application of these principles, as, for example, how it is to be proved that water is the universal substance, and in what way particular forms are deduced from it. But as to this we must say that of Thales in particular, we know nothing more than his principle, which is that water is the god over all. No more do we know anything further of Anaximander, Anaximenes and Diogenes than their principles. Aristotle brings forward a conjecture as to how Thales derived everything directly out of water, “Perhaps (_ἴσως_) the conclusions of Thales have been brought about from the reflection that it was evident that all nourishment is moist, and warmth itself comes out of moisture and thereby life continues. But that from which anything generates is the principle of all things. This was one reason for holding this theory, and another reason is contained in the fact that all germs are moist in character, and water is the principle of what is moist.” It is necessary to remark that the circumstances introduced by Aristotle with a “perhaps” which are supposed to have brought about the conclusions of Thales, making water the absolute essence of everything, are not adduced as the grounds acknowledged by Thales. And furthermore, they can hardly be called grounds, for what Aristotle does is rather to establish, as we would say from actuality, that the latter corresponds to the universal idea of water. His successors, as for instance Pseudo-Plutarch (De plac. phil. I. 3), have taken Thales’ assertion as positive and not hypothetical; Tiedmann (_Geist der spec. Phil._ vol. I. p. 36) remarks with great reason that Plutarch omits the “perhaps.” For Plutarch says, “Thales suggests (_στοχάζεται_) that everything takes its origin from water and resolves itself into the same, because as the germs of all that live have moisture as the principle of life, all else might likewise (_εἰκός_) take its principle from moisture; for all plants draw their nourishment, and thus bear fruit, from water, and if they are without it, fade away; and even the fires of sun, and stars and world are fed through the evaporation of water.” Aristotle is contented with simply showing in regard to moisture that, at least, it is everywhere to be found. Since Plutarch gives more definite grounds for holding that water is the simple essence of things, we must see whether things, in so far as they are simple essence, are water, (_α_) The germ of the animal, of moist nature, is undoubtedly the animal as the simple actual, or as the essence of its actuality, or undeveloped actuality. (_β_) If, with plants, water may be regarded as for their nourishment, nourishment is still only the being of a thing as formless substance that first becomes individualized by individuality, and thus succeeds in obtaining form. (_γ_) To make sun, moon and the whole world arise through evaporation, like the food of plants, certainly approximates to the idea of the ancients, who did not allow the sun and moon to have obtained independence as we do.

“There are also some,” continues Aristotle, “who hold that all the ancients who, at the first and long before the present generation, made theology their study, understood Nature thus. They made Oceanus and Tethys the producers of all origination (_τῆς γενέσεως_), and water, which by the poets is called Styx, the oath of the gods. For what is most ancient is most revered, and the oath is that most held in reverence.” This old tradition has within it speculative significance. If anything cannot be proved or is devoid of objective form, such as we have in respect of payment in a discharge, or in witnesses who have seen the transaction, the oath, the confirmation of myself as object, expresses the fact that my assurance is absolute truth. Now since, by way of confirmation, men swear by what is best, by what is absolutely certain, and the gods swore by the subterranean water, it follows that the essence of pure thought, the inmost being, the reality in which consciousness finds its truth, is water; I, so to speak, express this clear certainty of myself as object, as God.

1. The closer consideration of this principle in its bearings would have no interest. For since the whole philosophy of Thales lies in the fact that water is this principle, the only point of interest can be to ask how far that principle is important and speculative. Thales comprehends essence as devoid of form. While the sensuous certitude of each thing in its individuality is not questioned, this objective actuality is now to be raised into the Notion that reflects itself into itself and is itself to be set forth as Notion; in commencement this is seen in the world’s being manifested as water, or as a simple universal. Fluid is, in its Notion, life, and hence it is water itself, spiritually expressed; in the so-called grounds or reasons, on the contrary, water has the form of existent universal. We certainly grant this universal activity of water, and for that reason call it an element, a physical universal power; but while we find it thus to be the universal of activity, we also find it to be this actual, not everywhere, but in proximity to other elements—earth, air and fire. Water thus has not got a sensuous universality, but a speculative one merely; to be speculative universality, however, would necessitate its being Notion and having what is sensuous removed. Here we have the strife between sensuous universality and universality of the Notion. The real essence of nature has to be defined, that is, nature has to be expressed as the simple essence of thought. Now simple essence, the Notion of the universal, is that which is devoid of form, but this water as it is, comes into the determination of form, and is thus, in relation to others, a particular existence just like everything that is natural. Yet as regards the other elements, water is determined as formless and simple, while the earth is that which has points, air is the element of all change, and fire evidently changes into itself. Now if the need of unity impels us to recognize for separate things a universal, water, although it has the drawback of being a particular thing, can easily be utilized as the One, both on account of its neutrality, and because it is more material than air.

