PYTHAGORAS and PYTHAGOREANS. Pythagoras is one of those figures which have so impressed the imagination of succeeding times that their historical lineaments are difficult to discern through the mythical haze that envelops them. Animated, as it would appear, not merely by the philosophic thirst for knowledge but also by the enthusiasm of an ethico-religious reformer, he became, centuries after his death, the ideal hero or saint of those who grafted a mystical religious asceticism on the doctrines of Plato. Writings were forged in his name. Lives of him were written which gather up in his person all the traits of the philosophic wise man, and surround him besides with the nimbus of the prophet and wonder-worker. He is described by his Neoplatonic biographers as the favourite and even the son of Apollo, from whom he received his doctrines by the mouth of the Delphic priestess. We read that he had a golden thigh, which he displayed to the assembled Greeks at Olympia, and that on another occasion he was seen in Crotona and Metapontum at one and the same time. He is said to have tamed wild beasts by a word and to have foretold the future, while many stories turn upon the knowledge he was reported to retain of his personality and deeds in former states of existence. Thus, as Zeller truly remarks, the information respecting Pythagoreanism and its founder grows fuller and fuller the farther removed in time it is from its subject. The authentic details of Pythagoras’s career, on the other hand, are meagre enough and merely approximate in character. He was a native of Samos, and the first part of his life may therefore be said to belong to that Ionian seaboard which had already witnessed the first development of philosophic thought in Greece. The exact year of his birth has been ...variously placed between 586 and 569 b.c., but 582 may be taken as the most probable date. Some of the accounts make him the pupil of Anaximander; but such an assertion lies so ready to hand in the circumstances of time and place that we cannot build with any assurance upon the suggested connexion with the Ionic school. It is probable, however, that Pythagoras was aware of their speculations, seeing that he left behind him in Ionia the reputation of a learned and universally informed man. “Of all men Pythagoras, the son of Mnesarchus, was the most assiduous inquirer,” says Heraclitus, and then proceeds in his contemptuous fashion to brand his predecessor’s wisdom as only eclectically compiled information or polymathy (τroλυ∕χα0iα). This accumulated wisdom, as well as most of the tenets of the Pythagorean school, was attributed in antiquity to the extensive travels of Pythagoras, which brought him in contact (so it was said) pot only with the Egyptians, the Phoenicians, the Chaldaeans, the Jews, and the Arabians, but also with the Druids of Gaul, the Persian Magi, and the Brahmans. But these tales are told of too many of the early philosophers to be received implicitly; they represent rather the tendency of a later age to connect the beginnings of Greek speculation with the hoary religions and priesthoods of the East. There is no intrinsic improbability, however, in the statement that Pythagoras visited Egypt and other countries of the Mediterranean, for travel was then one of the few ways of gathering knowledge. Some of the accounts represent Pythagoras as deriving much of his mathematical knowledge from an Egyptian source. Herodotus traces the doctrine of metempsychosis to Egypt, as well as the practice of burying the dead exclusively in linen garments, but he does not mention any visit of Pythagoras to that country. There is thus little more than conjecture to fill out the first half of the philosopher’s life. The historically important part of his career begins with his emigration to Crotona, one of the Dorian colonies in the south of Italy. Nothing is known with certainty of the reasons that led to this step, which he appears to have taken about the year 529; perhaps the ethical temper which can be traced in the Pythagorean school attracted the founder towards the sterner Dorian character. At Crotona Pythagoras speedily became the centre of a widespread and influential organization, which seems to have resembled a religious brotherhood or an association for the moral reformation of society much more than a philosophic school. Pythagoras appears, indeed, in all the accounts more as a moral reformer than as a speculative thinker or scientific teacher; and it is noteworthy that the only one of the doctrines of the school which is definitely traceable to Pythagoras himself is the ethico-mystical doctrine of transmigration. The aim of the brotherhood was the moral education and purification