a celebrated ancient philosopher, and, according to a well-known story related by Cicero (Tusc. Quest. v. 3), the first who adopted that title, was a native of the island of Samos. Of the personal history of this man, to whom perhaps the most remarkable school of Greek philosophy owed its origin, and who, himself, one of the earliest speculators in his country, plainly exercised no small influence over his successors, little can be known for certain, nor are his philosophical tenets free from much doubt and obscurity. From a time shortly subsequent to his own age the most improbable legends seem to have been connected with the name of Pythagoras, arising probably in a great part from the extravagant esteem and reverence in which he was held by his disciples. Even the period in which he lived cannot be determined with anything like accuracy; the different accounts, all of them long posterior to the time in question, exhibiting a variation of about forty years. The testimony of all these accounts, however, furnishes us with two historical landmarks by which we may date the principal event in his life, and thus, approximately, the time when he flourished. All our authorities agree in representing him as leaving Samos during the reign of Polycrates as tyrant there (B.C. 532–22); and settling in Italy while Tarquinius Superbus was king of Rome (B.C. 532–508). Thus, as these events could not have been far removed in point of time, we may assume as probable that they took place sometime between 530 and 520 B.C. If we credit the statements of Aristoxenus and Iamblichus, we shall place the birth of Pythagoras about 570 B.C.; but if, on the other hand, we incline to the views of Eratosthenes and Antiochus, we must carry back the date nearly to 609 B.C. Perhaps none of the authorities is worthy of implicit credit, but the former account certainly appears in itself to be more probable; for it is unlikely, as we must on the other alternative suppose, that Pythagoras did not begin the great work of his life till he was considerably above seventy. The date given by Ritter, on the authority of Clemens Alex. (Ol. 49, B.C. 584–80), does not materially differ from the former of the two above mentioned. His father's name was Mnesarchus (Herod. iv. 93), and his family is said to have sprung from the Tyrrhenian Pelasgians, who were largely intermixed with the Greek settlers in Samos.

Of the early life of Pythagoras our knowledge may be said to be absolutely nothing. The island where he probably spent the first years of his life was then in arts and commerce one of the most flourishing communities in the world. It lay, too, in the very region where the earliest of the Greek philosophers were then conducting their magnificent speculations, with which the young philosopher was no doubt familiar; and we can form some idea of the influences that prompted him, with high hopes and daring enterprise, to follow their footsteps into the new field, not then, as now, strewed with the ruins of theories and systems. Tradition has ascribed to Pythagoras, as instructors in philosophy, various of the early sages, and especially Pherecydes of Syros; but as far as opinions are concerned, he does not appear to be indebted to any of them. As little is there any ground for supposing that the philosophy Pythagoras of Pythagoras was of foreign origin, though he seems undoubtedly to have been an extensive traveller in foreign countries. His scientific attainments must have been great for that age; and in all probability he soon acquired a great reputation for wisdom and ability. The mathematical sciences were those that chiefly attracted his attention, and he is reputed to be the author of several discoveries in geometry, music, and astronomy. The travels of the philosopher are said to have extended to Egypt and the East; countries which were then regarded by the Greeks as the repositories of all the highest wisdom. They would naturally, therefore, attract the attention of a searcher after truth; while at Samos he would have the utmost facilities for acquiring geographical knowledge, and penetrating into the most distant regions. It is vain to conjecture what effect these travels might have on him, or what were the peculiar influences with which he was brought in contact. From the priests in Egypt or the Magi in Persia he may have acquired a knowledge of their hidden lore; but it is equally probable that he was not thus initiated, and it is not necessary to have recourse to any such sources for his opinions, so far as we know them.

On his return to Samos after his travels, Pythagoras seems to have fully formed his great project which he afterwards carried out. This project was more of a religious and political than of a philosophical nature. It was to establish a society on a religious foundation, and with an ethical end, for the moral improvement of its members, who were to be instructed in a peculiar mode of life. (See Plato, Rep. x. 600 B.) He probably found that such a scheme was impracticable under the government of Polycrates, and for that reason, rather than any personal dislike to him, left his native island and migrated to Crotona. We do not know what induced him to select this place in particular as the scene of his new experiment. It was one of the colonies which the Greeks had at this time sent out in such numbers to Southern Italy as to obtain for that part of the country the name of Magna Graecia. It was not unnatural that Pythagoras should look in this direction for a place to settle in. These colonies were comparatively young communities, many of them rapidly rising in importance, opening up to Grecian enterprise new and unexplored regions; and he might reasonably hope to find fewer obstructions to his plans there than among the intricate political relations of the eastern world.

