Page:Encyclopædia Britannica, Ninth Edition, v. 20.djvu/150

Rh 138 PYTHAGORAS 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 metem- psychosis to Egypt, as well as the practice of burying the dead exclusively in linen garments, but he does not men- tion 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 organiza- tion, which seems to have resembled a religious brother- hood 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 hardi- hood along with certain other traits of a more definitely religious character, which were probably due to the influ- ence 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 repre- sented 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 ramifica- tions must latterly have become. Its entanglement with politics was in the end fatal to its existence. The authori- ties differ hopelessly in chronology, but ^ according to the balance of evidence the first reaction against the Pytha- goreans 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 ; men- tion 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 Grsecia 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, P/iaedo, 6 ID), 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 assert- ing 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 un- limited, 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 funda- mental 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 exist- ence 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 repre- sent 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 sur- face 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 poten- tial decade (1 + 2 + 3 + 4 = 10) ; Pythagoras is celebrated as the dis- coverer of the holy rerpaKr^, " the fountain and root of ever-living nature." "Seven" is called irap6tvos and 'AB-fiv-rj, 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 con- sidered as a number apart). The thought already becomes more fanciful when "one" is identified with reason, because it is un- changeable ; "two" with opinion, because it is unlimited and indeterminate ; "four" with justice, because it is the first square