§ 17.
1. About the time that Ionic Philosophy attained its highest development in Asia Minor, another phase of philosophical thought had its rise in the Greek Colonies of Italy. Here the inquiries of philosophers were no longer directed to the origin of things from Primary Matter, they turned rather on the Being or Essence of things in themselves. The Pythagorean school was the first to give this direction to philosophical investigation, but it made mathematics the basis of all its inquiries, and thus was led to certain mathematico-philosophical conceptions of the nature of things, which are altogether peculiar to the Pythagoreans.
2. Pythagoras, son of Mnesarchus, was born at Samos about the year B.C. 582. So many legends have become associated with his name that it is difficult to obtain a trustworthy account of his life and labours. Legends and traditions are, however, at one in representing him as a man of extraordinary knowledge. He is reckoned amongst the most remarkable of the founders of mathematical science. It is recorded of him that he succeeded in measuring the pitch of musical notes, and that he also made many discoveries in Astronomy. Some accounts make him the disciple of Pherecydes and Anaximander. It is probable that he travelled into Egypt, and there made acquaintance with the lore of the priests. About the year B.C. 529 he settled in Crotona, in Southern Italy, and there established a society whose aims were at once ethical, religious, and political.
3. In this Pythagorean association a rigid ethico-religious rule of life was enjoined. "A period of probation, during which the fitness of the candidate was tested, preceded admission into the society. The disciples were bound for a long time to mute obedience, and to unconditional subjection to the authority of the traditional teaching (autos epha): strict self-examination was required from all; it was forbidden to propagate the doctrines of the sect among the people." The members of the society were divided into classes, according to the extent of their initiation into the Pythagorean "orgies." Nothing certain is known regarding the names given to these classes, the terms Esoteric, and Exoteric, are usually employed to distinguish them.{1} They exercised themselves in gymnastics and music. They had their meals in common (sussitia), and they were subject to certain rules as to diet; for example, they were forbidden to eat beans, fish, or flesh. Hunting was not allowed amongst them.
4. In politics the Pythagorean sect belonged to the aristocratic party. Hence the Pythagorean doctrines gained supporters among the aristocratic classes in many Italian cities, and secured for the aristocratic party a certain intellectual standing. But these aristocratic leanings excited the opposition of the democratic party, and brought about the final extinction of the sect. Pythagoras himself, it is said, after twenty years' residence at Crotona, was expelled by a rival party under Cylon, and forced to retire to Metapontum, where he died soon after. The attacks of the democratic party on the Pythagoreans were renewed in subsequent times. A century after the death of Pythagoras, the Pythagoreans of Crotona were attacked by the "Cylonites" during a conference in the "house of Milo ;" the house was set on fire, and all perished, with the exception of Archippus of Tarentum and Lysis. Soon after this the political importance and power of the Pythagoreans in Italy came to an end; in the time of Plato, however, the Pythagorean Archytas was at the head of the administration in Tarentum.
5. The following are named as the most distinguished of the ancient Pythagoreans: Philolaus, a contemporary of Socrates, the first to make public in a written work the system of the school; Simmias and Cebes, who, according to Plato's "Phaedo," were friends of Socrates; Ocellus, the Lucanian; Timaeus, of Locri; Ecchecrates and Acrio; Archytas, of Tarentum; Lysis and Enrytus; Alcmaeon, of Crotona, a youthful contemporary of Pythagoras, who held the doctrine of contraries, of which he enumerated ten; Hippasus, of Metapontum, who held Fire to be the material principle of all things; Ecphantus, who combined the atomistic theory with that of the world-guiding Spirit, and who taught the revolution of the earth on its axis; Hippodamus, of Miletus, antitect and politician. Epicharmus, the comic poet, and others, are stated to have held doctrines akin to those of the Pythagoreans. -- (Cfr. Ueberweg.)