Crotona itself stood in the country of the Brutti, one of the most savage of the native Italian tribes. It was an Achaean colony, founded in 710 B.C., on a projecting headland nearly half-way between Sybaris on the N. and Locri on the S., while behind it stretched the primeval forests and mountain pastures of Sila. The government of the colony was at that time aristocratic, but the power of the nobility, though superior to any other, was not unquestioned; and the arrival of the philosopher added strength to the dominant party, whose cause he embraced; for he came with no small pretensions, and already many marvellous stories were in circulation about him. He was said to have received many of his doctrines from Empedocles, the priestess of Delphi; to have been initiated into the mysteries of the Idaean cave in Crete; to have shown at Olympia a golden thigh rivalling the mythical shoulder of Pelops; to have received from Hermes the gift of recollecting all the stages of his previous existence; and to have given many other proofs of a supernatural intercourse with the unseen and celestial powers. These honours were undoubtedly claimed for him, either by himself or by his followers, and their effect is said to have been such, that he was reverenced by the Crotoniats as the Hyperborean Apollo. The accounts which we have of the wonderful change effected at Crotona after his arrival may be dismissed as belonging to the same class with those which narrate his superhuman dignity and exploits. We cannot Pythagoras doubt, however, that here Pythagoras so far succeeded in his designs as to form a secret society, partly religious and partly political, which exercised a great influence in the city, and spread the doctrines of its founder over the other cities of Magna Graecia, where branches of the original society were probably established.

The sudden and violent catastrophe which soon after befell these societies was the occasion of a wider dissemination throughout Greece of the opinions they maintained. The constitution of Crotona had become, since the arrival of Pythagoras, more decidedly aristocratic than ever; the Pythagoreans are said to have even entertained a project for abolishing altogether the popular assembly. Meanwhile the neighbouring city of Sybaris had undergone a revolution; the popular party gained the upper hand there; and one of their leaders named Telys established himself as a tyrant. Five hundred of the opposite party left the city and took refuge in Crotona; and when Telys sent to demand them to be given up, the Crotoniats, at the instigation of the Pythagoreans, refused to do so. A war between the two cities was the result, in which the army of Crotona, under Milo, a Pythagorean, defeated a much superior force of Sybarites, and took and destroyed the city. A dispute then arose among the victors about the distribution of the spoil and conquered territories. The Senate, supported by the Pythagoreans, proposed to retain the whole as public property; but the people, indignant at this, rose in a body, and directing their rage mainly against the Pythagoreans, set fire to the house of Milo, where they were assembled, put many of them to death, and dispersed the rest. A general persecution of the sect throughout Magna Graecia ensued, and the disorder and bloodshed was only ended by the interference of the Achaeans in Greece, who established in Crotona and the other cities, a democratic government. Whether or not Pythagoras was personally involved in the outbreak at Crotona, which happened in 504 B.C., is not certain; he is generally supposed to have retired to Metapontum, where he died, and where the exact spot of his death was still pointed out in the time of Cicero. (De Finibus, v. 2.) The date of his death, and the age to which he lived, are as variously reported as that of his birth. The earliest date given for his death is 510, the latest 472; while, according to another account, it took place in 500. According to Iamblichus, who takes the latest date for his death, Pythagoras presided in his school thirty-nine years; while his whole life is generally said to have been ninety years, though some make it only eighty, and others as much as one hundred and four.

Of the philosophy of Pythagoras, as a whole, it is not difficult to ascertain the general character and principles; but when we descend to the minute details, the notices that we possess are so obscure and unconnected, that it only requires a little ingenuity to find in the Pythagorean doctrines any preconceived system that the critic may prefer. This indeed has been attempted more than once in the interest of different schools. The Neo-Platonic philosophers saw their own peculiar tenets in the philosophy of Pythagoras; and some learned Christians have found there the doctrine of the Trinity, and have identified the celebrated Tetractys of the Samian with the Tetragrammaton, or incommunicable name of the Supreme Being among the Jews. The truth is, that we have not the materials to enable us to re-construct the system of Pythagoras, or to state very minutely any of its particular doctrines. It is all but certain that the founder of the school committed none of his speculations to writing; and our knowledge of his opinions is derived from the fragments that remain of the later Pythagoreans, and from the notices of other philosophers, especially of Aristotle. He indeed is Pythagoras by far our safest authority on the subject; for we cannot take the representations of later writers, especially those of the Neo-Platonic school, without making allowance for their remoteness in point of time, and for their own peculiar philosophical opinions.