The proposition of Thales, that water is the Absolute, or as the ancients say, the principle, is the beginning of Philosophy, because with it the consciousness is arrived at that essence, truth, that which is alone in and for itself, are one. A departure from what is in our sensuous perception here takes place; man recedes from this immediate existence. We must be able to forget that we are accustomed to a rich concrete world of thought; with us the very child learns, “There is one God in Heaven, invisible.” Such determinations are not yet present here; the world of Thought must first be formed and there is as yet no pure unity. Man has nature before him as water, air, stars, the arch of the heavens; and the horizon of his ideas is limited to this. The imagination has, indeed, its gods, but its content still is natural; the Greeks had considered sun, mountains, earth, sea, rivers, &c., as independent powers, revered them as gods, and elevated them by the imagination to activity, movement, consciousness and will. What there is besides, like the conceptions of Homer, for instance, is something in which thought could not find satisfaction; it produces mere images of the imagination, endlessly endowed with animation and form, but destitute of simple unity. It must undoubtedly be said that in this unconsciousness of an intellectual world, one must acknowledge that there is a great robustness of mind evinced in not granting this plenitude of existence to the natural world, but in reducing it to a simple substance, which, as the ever enduring principle, neither originates nor disappears, while the gods have a Theogony and are manifold and changing. This wild, endlessly varied imagination of Homer is set at rest by the proposition that existence is water; this conflict of an endless quantity of principles, all these ideas that a particular object is an independent truth, a self-sufficient power over others existing in its own right, are taken away, and it is shown likewise that there is only one universal, the universal self-existent, the simple unimaginative perception, the thought that is one and one alone.

This universal stands in direct relationship to the particular and to the existence of the world as manifested. The first thing implied in what has been said, is that the particular existence has no independence, is not true in and for itself, but is only an accidental modification. But the affirmative point of view is that all other things proceed from the one, that the one remains thereby the substance from which all other things proceed, and it is only through a determination which is accidental and external that the particular existence has its being. It is similarly the case that all particular existence is transient, that is, it loses the form of particular and again becomes the universal, water. The simple proposition of Thales therefore, is Philosophy, because in it water, though sensuous, is not looked at in its particularity as opposed to other natural things, but as Thought in which everything is resolved and comprehended. Thus we approach the divorce of the absolute from the finite; but it is not to be thought that the unity stands above, and that down here we have the finite world. This idea is often found in the common conception of God—where permanence is attributed to the world and where men often represent two kinds of actuality to themselves, a sensuous and a supersensuous world of equal standing. The philosophic point of view is that the one is alone the truly actual, and here we must take actual in its higher significance, because we call everything actual in common life. The second circumstance to be remembered is that with the ancient philosophers, the principle has a definite and, at first, a physical form. To us this does not appear to be philosophic but only physical; in this case, however, matter has philosophic significance. Thales’ theory is thus a natural philosophy, because this universal essence is determined as real; consequently the Absolute is determined as the unity of thought and Being.

2. Now if we have this undifferentiated principle predominating, the question arises as to the determination of this first principle. The transition from universal to particular at once becomes essential, and it begins with the determination of activity; the necessity for such arises here. That which is to be a veritable principle must not have a one-sided, particular form, but in it the difference must itself be absolute, while other principles are only special kinds of forms. The fact that the Absolute is what determines itself is already more concrete; we have the activity and the higher self-consciousness of the spiritual principle, by which the form has worked itself into being absolute form, the totality of form. Since it is most profound, this comes latest; what has first to be done is merely to look at things as determined.

Form is lacking to water as conceived by Thales. How is this accorded to it? The method is stated (and stated by Aristotle, but not directly of Thales), in which particular forms have arisen out of water; it is said to be through a process of condensation and rarefaction (_πυκνότητι καὶ μανότητι_), or, as it may be better put, through greater or less intensity. Tennemann (vol. I. p. 59) in reference to this, cites from Aristotle, _De gen. et corrupt._ I. 1, where there is no mention of condensation and rarefaction as regards Thales, and further, _De cælo_, III. 5, where it is only said that those who uphold water or air, or something finer than water or coarser than air, define difference as density and rarity, but nothing is said of its being Thales who gave expression to this distinction. Tiedmann (vol. I. p. 38) quotes yet other authorities; it was, however, later on, that this distinction was first ascribed to Thales.[22] Thus much is made out, that for the first time in this natural philosophy as in the modern, that which is essential in form is really the quantitative difference in its existence. This merely quantitative difference, however, which, as the increasing and decreasing density of water, constitutes its only form-determination, is an external expression of the absolute difference; it is an unessential distinction set up through another and is not the inner difference of the Notion in itself; it is therefore not worth while to spend more time over it.

Difference as regards the Notion has no physical significance, but differences or the simple duality of form in the sides of its opposition, must be comprehended as universally in the Notion. On this account a sensuous interpretation must not be given to the material, that is to particular determinations, as when it is definitely said that rare water is air, rare air, fiery ether, thick water, mud, which then becomes earth; according to this, air would be the rarefaction of the first water, ether the rarefaction of air, and earth and mud the sediment of water. As sensuous difference or change, the division here appears as something manifested for consciousness; the moderns have experimented in making thicker and thinner what to the senses is the same.