6. As for the sources from which our knowledge of the Pythagorean doctrines is derived, we have to rely chiefly on Aristotle. Pythagoras himself left no written work (the "Carmen Aureum" attributed to him is undoubtedly spurious). Nor has any work of the older Pythagoreans come down to us which we can trust as genuine. Böckh has collected fragments of a work by Philolaus. They would help us to a knowledge of the early Pythagorean teaching if we could be certain they were genuine; but they have been subjected to damaging criticism, and have been finally assigned to the last century before Christ. In the same way the fragments of Archytas of Tarentum, collected by Orelli, have been disparaged. The same may be said of the treatise of Ocellus Lucanus: De rerum natura, and of Timaeus Lucanus. We have, therefore, to recur to Aristotle for our knowledge of the older Pythagorean system. Other accounts of the system we can accept only in so far as they are in accord with his.
7. All that we can with certainty trace back to Pythagoras himself are the doctrine of Metempsychosis, the system of Mathematico-theological speculation, and the fixing of certain ethical and religious rules of conduct. When, then, we speak of Pythagorean doctrines, we mean no more than the teaching of Pythagoras as developed by his disciples and followers. We have here to do not so much with the personal opinions of the philosopher himself, as with the tenets of the Pythagorean school.
8. According to Aristotle (Met. 1, 2, 5), the Pythagoreans contemplating the order of nature, and the regularity of natural formations, with minds formed to mathematical conceptions, were led to make numbers the essential constituents of things. It was the fundamental principle of their teaching that Number is the essence (ousia) or ultimate basis (archê) of all things. Every individual thing is a number, and the aggregate of all things is a vast system of numbers (Arist. Met. 1, 5., 6-12, 6., 8-13, 6). According to this view, all things are not only arranged in numerical order, numbers are not merely symbols of the cosmical system, they constitute the substantial essence of all things. Aristotle states expressly that the Pythagoreans did not conceive numbers to be actually distinct from things (Met. 1, 6-13, 6):
9.
Everything which is the object of knowledge includes Number; without this element it could not possibly be the object of thought or knowledge. Now truth is a peculiar innate attribute of Number; it is of the very nature of Number or Harmony to reject deception as inimical and antagonistic. It is its function to rule and regulate, and to teach the hitherto unknown. Hence the conclusion that what is the most fixed and indefectible in our knowledge must also be the unchangeable essence of things in themselves." Things are therefore to be regarded as copies of numbers, because in them the universal nature of Number is reduced to individual existence.10. The originating principles of Number are Indefiniteness and Limit. The union of both constitute Number, as well of the "monadic" (mathematical) order, as of the "geometrical;" in each case, Number is the outcome of the combination in harmony of the two principles. Number is either odd or even; the former is the symbol of the Perfect, the latter of the Imperfect. The Pythagoreans assigned specially prominent functions in their system to the numbers four (tetraktus) and ten (dekas).
11. If it be true that Number constitutes the essential being of all things, it follows that the generating principles of Number -- Indefiniteness and Limit -- are the ultimate principles of all things. Everything consists of an unlimited and a limited (limiting) element, whereby its being is constituted. The unlimited is the indeterminate basis of being (in Aristotelian phraseology, the Matter); the limit is the determining principle by which the indeterminate is reduced to definite being (in Aristotelian phraseology, the Form). These two elements when combined constitute the essence of the determinate object.
12. We have now to consider in what fashion the Pythagoreans applied these general principles to explain the actual being of things in themselves, and in their relation to one another. Here we come upon their teaching regarding the nature of bodies. Having assumed that the ultimate elements of all things are the Undefined, and the Defining or Limiting, the Pythagoreans, when investigating corporeal nature, seem to have regarded the Undefined as vacuum, the Limit or defining element as a multitude of points fixed in some way or other in this empty space. So that their general principle: "All things are either numbers, or consist of numbers that are contained in them," is in this connection transformed into the other: "All bodies consist of points or units in space, which when taken together constitute a number." This is an assertion of the theory that the constitutent parts of the corporeal substance are themselves simple elements, and on this theory only can their nature be explained.