The peculiar form assumed by the Pythagorean philosophy seems to have been derived from those mathematical studies in which its founder was proficient. The principles of mathematics were supposed to be the principles of all real existences; and as numbers are the primary constituents of mathematical quantities, and at the same time present many analogies to various realities, it was further inferred that the elements of numbers were the elements of realities. Now the elements of numbers were considered to be the odd and the even; the former of which was regarded as limited, and the latter as unlimited. (Arist. Metaph. i. 6.) Unity, again, seems to have been viewed in a twofold light: on the one hand as identical with the odd or the limited; and on the other as partaking of the nature both of the odd and of the even, and being the source of both. Thus all things depend on numbers; numbers themselves on the two principles odd and even; and these, again, on the primary unit. The doctrine was further illustrated by an arrangement of the principles of things in ten pairs, not as twenty distinct and separate principles, but as ten several ways of expressing the two great principles. The first three of these pairs are the most important, and they are—the limited and the unlimited,—the odd and the even,—the one and the many; while the peculiar character of the principles are brought out by the names which occur lower down in the list—light and darkness, good and evil. The latter member of each antithesis was regarded as inferior to the former (Arist. Eth. Nic. i. 6), and as being in fact somehow a mere negation of it. Thus the one, the odd, the limited, was in reality the only cause of all; the many, the even, the unlimited, being a mere nonentity, till called into existence by union with the other. We see then, under what to us appears a fanciful and cumbrous symbolism, a system of pantheism. As numbers are evolved from unity, so from the primary unit all the universe is evolved; or in other words, as we are told by Cicero (De Nat. Deor. i. 11), Pythagoras held that the Deity was the soul of the world, diffused throughout all its parts. The origin of evil was by this system referred not so much to the primary unit as to the second negative principle, without which it was impossible for the world to exist.

Such were the fundamental principles of the Pythagorean philosophy; and so far as they are concerned there is little doubt. But the theory of numbers was carried to a much greater length, and with much more minuteness of detail, for besides the unit, a special meaning was attached to each separate number up to ten. Here it is safest at once to confess our ignorance, for we leave the region of well-ascertained facts, and enter one where plausible conjecture is the best that we can put in their place. The view of Alexander Aphrodisiensis, followed by Ritter, that the monads being points, and the unlimited, void space; the dual is the line, composed of two such monads, with the intervening space; the triad, the surface, of three monads; and the tetrad, the solid, of four such; was probably held by some of the Pythagoreans, though it has been doubted whether Pythagoras himself taught it. We must suppose that his theory of the material world resembled it in this, that it was idealistic in its character, resolving matter into mere negative or immaterial principles. The pantheism of Pythagoras was certainly more akin to the idealistic than to the materialistic form of that theory. The way in which the principle of numbers was carried out by Pythagoras in natural philosophy is illustrated by his astronomical speculations. He assumed that the number of the heavenly spheres could be neither more nor less than the perfect number ten, which played an important part in his symbolism; and in order to make up this number, supposed the existence of another body, the counter-earth (ἀντίγηρος), on the other side of this earth. Thus the ten spheres revolving round the central fire, which had the form of a cube, and was called the watch-tower of Zeus, were those of the counter-earth, the earth, the moon, the sun, the five planets in order, and the fixed stars,—the whole universe thus forming a sphere. The perfection and harmony of the whole was reconciled with the too obvious evils prevalent in this mundane sphere, by supposing that the earth was the principal seat of the imperfection in the world, being the second in number, and thus associated with the principle of evil in the Pythagorean system—the even, the many, the unlimited. Further, as the intervals between the several spheres and the velocities of their motions were regularly proportioned according to the musical scale, hence arose the doctrine of the music of the spheres (Cic. De Nat. Deor. iii. 11), which is inaudible to us, either from the effects of custom, or from being too powerful for our faculties. The doctrine of numbers, when thus carried into physical science, seems to have been regarded by the Pythagoreans rather as deriving illustration than scientific proof from the phenomena, for they considered objects to be an imitation of the numbers (ἀπόγραφε τῶν ἀπόγραφων. Arist. Metaph. i. 6).

The psychological opinions of Pythagoras were not less memorable or characteristic than the other parts of his system. In accordance with his theory, the soul was termed a number or a harmony, and was regarded as homogeneous with the divine soul of the world, from whence it sprung. An immaterial principle was thus asserted, capable of existing apart from the body; and indeed the pre-existence of the soul, before entering its present body, was with Pythagoras, as with Plato afterwards, a conspicuous article of belief. After its departure from the body at death the soul may, according to the celebrated doctrine of metempsychosis, pass into another body, and that not necessarily a human body, but often that of one of the lower animals. Pythagoras himself professed to have once animated the body of Euphorbus, the son of Panthus; and, as Horace says,

"Clypeo Trojana refixo Tempora testatus: nihil ultra Nervos aquae cutem morti concesserat atm." (Od. i. 28.)