of the community; and it seems to have been largely based upon a revival of the Dorian ideal of abstinence and hardihood along with certain other traits of a more definitely religious character, which were probably due to the influence of the mysteries. But many details of life and ritual, such as abstinence from animal food and from beans, celibacy, and even community of goods, have been fathered by the organized asceticism of a later period upon the original followers of Pythagoras. Ethics, according to the Greek and especially according to the Dorian conception, being inseparably bound up with the general health of the state, we are not surprised to find the Pythagoreans represented as a political league; nor is it wonderful that their following was among the aristocracy, and that they formed the staunchest supporters of the old Dorian constitutions. It is unfair, however, to speak of the league as primarily a political organization, wide though its political ramifications must latterly have become. Its entanglement with politics was in the end fatal to its existence. The authorities differ hopelessly in chronology, but according to the balance of evidence the first reaction against the Pythagoreans took place in the lifetime of Pythagoras himself after the victory gained by Crotona over Sybaris in the year 510. Dissensions seem to have arisen about the allotment of the conquered territory, and an adverse party was formed in Crotona under the leadership of Cylon. This was probably the cause of Pythagoras’s withdrawal to Metapontum, which an almost unanimous tradition assigns as the place of his death in the end of the 6th or the beginning of the 5th century. The league appears to have continued powerful in Magna Graecia till the middle of the 5th century, when it was violently trampled out by the successful democrats. The meeting-houses of the Pythagoreans were everywhere sacked and burned; mention is made in particular of “.the house of Milo” in Crotona, where fifty or sixty of the leading Pythagoreans were surprised and slain. The persecution to which the brotherhood was subjected throughout Magna Graecia was the immediate cause of the spread of the Pythagorean philosophy in Greece proper. Philolaus, who resided at Thebes in the end of the 5th century (cf. Plato, Phaedo, 6ID), was the author of the first written exposition of the system. Lysis, the instructor of Epaminondas, was another of these refugees. This Theban Pythagoreanism was not without an important influence upon Plato, and Philolaus had also disciples in the stricter sense. But as a philosophic school Pythagoreanism became extinct in Greece about the middle of the 4th century. In Italy— where, after a temporary suppression, it attained a new importance in the person of Archytas, ruler of Tarentum— the school finally disappeared about the same time.
Pythagorean Philosophy.
The central thought of the Pythagorean philosophy is the idea of number, the recognition of the numerical and mathematical relations of things. In the naive speculation of an early age the abstract consideration of these relations was tantamount to asserting their essential existence as the causes of phenomena. Hence the Pythagorean thought crystallized into the formula that all things are number, or that number is the essence of everything. “The Pythagoreans seem,” says Aristotle, “to have looked upon number as the principle and, so to speak, the matter of which existences consist”; and again, “they supposed the elements of numbers to be the elements of existence, and pronounced the whole heaven to be harmony and number.” “Number,” says Philolaus, “is great and perfect and omnipotent, and the principle and guide of divine and human life.” Fantastical as such a proposition sounds, we may still recognize the underlying truth that prompted it if we reflect that it is number or definite mathematical relation that separates one thing from another and so in a sense makes them things. Without number and the limitation which number brings there would be only chaos and the illimitable, a thought abhorrent to the Greek mind. Number, then, is the principle of order, the principle by which a cosmos or ordered world subsists. So we may perhaps render the thought that is crudely and sensuously expressed in the utterances of the school. They found the chief illustrations, or rather grounds, of their position in the regular movements of the heavenly bodies and in the harmony of musical sounds, the dependence of which on regular mathematical intervals they were apparently the first to discover. The famous theory of the harmony of the spheres combines both ideas: the seven planets are the seven golden chords of the heavenly heptachord.