Change has consequently a double sense; one with reference to existence and another with reference to the Notion. When change is considered by the ancients, it is usually supposed to have to do with a change in what exists, and thus, for instance, inquiry would be made as to whether water can be changed through chemical action, such as heat, distillation, &c., into earth; finite chemistry is confined to this. But what is meant in all ancient philosophies is change as regards the Notion. That is to say, water does not become converted into air or space and time in retorts, &c. But in every philosophic idea, this transition of one quality into another takes place, _i.e._ this inward connection is shown in the Notion, according to which no one thing can subsist independently and without the other, for the life of nature has its subsistence in the fact that one thing is necessarily related to the other. We certainly are accustomed to believe that if water were taken away, it would indeed fare badly with plants and animals, but that stones would still remain; or that of colours, blue could be abstracted without harming in the least yellow or red. As regards merely empirical existence, it may easily be shown that each quality exists on its own account, but in the Notion they only are, through one another, and by virtue of an inward necessity. We certainly see this also in living matter, where things happen in another way, for here the Notion comes into existence; thus if, for example, we abstract the heart, the lungs and all else collapse. And in the same way all nature exists only in the unity of all its parts, just as the brain can exist only in unity with the other organs.

3. If the form is, however, only expressed in both its sides as condensation and rarefaction, it is not in and for itself, for to be this it must be grasped as the _absolute Notion_, and as an endlessly forming unity. What is said on this point by Aristotle (De Anima, I. 2, also 5) is this: “Thales seems, according to what is said of him, to consider the soul as something having movement, for he says of the loadstone that it has a soul, since it moves the iron.” Diogenes Laertius (I. 24) adds amber to this, from which we see that even Thales knew about electricity, although another explanation of it is that _ἤλεκτρον_ was besides a metal. Aldobrandini says of this passage in Diogenes, that it is a stone which is so hostile to poison that when touched by such it immediately hisses. The above remark by Aristotle is perverted by Diogenes to such an extent that he says: “Thales has likewise ascribed a soul to what is lifeless.” However, this is not the question, for the point is how he thought of absolute form, and whether he expressed the Idea generally as soul so that absolute essence should be the unity of simple essence and form.

Diogenes certainly says further of Thales (I. 27), “The world is animated and full of demons,” and Plutarch (De plac. phil. I. 7) says, “He called God the Intelligence (_νοῦς_) of the world.” But all the ancients, and particularly Aristotle, ascribe this expression unanimously to Anaxagoras as the one who first said that the _νοῦς_ is the principle of things. Thus it does not conduce to the further determination of form according to Thales, to find in Cicero (De Nat. Deor. I. 10) this passage: “Thales says that water is the beginning of everything, but God is the Mind which forms all that is, out of water.” Thales may certainly have spoken of God, but Cicero has added the statement that he comprehended him as the _νοῦς_ which formed everything out of water. Tiedmann (vol. I. p. 42) declares the passage to be possibly corrupt, since Cicero later on (c. 11) says of Anaxagoras that “he first maintained the order of things to have been brought about through the infinite power of Mind.” However, the Epicurean, in whose mouth these words are put, speaks “with confidence only fearing that he should appear to have any doubts” (c. 8) both previously and subsequently of other philosophers rather foolishly, so that this description is given merely as a jest. Aristotle understands historic accuracy better, and therefore we must follow him. But to those who make it their business to find everywhere the conception of the creation of the world by God, that passage in Cicero is a great source of delight, and it is a much disputed point whether Thales is to be counted amongst those who accepted the existence of a God. The Theism of Thales is maintained by Plouquet, whilst others would have him to be an atheist or polytheist, because he says that everything is full of demons. However, this question as to whether Thales believed in God does not concern us here, for acceptation, faith, popular religion are not in question; we only have to do with the philosophic determination of absolute existence. And if Thales did speak of God as constituting everything out of this same water, that would not give us any further information about this existence; we should have spoken unphilosophically of Thales because we should have used an empty word without inquiring about its speculative significance. Similarly the word world-soul is useless, because its being is not thereby expressed.

Thus all these further, as also later, assertions do not justify us in maintaining that Thales comprehended form in the absolute in a definite manner; on the contrary, the rest of the history of philosophical development refutes this view. We see that form certainly seems to be shown forth in existence, but as yet this unity is no further developed. The idea that the magnet has a soul is indeed always better than saying that it has the power of attraction; for power is a quality which is considered as a predicate separable from matter, while soul is movement in unison with matter in its essence. An idea such as this of Thales stands isolated, however, and has no further relation to his absolute thought. Thus, in fact, the philosophy of Thales is comprised in the following simple elements: (_a_) It has constituted an abstraction in order to comprehend nature in a simple sensuous essence. (_b_) It has brought forth the Notion of ground or principle; that is, it has defined water to be the infinite Notion, the simple essence of thought, without determining it further as the difference of quantity. That is the limited significance of this principle of Thales.

2. _Anaximander._

Anaximander was also of Miletus, and he was a friend of Thales. “The latter,” says Cicero (Acad. Quaest. IV. 37), “could not convince him that everything consisted of water.” Anaximander’s father was called Praxiades; the date of his birth is not quite certain; according to Tennemann (vol. I. p. 413), it is put in Olympiad 42, 3 (610 B.C.), while Diogenes Laertius (II. I, 2) says, taking his information from Apollodorus, an Athenian, that in Ol. 58, 2 (547 B.C.), he was sixty-four years old, and that he died soon after, that is to say about the date of Thales’ death. And taking for granted that he died in his ninetieth year, Thales must have been nearly twenty-eight years older than Anaximander. It is related of Anaximander that he lived in Samos with the tyrant Polycrates, where were Pythagoras and Anacreon also. Themistius, according to Brucker (Pt. I. p. 478), says of him that he first put his philosophic thoughts into writing, but this is also recorded of others, as for example, of Pherecydes, who was older than he. Anaximander is said to have written about nature, the fixed stars, the sphere, besides other matters; he further produced something like a map, showing the boundary (_πρίμετρον_) of land and sea; he also made other mathematical inventions, such as a sun-dial that he put up in Lacedæmon, and instruments by which the course of the sun was shown, and the equinox determined; a chart of the heavens was likewise made by him.