13. True to their mathematical conceptions the Pythagoreans regarded material bodies as proximately formed of super-imposed surfaces; these surfaces as formed of lines, and the lines formed of points. These purely mathematical conceptions they transferred to the real order, and taught accordingly that the single constituent elements of the mathematical body were also the real constituent elements, or, to use the words of Aristotle, the substance of the body in nature (Met. 7. 2.) By the juxtaposition of several points a line is generated, not merely in the scientific imagination of the mathematician but in external reality also; in the same way the surface is generated by the juxtaposition of several lines, and finally the body by the combination of several surfaces. Points, lines, and surfaces are therefore the real units which compose all bodies in nature, and in this sense all bodies must be regarded as numbers. In fact every material body is an expression of the number Four (tetraktus) since it results, as a fourth term, from three constituent elements (Points, Lines, Surfaces).
14. Simple points are not, however, enough of themselves to explain the nature of material bodies; we must also call to our aid the notion of vacuum, for it is by this that intervals of space are interposed between the points, without which they could not form lines, surfaces and bodies. If we suppose two points to co-exist without an interposed space, they coalesce and become one, and the formation of a line or body becomes impossible. Combinations of the unextended cannot produce extension unless we suppose intervals of space interposed, and this supposition becomes possible only when we assume the existence of a vacuum in which the points are distributed.
15. This vacuum is the Undefined which we must assume as the substratum of the defining element -- the points. This vacuum affording intervals of empty space between the points, they are able to arrange themselves in juxtaposition and so to form bodies. In this way then do the Undefined and Defining constitute the very being of material bodies. Vacuum, the Undefined, is, however, something negative in character, it does not contribute positively to the formation of bodies, it is merely a condition pre-supposed in order to make it possible for the positive unextended units to combine in a natural formation and constitute a body. The positive elements in the body are these units -- their "number;" they are the "substance" of all things corporeal.
16. It is thus that the Pythagoreans developed their principle that everything is Number in its application to material things, arriving in this fashion at a purely idealistic conception of the material world. Matter, as such, disappears, and there remain only ideal elements and ideal relations. The differences between bodies are explained by assuming different modes of combination on the part of the units, i.e., different intervals of separation between them. In the same way are explained the several mathematical forms with which the Pythagoreans invested the several bodies, the Cube -- the form of the Earth, the Icosahedron -- the form of the Air, the Sphere -- the form of Water, the Pyramid -- the form of Fire.
17. It would also appear that the Pythagoreans not only regarded each individual body as a number, but furthermore regarded the entire world as a vast arrangement of numbers. This numerical system of the Universe was framed upon the number ten. As the number ten is the most prominent in the system of numbers, so the whole universe consists of ten bodies, namely -- the heaven of the fixed stars, the five planets, the sun, the moon, the earth, and the counter-earth.{2} The wholly unchangeable portion of the Universe is that which stretches from the heaven of the fixed stars to the moon.{3} A less perfect part of the Universe exends from the moon to the earth; here again we meet with defect and change in individuals, immutability only in genera and species.
18. In the centre of the Universe is the Middle Fire. This is the animating principle of the whole. It diffuses light and heat through the Universe and is the source of life to all-things. The great bodies composing the world revolve round this Middle Fire. Their motion is not purely natural, i.e., determined by a blind necessity of nature; the evidences which it gives of Reason and Purpose force us to attribute it to sell-impulsion, and lead us to the conclusion that these bodies are endowed with Reason. In accordance with this reasoning the Pythagoreans reverenced the stars as gods.
19. An all-embracing harmony prevails throughout the Universe. For as the numerical system, reducing to unity a number of constituent parts, is harmony in itself, so must the Universe, which is the numerical system actualized, be regarded as a harmoniously arranged whole, and be described as the kosmos in the veritable sense of the word. Admitting that the heavenly bodies are arranged in an order determined by mathematical relations it follows that their movements must contribute to this general harmony, that from their movements a musical harmony must result -- the music of the spheres.
