PYTH'AGO'REANISM. The philosophical system advocated by the followers of Pythagoras. No point in Greek philosophy is more disputed than the proper interpretation of Pythagorean ism. According to Zeller's exposition "the Pytha gorean system started from the proposition that all is, in its essence. number. From this results the doctrine of the primitive opposites; and consequently, the opposition of the odd and the even, the limited and the unlimited precede all others. The unity likewise of these opposites was sought in number alone, which was therefore defined more particularly as harmony. Many of our authorities, however, represent the matter differently. They assert that the entire system was founded on the opposition of unity and dual ity, which is then reduced to the opposition of spiritual and corporeal. of form and substance, of the Deity and matter. and is itself derived from the Deity as the original Unity. According to another theory. the starting point of the sys tem was not the arithmetical conception of num ber and its constituents, but the geometrical con ception of the limits of space and of unlimited space." A fourth opinion "bases the system not on the consideration of number, but on the dis tinction of the limited and unlimited." This is not the place to canvass the arguments for and against each of these interpretations. The probability is that there was no one single consistent theory accepted by all Pythagoreans, but that each of these theories was held by some one or more of their number. The real question is not what Pythagoreans taught, but what was the earliest statement of philosophical problems given by accredited Pythagoreans. Even this question cannot be answered with assurance, as far as the fundamental principle of the system is concerned. Pythagoras himself probably gave no clear expression of philosophical opinion, be cause lie was not so much interested in philo sophical theory as in religious and moral reform. See PYTHAGORAS.
Philolaus, a contemporary of Socrates and De mocritus, was probably the first distinctively philosophical Pythagorean, and although lie com mitted his views to writing, unfortunately we have only fragments of his works, and even they are of doubtful authenticity. Nor is the witness of Plato and Aristotle to his teachings wholly unambiguous. Although the weight of Zeller's great name is given to the arithmetical inter pretation of his views. it seems more satisfactory
to regard Philolaus as having started from geo metrical facts and the phenomena of sounds pre sented by the strings of the heptachord. If this hypothesis be correct Philolaus held an atomistic view of the constitution of the world. The ulti mate units of reality were considered to be per ceptible spatial points of material character. Two such points made a line, three made a surface, and four made a solid. By number lie did not mean an abstraction, but the concrete quantum of such points. "The Pythagorean Un limited is, in fact. the res eitc»,s.a; it is an early attempt to conceive Space in a realistic way and not merely as the place of body. Being an early attempt, it was not very successful: and. if the Pythagoreans did not make the Unlimited a mere predicate of Air like Anaximenes, they fell into the opposite extreme of simply identifying it with Air and the Void. The Limit must, of course, be strictly correlative with the Unlimited. It will then be a spatial limit, and not an ideal one. The theory that things are numbers, then. comes simply to this, that things are built up of geometrical figures. that they are portions of space limited in a variety of ways." (Burnet.) The smallest constituent parts of the earth were considered cubical, those of lire tetrahedral, those of water icosahedral. \slide those of "the fifth element which embraces all the others" were dodecahedral. But the Pythagoreans went fur ther and gave quantitative values to things im material, which were thus construed in a ma terial way. The soul was correlated in some way with the number six: reason, health, and light with seven; love, friendship, and prudence with eight. Such phantasy is the result of an attempt to reduce all reality to terms found sat isfactory in explaining sensible reality. Along with this curious fiction went a mystical signifi cance of numbers. The Pythagoreans were fond also of arranging things by opposites and finding ten such pairs. Thus one favorite classification gives us the following ten antitheses: (1) Lim ited and unlimited; 12) odd and even; 13) one and many: (4) right and left: (5 t male and female; (6) rest and motion: (7) straight anti crooked; (S) light and darkness; (9) good and evil; (10) square and rectangle.