His philosophical reflections are not comprehensive, and do not extend as far as to determination. Diogenes says in the passage quoted before: “He adduced the Infinite” (_τὸ ἄπειρον_, the undetermined), “as principle and element; he neither determined it as air or water or any such thing.” There are, however, few attributes of this Infinite given. (_α_.) “It is the principle of all becoming and passing away; at long intervals infinite worlds or gods rise out of it, and again they pass away into the same.” This has quite an oriental tone. “He gives as a reason that the principle is to be determined as the Infinite, the fact that it does not need material for continuous origination. It contains everything in itself and rules over all: it is divine, immortal, and never passes away.”[23] (_β_.) Out of the one, Anaximander separates the opposites which are contained in it, as do Empedocles and Anaxagoras; thus everything in this medley is certainly there, but undetermined.[24] That is, everything is really contained therein in possibility (_δυνάμει_), “so that,” says Aristotle (Metaphys. XI. 2), “it is not only that everything arises accidentally out of what is not, but everything also arises from what is, although it is from incipient being which is not yet in actuality.” Diogenes Laertius adds (II. 1): “The parts of the Infinite change, but it itself is unchangeable.” (_γ_.) Lastly, it is said that the infinitude is in size and not in number, and Anaximander differs thus from Anaxagoras, Empedocles and the other atomists, who maintain the absolute discretion of the infinite, while Anaximander upholds its absolute continuity.[25] Aristotle (Metaphys. I. 8) speaks also of a principle which is neither water nor air, but is “thicker than air and thinner than water.” Many have connected this idea with Anaximander, and it is possible that it belongs to him.

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 one, just because the followers of Pythagoras were not only numerous, necessitating a definite form and order, but also, generally speaking, they lived continually together. Thus a particular form was natural to Pythagoras, because it was the very first time that a teacher in Greece arrived at a totality, or a new principle, through the cultivation of the intelligence, mind and will. This common life had not only the educational side and that founded on the exercise of physical ingenuity or skill, but included also that of the moral culture of practical men. But even now everything relating to morality appears and is or becomes altogether formal, or rather this is so in as far as it is consciously thought of as in this relation, for to be formal is to be universal, that which is opposed to the individual. It appears so particularly to him who compares the universal and the individual and consciously reflects over both, but this difference disappears for those living therein, to whom it is ordinary habit.

Finally, we have sufficient and full accounts of the outward forms observed by the Pythagoreans in their common life and also of their discipline. For much of this, however, we are indebted to the impressions of later writers. In the league, a life regulated in all respects was advocated. First of all, it is told us, that the members made themselves known by a similar dress—the white linen of Pythagoras. They had a very strict order for each day, of which each hour had its work. The morning, directly after rising, was set aside for recalling to memory the history of the previous day, because what is to be done in the day depends chiefly on the previous day; similarly the most constant self-examination was made the duty of the evening in order to find whether the deeds done in the day were right or wrong. True culture is not the vanity of directing so much attention to oneself and occupying oneself with oneself as an individual, but the self-oblivion that absorbs oneself in the matter in hand and in the universal; it is this consideration of the thing in hand that is alone essential, while that dangerous, useless, anxious state does away with freedom. They had also to learn by heart from Homer and from Hesiod; and all through the day they occupied themselves much with music—one of the principal parts of Greek education and culture.[37] Gymnastic exercises in wrestling, racing, throwing, and so on, were with them also enforced by rule. They dined together, and here, too, they had peculiar customs, but of these the accounts are different. Honey and bread were made their principal food, and water the principal, and indeed only, drink; they must thus have entirely refrained from eating meat as being associated with metempsychosis. A distinction was also made regarding vegetables—beans, for example, being forbidden. On account of this respect for beans, they were much derided, yet in the subsequent destruction of the political league, several Pythagoreans, being pursued, preferred to die than to damage a field of beans.[38]

The order, the moral discipline which characterized them, the common intercourse of men, did not, however, endure long; for even in Pythagoras’ life-time the affairs of his league must have become involved, since he found enemies who forcibly overthrew him. He drew down upon him, it is said, the envy of others, and was accused of thinking differently from what he seemed to indicate, and thus of having an _arrière pensée_. The real fact of the case was that the individual belonged, not entirely to his town, but also to another. In this catastrophe, Pythagoras himself, according to Tennemann (Vol. I. p. 414), met his death in the 69th Olympiad (504, B.C.) in a rising of the people against these aristocrats; but it is uncertain whether it happened in Crotona or in Metapontum, or in a war between the Syracusans and the Agrigentines. There is also much difference of opinion about the age of Pythagoras, for it is given sometimes as 80, and sometimes as 104.[39] For the rest, the unity of the Pythagorean school, the friendship of the members, and the connecting bond of culture have even in later times remained, but not in the formal character of a league, because what is external must pass away. The history of Magna Græcia is in general little known, but even in Plato’s[40] time we find Pythagoreans appearing at the head of states or as a political power.