20. This peculiar notion of a music of the spheres was thus set forth in more detailed explanation by the Pythagoreans. The velocity of the celestial bodies in their motion round the Middle Fire must be proportioned to their distance from one another, and as every regularly vibrating body emits a note, it follows that harmony must result from the simultaneous movements of the heavenly bodies; that the sphere of the fixed stars must emit the deepest note, the sphere of the moon the highest, while the intermediate spheres will emit intermediate notes. Our ears are not sensible to the music of the spheres. But this arises either from the circumstance that we have been hearing it from our birth, and we distinguish a note only when we can contrast it with a previous silence, or because the harmony of the universe is a combination of sounds too intense to affect our sense of hearing.
21. Above the Universe, which is thus disposed in whole and in part according to number and measure, stands the Divine Monad, the Divine Spirit. As the unit is above all numbers, and is yet the basis of all numbers, so the Divine Being, though raised above all things which are numbered and measured, is yet the source of the being of all. God is the one, eternal, enduring, unchangeable Being, resembling only Himself, different from all other things, the one cause of all corporeal reality, who from eternity determines and upholds the universal order. Under the rule of this Divine Being, the world has subsisted from eternity, and will so subsist without end, for neither within it nor without it is there any other cause which can affect it. God is the ruler and guide of all things. He alone is wise. Nearest to Him in the perfection of its nature is that Fire which occupies the centre of the world. There is a sense, therefore, in which it may be said that the Middle Fire is the home of God. Hence the Pythagoreans sometimes named it the Watch-station, or Citadel of Jove (Dios phulakê Zênos purgos). The demons occupy an intermediate position between God and man.
22. In their view of the human soul the Pythagoreans are also influenced by their mathematical speculations. The Soul, too, is a number; it moves itself (Arist. de anim. 1, 2). They hold it to be an efflux from the Middle Fire, and to share in the divine nature in the same way as the source from which it comes. By number and harmony it is bound to the body, which is at once its instrument and its prison. A distinction must be made between what is rational and what is irrational in the soul. The latter alone is possessed by brutes, man possesses both.
23. The soul is indestructible; it outlives the body. The present life must be regarded as a process of purification for the soul. This process is continued after death, the soul is fated to inhabit other bodies, animal or human (metempsychosis). With this theory is associated the doctrine of retribution. The souls that are incurable are at last flung into Tartarus, while those which purify themselves rise higher and higher in the scale of life, and at last attain to life incorporeal.
24. The Pythagoreans seem to have held the view that the supreme good for man was assimilation with God, and the bliss thence resulting. The means to reach this end is Virtue. Virtue is essentially Harmony. It consists in the harmonious equilibrium of the faculties of the soul, by which the tendencies of the irrational part of the soul are subordinated to Reason. To establish this interior harmony in himself is the task of man in life. He can effect it by striving after true knowledge (philosophy), and by ascetic exercises. To this end the ordinances and the rule of life of the Pythagoreans were directed. They all aimed at repressing the tendencies of the irrational soul, and bringing them under the control of Reason. The moral maxims which were expressed in the symbolical language of the Pythagoreans were no more than the commendations of virtue as the harmony of man's inner nature. The Pythagoreans also employed music to charm the passions to rest, and to excite healthy energy. Gymnastics served the same purpose. The essence of justice consists in retribution (to antipepanthos.). Justice is a number which taken an equal number of times is equal (arithmos isakis isos -- square number).
{1} According to Iamblichus the Esoterics were further divided into the class of the strivers (ton spoudaiôn), the class of the spiritualized (ton daimoniôn), and the class of the divinized (ton Theon.)
{2} By Counter-earth the Pythagoreans meant a hemisphere detached from that which we inhabit, and moving parallel to it.
{3} Beyond the sphere of the fixed stars lies the encompassing fire (periechon puo.