Immediately connected with their central doctrine is the theory of opposites held by the Pythagoreans. Numbers are divided into odd and even, and from the combination of odd and even the numbers themselves (and therefore all things) seem to result. The odd number was identified with the limited, the even with the unlimited, because even numbers may be perpetually halved, whereas the odd numbers (at least the earlier ones), being without factors, seem to stand in solid singleness. All things, accordingly, were derived by the Pythagoreans from the combination of the limited and the unlimited; and it is in harmony with the Greek spirit that the place of honour is accorded to the odd or the limited. Following out the same thought, they developed a list of ten fundamental oppositions, which roughly resembles the tables of categories framed by later philosophers :—(1) limited and unlimited; (2) odd and even; (3) one and many; (4) right and left; (5) masculine and feminine; (6) rest and motion; (7) straight and crooked; (8) light and darkness; (9) good and evil; (10) square and oblong. The arbitrariness of the list and the mingling of mathematical, physical, and ethical contrasts are characteristic of the infancy of speculation. The union of opposites in which consists the existence of things is harmony; hence the expression already quoted that the whole heaven or the whole universe is harmony. But it is to be noted that interpretations of Pythagoreanism which represent the whole system as founded on the opposition of unity and duality, and suppose this to have been explicitly identified with the opposition of form and matter, of divine activity and passive material, must be unhesitatingly rejected as betraying on the surface their post-Platonic origin. Still more is this the case when in Neoplatonic fashion they go on to derive this original opposition from the supreme Unity or God. The further speculations of the Pythagoreans on the subject of number rest mainly on analogies, which often become capricious and tend to lose themselves at last in a barren symbolism. The decade, as the basis of the numerical system, appeared to them to comprehend all other numbers in itself, and to it are applied, therefore, the epithets quoted above of number in general. Similar language is held of the number “four,” because it is the first square number and is also the potential decade (1 + 2 4- 3 + 4 = 10); Pythagoras is celebrated as the discoverer of the holy τeτpaκτiς, “the fountain and root of ever-living nature.” “Seven” is called παρθένος and Άθ-ήνη, because within the decade it has neither factors nor product. “Five,” on the other hand, signifies marriage, because it is the union of the first masculine with the first feminine number (3 + 2, unity being considered as a number apart). The thought already becomes more fanciful when “one” is identified with reason, because it is unchangeable; “two” with opinion, because it is unlimited and indeterminate; “four” with justice, because it is the first square
number, the product of equals. More legitimate is their application of number to geometry, according to which “one” was identified with the point, “two” with the line, “three” with the surface, and “four” with the cube. In the history of music the Pythagorean school is also of considerable importance from the development which the theory of the octave owes to its members; according to some accounts the discovery of the harmonic system is due to Pythagoras himself.
As already mentioned, the movements of the heavenly bodies formed for the Pythagoreans an illustration on a grand scale of the truth of their theory. Their cosmological system is also interesting on account of peculiarities which mark it out from the current conceptions of antiquity and bring it curiously near to the modern theory. Conceiving the universe, like many early thinkers, as a sphere, they placed in the heart of it the central fire, to which they gave the name of Hestia, the hearth or altar of the universe, the citadel or throne of Zeus. Around this move the ten heavenly bodies—farthest off the heaven of the fixed stars, then the five planets known to antiquity, then the sun, the moon, the earth, and lastly the counter-earth (avτιχθωv'), which revolves between the earth and the central fire and thus completes the sacred decade. Revolving along with the earth, the last-mentioned body is always interposed as a shield between us and the direct rays of the central fire. Our light and heat come to us indirectly by way of reflexion from the sun. When the earth is on the same side of the central fire as the sun, we have day; when it is on the other side, night. This attribution of the changes of day and night to the earth’s own motion led up directly to the true theory, as soon as the machinery of the central fire and the counter-earth was dispensed with. The counter-earth became the western hemisphere, and the earth revolved on its own axis instead of round an imaginary centre. But, as appears from the above, the Pythagorean astronomy is also remarkable as having attributed a planetary motion to the earth instead of making our globe the centre of the universe. Long afterwards, when the church condemned the theory of Copernicus, the indictment that lay against it was its heathen and “Pythagorean” character.
The doctrine which the memory of mankind associates most closely with Pythagoras’s name is that of the transmigration of souls— Metempsychosis (g ’.u). Though evidently of great importance for Pythagoras himself, it does not stand in any very obvious connexion with his philosophy proper. He seems to have adopted the idea from the Orphic Mysteries. The bodily life of the soul, according to this doctrine, is an imprisonment suffered for sins committed in a former state of existence. At death the soul reaps what it has sown in the present life. The reward of the best is to enter the cosmos, or the higher and purer regions of the universe, while the direst crimes receive their punishment in Tartarus. But the general lot is to live afresh in a series of human or animal forms, the nature of the bodily prison being determined in each case by the deeds done in the life just ended. This is the same doctrine of retribution and purificatory wandering which meets us in Plato’s mythical descriptions of a future life. They are borrowed by him in their substance from the Pythagoreans or from a common source in the Mysteries. In accordance with this religious view of life as a stage of probation were the ethical precepts of the school, inculcating reverence towards the gods and to parents, justice, gentleness, temperance, purity of life, prayer, regular self-examination, and. the observance of various ritual requirements.