The Pythagorean brotherhood had no relation with Greek public and religious life, and therefore could not endure for long: in Egypt and in Asia exclusiveness and priestly influence have their home, but Greece, in its freedom, could not let the Eastern separation of caste exist. Freedom here is the principle of civic life, but still it is not yet determined as principle in the relations of public and private law. With us the individual is free since all are alike before the law; diversity in customs, in political relations and opinions may thus exist, and must indeed so do in organic states. In democratic Greece, on the contrary, manners, the external mode of life, necessarily preserved a certain similarity, and the stamp of similarity remained impressed on these wider spheres; for the exceptional condition of the Pythagoreans, who could not take their part as free citizens, but were dependent on the plans and ends of a combination and led an exclusive religious life, there was no place in Greece. The preservation of the mysteries certainly belonged to the Eumolpidæ, and other special forms of worship to other particular families, but they were not regarded in a political sense as of fixed and definite castes, but as priests usually are, politicians, citizens, men like their fellows; nor, as with the Christians, was the separation of religious persons driven to the extreme of monastic rule. In ordinary civic life in Greece, no one could prosper or maintain his position who held peculiar principles, or even secrets, and differed in outward modes of life and clothing; for what evidently united and distinguished them was their community of principles and life—whether anything was good for the commonwealth or not, was by them publicly and openly discussed. The Greeks are above having particular clothing, maintaining special customs of washing, rising, practising music, and distinguishing between pure and impure foods. This, they say, is partly the affair of the particular individual and of his personal freedom, and has no common end in view, and partly it is a general custom and usage for everybody alike.

What is most important to us is the Pythagorean philosophy—not the philosophy of Pythagoras so much as that of the Pythagoreans, as Aristotle and Sextus express it. The two must certainly be distinguished, and from comparing what is given out as Pythagorean doctrine, many anomalies and discrepancies become evident, as we shall see. Plato bears the blame of having destroyed Pythagorean philosophy through absorbing what is Pythagorean in it into his own. But the Pythagorean philosophy itself developed to a point which left it quite other than what at first it was. We hear of many followers of Pythagoras in history who have arrived at this or that conclusion, such as Alcmæon and Philolaus; and we see in many cases the simple undeveloped form contrasted with the further stages of development in which thought comes forth in definiteness and power. We need, however, go no further into the historical side of the distinction, for we can only consider the Pythagorean philosophy generally; similarly we must separate what is known to belong to the Neo-Platonists and Neo-Pythagoreans, and for this end we have sources to draw from which are earlier than this period, namely the express statements found in Aristotle and Sextus.

The Pythagorean philosophy forms the transition from realistic to intellectual philosophy. The Ionic school said that essence or principle is a definite material. The next conclusion is (_α_) that the absolute is not grasped in natural form, but as a thought determination. (_β_) Then it follows that determinations must be posited while the beginning was altogether undetermined. The Pythagorean philosophy has done both.

1. _The System of Numbers_. Thus the original and simple proposition of the Pythagorean philosophy is, according to Aristotle (Metaph. I. 5), “that number is the reality of things, and the constitution of the whole universe in its determinations is an harmonious system of numbers and of their relations.” In what sense is this statement to be taken? The fundamental determination of number is its being a measure; if we say that everything is quantitatively or qualitatively determined, the size and measure is only one aspect or characteristic which is present in everything, but the meaning here is that number itself is the essence and the substance of things, and not alone their form. What first strikes us as surprising is the boldness of such language, which at once sets aside everything which to the ordinary idea is real and true, doing away with sensuous existence and making it to be the creation of thought. Existence is expressed as something which is not sensuous, and thus what to the senses and to old ideas is altogether foreign, is raised into and expressed as substance and as true Being. But at the same time the necessity is shown for making number to be likewise Notion, to manifest it as the activity of its unity with Being, for to us number does not seem to be in immediate unity with the Notion.

Now although this principle appears to us to be fanciful and wild, we find in it that number is not merely something sensuous, therefore it brings determination with it, universal distinctions and antitheses. The ancients had a very good knowledge of these. Aristotle (Metaph. I. 6) says of Plato: “He maintained that the mathematical elements in things are found outside of what is merely sensuous, and of ideas, being between both; it differs from what is sensuous in that it is eternal and unchangeable, and from ideas, in that it possesses multiplicity, and hence each can resemble and be similar to another, while each idea is for itself one alone.” That is, number can be repeated; thus it is not sensuous, and still not yet thought. In the life of Pythagoras, this is further said by Malchus (46, 47): “Pythagoras propounded philosophy in this wise in order to loose thought from its fetters. Without thought nothing true can be discerned or known; thought hears and sees everything in itself, the rest is lame and blind. To obtain his end, Pythagoras makes use of mathematics, since this stands midway between what is sensuous and thought, as a kind of preliminary to what is in and for itself.” Malchus quotes further (48, 53) a passage from an early writer, Moderatus: “Because the Pythagoreans could not clearly express the absolute and the first principles through thought, they made use of numbers, of mathematics, because in this form determinations could be easily expressed.” For instance, similarity could be expressed as one, dissimilarity as two. “This mode of teaching through the use of numbers, whilst it was the first philosophy, is superseded on account of its mysterious nature. Plato, Speusippus, Aristotle, &c., have stolen the fruits of their work from the Pythagoreans by making a simple use of their principle.” In this passage a perfect knowledge of numbers is evident.