There must indeed always be some sort of fitness or adaptation of the soul to the body it assumes, and it is as a punishment that it is compelled at all to assume a corporeal nature, in which it is, as it were, buried. Thus, while the wicked have their final place of abode in Tartarus (Arist. Anal. Post. ii. 11), the good on the other hand are raised to the highest position. The Pythagorean psychology, according to one account, recognised two, and, according to another, three parts in the soul. According to Cicero (Tusc. Quest. iv. 5) it was divided into a rational and irrational part; the former peculiar to man, and the latter common to the brutes; but the account given by Diogenes Laertius, from its peculiar phraseology, is more likely to represent the views of Pythagoras. That part of the soul which is peculiar to man is there called ἄρχοντας, and located in the brain, the ὀνειδος, also placed in that organ, and the ἀρχοντας, which had its seat in the heart, were possessed also by the lower animals.

The science of ethics owed much to the Pythagorean school; for, according to Aristotle, they were the first who attempted anything in this field. It is impossible to ascertain with any certainty or distinctness, what were their peculiar opinions on this subject. The same peculiar phraseology was kept up here also, and they attempted to express, by means of numbers, such ideas as virtue, justice, Pythagorean marriage, and opportunity. (Arist. Metaph. i. 5; xii. 4.)

The whole doctrines of the sect were probably made in some degree, like those of Platonism, subservient to ethical purposes, and the precepts that were inculcated seem to have been intended for the production in the soul of that order and harmony which characterize the external world. They partake very much of an ascetic character, recommending the controlling of the passions and desires, the endurance of bodily hardships of all kinds, and the observance of the duties of friendship, for which some of the sect became very celebrated. On political subjects the opinions of Pythagoras were, as we have already seen, inclined towards aristocratical institutions, in which he would probably see more of that order and harmony which constitutes excellence on his view, than in the more popular forms of government.

It now only remains to state briefly the chief facts known about the peculiar external observances of the Pythagorean societies. They possessed much of the character of the ancient mysteries or secret societies wherein peculiar doctrines were taught, that were hidden from the vulgar eye. Candidates for admission were not initiated until they had passed through a lengthened course of probation, one part of which consisted in the injunction of silence for a period. The members admitted were divided into several classes, according as they were more or less intimately acquainted with the peculiarly sacred and mysterious doctrines of the sect; though, from the diverse statements of ancient authors, it is impossible to say for certain what was the number or names of these classes. They lived together, taking their meals at a common table, and engaged in common in those exercises, especially of gymnastics and music, which were held to be conducive to their bodily and mental wellbeing. Implicit faith in the founder of the system was inculcated; so that their formula of assentation, "άριστος ἐόντως," became proverbial. There were, besides, various symbolical observances enforced, such as abstinence from animal food, from fish, and from beans; but considerable doubt and obscurity hang over these injunctions, though they are noticed by several of the classical writers. Perhaps we will acquire the most correct views of the Pythagorean mysteries or orgies if we adopt the opinion of Herodotus (ii. 81), who identifies them with those of Orpheus and Bacchus, a view which seems to be confirmed by general similarity of the Pythagorean to what we know of the Orphic doctrines. Orpheus seems to have taught a system of pantheism; and it is remarkable that Virgil, in his description of the lower world, where he seems partially to adopt Pythagorean principles (Ene. vi. 724-752), introduces as an important personage the long-robed Thracian priest. On this view we may suppose that much of what Pythagoras embodied in his system formed part of a previously existing religion, and was made by him a vehicle for conveying his peculiar doctrines with more authority to his disciples. Thus perhaps the theory of metempsychosis was but a peculiar form into which the doctrine of immortality and a future retribution was cast. A very similar theory to that of the philosopher is certainly adopted by Pindar (Ol. ii.), within a time apparently too short for a totally new doctrine to have gained acceptance. All that belongs to the theory of number must evidently be ascribed to Pythagoras himself; but it is not improbable that many of his minor doctrines and peculiar precepts were borrowed from previously existing notions and observances. Even the scantiness of our knowledge of Pythagoras cannot conceal from us the fact that he must have been one of the most remarkable men that have ever lived. As to his philosophy, perhaps the highest praise we can give it is, that it contributed greatly to give rise to the lofty speculations of Plato, of whom he was the precursor; and as to his institutions, they long survived to perpetuate the memory and fame of their founder. (See Ritter's History of Ancient Philosophy; Smith's Dictionary of Greek and Roman Biography; Archer Butler's Lectures on the History of Ancient Philosophy, &c.)