Connecting its ethics in this way with religion and the idea of a future life, the Pythagorean societies had in them from the beginning a germ of asceticism and contemplative mysticism which it was left for a later age fully to develop. The Pythagorean life was destined to survive the peculiar doctrines of the Pythagorean philosophy and to be grafted on later philosophic ideas. The asceticism which characterized it appears in the 4th century b.c. inclose connexion with the Orphic Mysteries; and the “Pythagoreans” of that time are frequently the butts of the New Athenian Comedy. In the Alexandrian period the Pythagorean tradition struck deeper roots; in Alexandria and elsewhere schools of men arose calling themselves Pythagoreans, but more accurately distinguished by modern criticism as Neopythagoreans, seeing that their philosophical doctrines are evidently derived in varying proportions from Plato, Aristotle, and the Stoics. In general it may be said that they develop the mystic side of the Platonic doctrine; and only so far as this is connected with the similar speculations of Pythagoras can they claim to be followers of the latter. Hence men like Plutarch, who personally prefer to call themselves Platonists, may also be considered as within the scope of this Pythagorean revival. The link that really connects these Neopythagoreans with the Samian philosopher and distinguishes them from the other schools of their time is their ascetic ideal of life and their preoccupation with religion. In religious speculation they paved the way for the Neoplatonic conception of God as immeasurably transcending the world; and in their thirst for prophecies, oracles, and signs they gave expression to the prevalent longing for a supernatural revelation of the divine nature and will. The asceticism of the Jewish sect of the Essenes seems, as Zeller contends, to be due to a strong infusion of Neopythagorean elements. At a still later period Neopythagoreanism set up Pythagoras and Apollonius of Tyana not only as ideals of the philosophic life but also as prophets and wonder-workers in immediate communication with another world, and in the details of their “lives” it is easy to read the desire to emulate the narrative of the Gospels. The Life of Apollonius by Philostratus, which is for the most part an historical romance, belongs to the 3d Christian century.
Zeller’s discussion of Pythagoreanism, in his Philosophie d. Griechen, book i., is very full; he also deals at considerable length in the last volume of the work with the Neopythagoreans, considered as the precursors of Neoplatonism and the probable origin of the Essenes. The numerous monographs dealing with special parts of the subject are there examined and sifted. (A. SE.)
Pythagorean Geometry.
As the introduction of geometry into Greece is by common consent attributed to Thales, so all are agreed that to Pythagoras is due the honour of having raised mathematics to the rank of a science. We know that the early Pythagoreans published nothing, and that, moreover, they referred all their discoveries back to their master. (See Philolaus.) Hence it is not possible to separate his work from that of his early disciples, and we must therefore treat the geometry of the early Pythagorean school as a whole. We know that Pythagoras made numbers the basis of his philosophical system, as well physical as metaphysical, and that he united the study of geometry with that of arithmetic.
The following statements have been handed down to us. (a) Aristotle (J∕ei., i. 5, 985) says “the Pythagoreans first applied themselves to mathematics, a science which they improved; and, penetrated with it, they fancied that the principles of mathematics were the principles of all things.” (ό) Eudemus informs us that “Pythagoras changed geometry into the form of a liberal science, regarding its principles in a purely abstract manner, and investigated its theorems from the immaterial and intellectual point of view (dυλωs καi voepω<s). ,1 (c) Diogenes Laertius (viii. 11) relates that “it was Pythagoras who carried geometry to perfection, after Moeris had first found out the principles of the elements of that science, as Anticlides tells us in the second book of his History of Alexander ∙, and the part of the science to which Pythagoras applied himself above all others was arithmetic.” (c?) According to Aristoxenus, the musician, Pythagoras seems to have esteemed arithmetic above everything, and to have advanced it by diverting it from the service of commerce and by likening all things to numbers. (e) Diogenes Laertius (viii 13) reports on the same authority that Pythagoras was the first person who introduced measures and weights among the Greeks. (∕) He discovered the numerical relations of the musical scale (Diog. Laert., viii. 11). (g) Proclus says that “the word ‘mathematics’ originated with the Pythagoreans.” (Ä) We learn also from the same authority that the Pythagoreans made a fourfold division of mathematical science, attributing one of its parts to the “howmany” (το ττόσον) and the other...
[7,184 words — estimated reading time: 45 minutes]