The enigmatic character of the determination through number is what most engages our attention. The numbers of arithmetic answers to thought-determinations, for number has the “one” as element and principle; the one, however, is a category of being-for-self, and thus of identity with self, in that it excludes all else and is indifferent to what is “other.” The further determinations of number are only further combinations and repetitions of the one, which all through remains fixed and external; number, thus, is the most utterly dead, notionless continuity possible; it is an entirely external and mechanical process, which is without necessity. Hence number is not immediate Notion, but only a beginning of thought, and a beginning in the worst possible way; it is the Notion in its extremest externality, in quantitative form, and in that of indifferent distinction. In so far, the one has within itself both the principle of thought and that of materiality, or the determination of the sensuous. In order that anything should have the form of Notion, it must immediately in itself, as determined, relate itself to its opposite, just as positive is related to negative; and in this simple movement of the Notion we find the ideality of differences and negation of independence to be the chief determination. On the other hand, in the number three, for instance, there are always three units, of which each is independent; and this is what constitutes both their defect and their enigmatic character. For since the essence of the Notion is innate, numbers are the most worthless instruments for expressing Notion-determinations.

Now the Pythagoreans did not accept numbers in this indifferent way, but as Notion. “At least they say that phenomena must be composed of simple elements, and it would be contrary to the nature of things if the principle of the universe pertained to sensuous phenomena. The elements and principles are thus not only intangible and invisible, but altogether incorporeal.”[41] But how they have come to make numbers the original principle or the absolute Notion, is better shown from what Aristotle says in his Metaphysics (I. 5), although he is shorter than he would have been, because he alleges that elsewhere (infra., p. 214) he has spoken of it. “In numbers they thought that they perceived much greater similitude to what is and what takes place than in fire, water, or earth; since a certain property of numbers (_τοιονδὶ πάθος_) is justice, so is it with (_τοιονδὶ_) the soul and understanding; another property is opportunity, and so on. Since they further saw the conditions and relations of what is harmonious present in numbers, and since numbers are at the basis of all natural things, they considered numbers to be the elements of everything, and the whole heavens to be a harmony and number.” In the Pythagoreans we see the necessity for one enduring universal idea as a thought-determination. Aristotle (Met. XII. 4), speaking of ideas, says: “According to Heraclitus, everything sensuous flows on, and thus there cannot be a science of the sensuous; from this conviction the doctrine of ideas sprang. Socrates is the first to define the universal through inductive methods; the Pythagoreans formerly concerned themselves merely with a few matters of which they derived the notions from numbers—as, for example, with what opportuneness, or right, or marriage are.” It is impossible to discern what interest this in itself can have; the only thing which is necessary for us as regards the Pythagoreans, is to recognize any indications of the Idea, in which there may be a progressive principle.

This is the whole of the Pythagorean philosophy taken generally. We now have to come to closer quarters, and to consider the determinations, or universal significance. In the Pythagorean system numbers seem partly to be themselves allied to categories—that is, to be at once the thought-determinations of unity, of opposition and of the unity of these two moments. In part, the Pythagoreans from the very first gave forth universal ideal determinations of numbers as principles, and recognized, as Aristotle remarks (Metaph. I. 5), as the absolute principles of things, not so much immediate numbers in their arithmetic differences, as the principles of number, _i.e._ their rational differences. The first determination is unity generally, the next duality or opposition. It is most important to trace back the infinitely manifold nature of the forms and determinations of finality to their universal thoughts as the most simple principles of all determination. These are not differences of one thing from another, but universal and essential differences within themselves. Empirical objects distinguish themselves by outward form; this piece of paper can be distinguished from another, shades are different in colour, men are separated by differences of temperament and individuality. But these determinations are not essential differences; they are certainly essential for the definite particularity of the things, but the whole particularity defined is not an existence which is in and for itself essential, for it is the universal alone which is the self-contained and the substantial. Pythagoras began to seek these first determinations of unity, multiplicity, opposition, &c. With him they are for the most part numbers; but the Pythagoreans did not remain content with this, for they gave them the more concrete determinations, which really belong to their successors. Necessary progression and proof are not to be sought for here; comprehension, the development of duality out of unity are wanting. Universal determinations are only found and established in a quite dogmatic form, and hence the determinations are dry, destitute of process or dialectic, and stationary.

a. The Pythagoreans say that the first simple Notion is unity (_μονάς_); not the discrete, multifarious, arithmetic one, but identity as continuity and positivity, the entirely universal essence. They further say, according to Sextus (adv. Math. X. 260, 261): “All numbers come under the Notion of the one; for duality is one duality and triplicity is equally a ‘one,’ but the number ten is the one chief number. This moved Pythagoras to assert unity to be the principle of things, because, through partaking of it, each is called one.” That is to say, the pure contemplation of the implicit being of a thing is the one, the being like self; to all else it is not implicit, but a relationship to what is other. Things, however, are much more determined than being merely this dry “one.” The Pythagoreans have expressed this remarkable relationship of the entirely abstract one to the concrete existence of things through “simulation” (_μίμησις_). The same difficulty which they here encounter is also found in Plato’s Ideas; since they stand over against the concrete as species, the relation of concrete to universal is naturally an important point. Aristotle (Metaph. I. 6) ascribes the expression “participation” (_μέθεξις_) to Plato, who took it in place of the Pythagorean expression “simulation.” Simulation is a figurative, childish way of putting the relationship; participation is undoubtedly more definite. But Aristotle says, with justice, that both are insufficient; that Plato has not here arrived at any further development, but has only substituted another name. “To say that ideas are prototypes and that other things participate in them is empty talk and a poetic metaphor; for what is the active principle that looks upon the ideas?” (Metaph. I. 9). Simulation and participation are nothing more than other names for relation; to give names is easy, but it is another thing to comprehend.

b. What comes next is the opposition, the duality (_δυάς_), the distinction, the particular; such determinations have value even now in Philosophy; Pythagoras merely brought them first to consciousness. Now, as this unity relates to multiplicity, or this being-like-self to being another, different applications are possible, and the Pythagoreans have expressed themselves variously as to the forms which this first opposition takes.

(_α_) They said, according to Aristotle (Metaph. I. 5): “The elements of number are the even and the odd; the latter is the finite” (or principle of limitation) “and the former is the infinite; thus the unity proceeds from both and out of this again comes number.” The elements of immediate number are not yet themselves numbers: the opposition of these elements first appears in arithmetical form rather than as thought. But the one is as yet no number, because as yet it is not quantity; unity and quantity belong to number. Theon of Smyrna[42] says: “Aristotle gives, in his writings on the Pythagoreans, the reason why, in their view, the one partakes of the nature of even and odd; that is, one, posited as even, makes odd; as odd, it makes even. This is what it could not do unless it partook of both natures, for which reason they also called the one, even-odd” (_ἀρτιοπέριττον_).

(_β_) If we follow the absolute Idea in this first mode, the opposition will also be called the undetermined duality (_ἀόριστος δυάς_). Sextus speaks more definitely (adv. Math. X. 261, 262) as follows: “Unity, thought of in its identity with itself (_κατ̓ αὐτότητα ἑαυτῆς_), is unity; if this adds itself to itself as something different (_καθ̓ ἑτερότητα_), undetermined duality results, because no one of the determined or otherwise limited numbers is this duality, but all are known through their participation in it, as has been said of unity. There are, according to this, two principles in things; the first unity, through participation in which all number-units are units, and also undetermined duality through participation in which all determined dualities are dualities.” Duality is just as essential a moment in the Notion as is unity. Comparing them with one another, we may either consider the unity to be form and duality matter, or the other way; and both appear in different modes. (_αα_) Unity, as the being-like-self, is the formless; but in duality, as the unlike, there comes division or form. (_ββ_) If, on the other hand, we take form as the simple activity of absolute form, the one is what determines; and duality as the potentiality of multiplicity, or as multiplicity not posited, is matter. Aristotle (Met. I. 6) says that it is characteristic of Plato that “he makes out of matter many, but with him the form originates only once; whereas out of one matter only one table proceeds, whoever brings form to matter, in spite of its unity, makes many tables.” He also ascribes this to Plato, that “instead of showing the undetermined to be simple (_ἀντὶ τοῦ ἀπείρου ὡς ἑνός_), he made of it a duality—the great and small.”

(_γ_) Further consideration of this opposition, in which Pythagoreans differ from one another, shows us the imperfect beginning of a table of categories which were then brought forward by them, as later on by Aristotle. Hence the latter was reproached for having borrowed these thought-determinations from them; and it certainly was the case that the Pythagoreans first made the opposite to be an essential moment in the absolute. They further determined the abstract and simple Notions, although it was in an inadequate way, since their table presents a mixture of antitheses in the ordinary idea and the Notion, without following these up more fully. Aristotle (Met. I. 5) ascribes these determinations either to Pythagoras himself, or else to Alcmæon “who flourished in the time of Pythagoras’ old age,” so that “either Alcmæon took them from the Pythagoreans or the latter took them from him.” Of these antitheses or co-ordinates to which all things are traced, ten are given, for, according to the Pythagoreans, ten is a number of great significance:—

1. The finite and the infinite. 2. The odd and the even. 3. The one and the many. 4. The right and the left. 5. The male and the female. 6. The quiescent and the moving. 7. The straight and the crooked. 8. Light and darkness. 9. Good and evil. 10. The square and the parallelogram.

This is certainly an attempt towards a development of the Idea of speculative philosophy in itself, _i.e._ in Notions; but the attempt does not seem to have gone further than this simple enumeration. It is very important that at first only a collection of general thought-determinations should be made, as was done by Aristotle; but what we here see with the Pythagoreans is only a rude beginning of the further determination of antitheses, without order and sense, and very similar to the Indian enumeration of principles and substances.

(_δ_) We find the further progress of these determinations in Sextus (adv. Math. X. 262-277), when he speaks about an exposition of the later Pythagoreans. It is a very good and well considered account of the Pythagorean theories, which has some thought in it. The exposition follows these lines: “The fact that these two principles are the principles of the whole, is shown by the Pythagoreans in manifold ways.”

א. “There are three methods of thinking things; firstly, in accordance with diversity, secondly, with opposition, and thirdly, according to relation. (_αα_) What is considered in its mere diversity, is considered for itself; this is the case with those subjects in which each relates only to itself, such as horse, plant, earth, air, water and fire. Such matters are thought of as detached and not in relation to others.” This is the determination of identity with self or of independence. (_ββ_) “In reference to opposition, the one is determined as evidently contrasting with the other; we have examples of this in good and evil, right and wrong, sacred and profane, rest and movement, &c. (_γγ_) According to relation (_πρός τι_), we have the object which is determined in accordance with its relationship to others, such as right and left, over and under, double and half. One is only comprehensible from the other; for I cannot tell which is my left excepting by my right.” Each of these relations in its opposition, is likewise set up for itself in a position of independence. “The difference between relationship and opposition is that in opposition the coming into existence of the ‘one’ is at the expense of the ‘other,’ and conversely. If motion is taken away, rest commences; if motion begins, rest ceases; if health is taken away, sickness begins, and conversely. In a condition of relationship, on the contrary, both take their rise, and both similarly cease together; if the right is removed, so also is the left; the double goes and the half is destroyed.” What is here taken away is taken not only as regards its opposition, but also in its existence. “A second difference is that what is in opposition has no middle; for example, between sickness and health, life and death, rest and motion, there is no third. Relativity, on the contrary, has a middle, for between larger and smaller there is the like; and between too large and too small the right size is the medium.” Pure opposition passes through nullity to opposition; immediate extremes, on the other hand, subsist in a third or middle state, but in such a case no longer as opposed. This exposition shows a certain regard for universal, logical determinations, which now and always have the greatest possible importance, and are moments in all conceptions and in everything that is. The nature of these opposites is, indeed, not considered here, but it is of importance that they should be brought to consciousness.

ב. “Now since these three represent three different genera, the subjects and the two-fold opposite, there must be a higher genus over each of them which takes the first place, since the genus comes before its subordinate kinds. If the universal is taken away, so is the kind; on the other hand, if the kind, not the genus, for the former depends on the latter, but not the contrary way.” (_αα_) “The Pythagoreans have declared the one to be the highest genus of what is considered as in and for itself” (of subjects in their diversity); this is, properly speaking, nothing more than translating the determinations of the Notion into numbers. (_ββ_) “What is in opposition has, they say, as its genus the like and the unlike; rest is the like, for it is capable of nothing more and nothing less; but movement is the unlike. Thus what is according to nature is like itself; it is a point which is not capable of being intensified (_ἀνεπίτατος_); what is opposed to it is unlike. Health is like, sickness is unlike. (_γγ_) The genus of that which is in an indifferent relationship is excess and want, the more and the less;” in this we have the quantitative relation just as we formerly had the qualitative.

ג. We now come for the first time to the two opposites: “These three genera of what is for itself, in opposition and in relationship, must now come under”—yet simpler, higher—“genera,” _i.e._ thought-determinations. “Similarity reduces itself to the determination of unity.” The genus of the subjects is the very being on its own account. “Dissimilarity, however, consists of excess and want, but both of these come under undetermined duality;” they are the undetermined opposition, opposition generally. “Thus from all these relationships the first unity and the undetermined duality proceed;” the Pythagoreans said that such are found to be the universal modes of things. “From these, there first comes the ‘one’ of numbers and the ‘two’ of numbers; from the first unity, the one; from the unity and the undetermined duality the two; for twice the one is two. The other numbers take their origin in a similar way, for the unity over moves forward, and the undetermined duality generates the two.” This transition of qualitative into quantitative opposition is not clear. “Hence underlying these principles, unity is the active principle” or form, “but the two is the passive matter; and just as they make numbers arise from them, so do they make the system of the world and that which is contained in it.” The nature of these determinations is to be found in transition and in movement. The deeper significance of this reflection rests in the connection of universal thought-determinations with arithmetic numbers—in subordinating these and making the universal genus first.

Before I say anything of the further sequence of these numbers, it must be remarked that they, as we see them represented here, are pure Notions. (_α_) The absolute, simple essence divides itself into unity and multiplicity, of which the one sublates the other, and at the same time it has its existence in the opposition. (_β_) The opposition has at the same time subsistence, and in this is found the manifold nature of equivalent things. (_γ_) The return of absolute essence into itself is the negative unity of the individual subject and of the universal or positive. This is, in fact, the pure speculative Idea of absolute existence; it is this movement: with Plato the Idea is nothing else. The speculative makes its appearance here as speculative; whoever does not know the speculative, does not believe that in indicating simple Notions such as these, absolute essence is expressed. One, many, like, unlike, more or less, are trivial, empty, dry moments; that there should be contained in them absolute essence, the riches and the organization of the natural, as of the spiritual world, does not seem possible to him who, accustomed to ordinary ideas, has not gone back from sensuous existence into thought. It does not seem to such a one that God is, in a speculative sense, expressed thereby—that what is most sublime can be put in those common words, what is deepest, in what is so well known, self-evident and open, and what is richest, in the poverty of these abstractions.

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.