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History of Philosophy
The Pythagorean School
by Turner, William (S.T.D.)

About the time the Ionic philosophy attained its highest development in Asia Minor, another phase of philosophical thought appeared in the Greek colonies of Italy. As we turn to the Pythagorean philosophy, the first philosophy of the West, we are struck with the importance which the ethico-religious aspect assumes from the outset; philosophy now is not so much an inquiry into the causes of things as a rule of life, a way of salvation. It is remarkable, too, that this notion of philosophy never wholly died out in the subsequent development of Greek thought. Plato, Aristotle, and the Stoics constantly referred philosophy to life as well as to knowledge.

The Pythagorean system of speculation is sometimes contrasted with the Ionian as being an embodiment of the Doric spirit, which was artistic, conservative, ethical, while the Greeks of the Ionian colonies were characterized by worldly sense, versatility, curiosity, and commercial enterprise. Both philosophies, however, are wholly Greek.

Life of Pythagoras. Samos was the home and probably the birthplace of Pythagoras. It is certain that he journeyed to Italy about the year 530 B.C., and that he founded in Crotona a philosophico-religious society. The story of his journey through Egypt, Persia, India, and Gaul is part of the Neo-Pythagorean legend, though there is good reason for believing that the account of his death at Metapontum is true.

Sources. Primary sources. The Neo-Pythagoreans mention an extensive Pythagorean literature as dating from the days of the founder. Modern scholarship has, however, shown that (1) the reputed writings of Pythagoras are certainly spurious; (2) the fragments of Philolaus (peri phusi˘s) are for the most part genuine: it was probably from these that Aristotle derived his knowledge of the Pythagorean doctrines; Philolaus lived towards the end of the fifth century; (3) the fragments of Archytas of Tarentum are spurious, with the exception of a few, which do not add to our knowledge of the Pythagorean doctrines, as they bear too evident marks of Platonic influence.

Secondary sources.[1] There is no school the history of which is so overgrown with legend as the Pythagorean. Indeed, Pythagoras and his disciples are seldom mentioned by writers anterior to Plato and Aristotle, and even the latter does not mention Pythagoras more than once or twice; he speaks rather of the Pythagoreans. Thus, the nearer we approach the time of Pythagoras the more scanty do our data become, while the farther the tradition is removed from Pythagoras the fuller they grow. Obviously, therefore, the Neo-Pythagoreans of the first century B.C. are not to be relied on when they speak of Pythagoras and his doctrines.
[1] Cf. Burnet, op. cit., pp. 301 ff.
The Pythagorean School was a society formed for an ethico-religious purpose. It was governed by a set of rules (ho tropos tou biou). The members recognized one another by means of secret signs; simplicity of personal attire and certain restrictions in matter of diet were required. Celibacy and the strict observance of secrecy in matters of doctrine were also insisted upon. The political tendency of the school was towards the aristocratic party in Magna Graecia, a tendency which led to the persecution and final dispersion of the society.


All that can with certainty be traced to Pythagoras is the doctrine of metempsychosis, the institution of certain ethical rules, and the germ idea of the mathematico-theological speculation, which was afterwards carried to a high degree of development. Consequently, by Pythagorean doctrines we must understand the doctrines of the disciples of Pythagoras, though these referred nearly all their doctrines to the founder. (Indeed, they carried this practice so far that they constantly introduced a question by quoting the autos epha, the ipse dixit of the Master.)

The Number Theory. The most distinctive of the Pythagorean doctrines is the principle that number is the essence and basis (archŕ) of all things. To this conclusion the Pythagoreans were led "by contemplating with minds trained to mathematical concepts" the order of nature and the regularity of natural changes.[2]
[2] Arist., Met., I, 5, 986 a, 23.
To the question, Did the Pythagoreans regard numbers as the physical substance of things, or merely as symbols or prototypes? the answer seems to be that they meant number to stand to things in the double relation of prototype and substance. And if the assertion, "All is number," sounds strange to us, we must consider how profound was the impression produced on the minds of these early students of nature by the first perception of the unalterable universal order of natural changes. Then we shall cease to wonder at the readiness with which number -- the formula of the order and regularity of those changes -- was hypostatized into the substance and basis of all things that change.

Philolaus (frag. 3) distinguishes three natural kinds of number: odd, even, and the odd-even. Aristotle [3] says that the Pythagoreans considered odd and even to be the elements (stoicheia) [4] of number. "Of these," he continues, "the one is definite and the other is unlimited, and the unit is the product of both, for it is both odd and even, and number arises from the unit, and the whole heaven is number." [5] From the dualism which is thus inherent in the unit, and consequently in number, comes the doctrine of opposites, finite and infinite, odd and even, left and right, male and female, and so forth. From the doctrine of opposites proceeds the notion of harmony, which plays such an important part in the Pythagorean philosophy, for harmony is the union of opposites.
[3] Met., I, 5, 985 b, 24.

[4] The term was first used in the technical scientific sense by Plato.

[5] On the Pythagorean concept of the Infinite, cf. Archiv f. Gesch. der Phil. (April, 1901), Bd. VII, Heft 3.
Application of the Doctrine of Number: 1. To physics. True to their mathematical concept of the world, the Pythagoreans analyzed bodies into surfaces, surfaces into lines, and lines into points. From this, however, we must not conclude that they conceived the numerical unit of all things as material; they apparently used numbers and geometrical quantities merely as quantities, abstracting from their contents, that is, without determining whether the contents were material or immaterial, a distinction which belongs to a later date.

Every body is an expression of the number four; the surface is three, because the triangle is the simplest of figures; the line is two, because of its terminations; and the point is one. Ten is the perfect number, because it is the sum of the numbers from one to four.

2. To the theory of music. The application of the number theory to the arrangement of tones is obvious. The story, [6] however, of the discovery of the musical scale by Pythagoras, as told by Iamblichus and others, is one of many instances in which discoveries made by the successors of Pythagoras were attributed to Pythagoras himself.
[6] Cf. Zeller, op. cit., I, 431, n.
3. To cosmology. Not only is each body a number, but the entire universe is an arrangement of numbers, the basis of which is the perfect number, ten. For the universe consists of ten bodies, -- the five planets, the sun, the moon, the heaven of the fixed stars, the earth, and the counter-earth (antichth˘n). The earth is a sphere; the counter-earth, which is postulated in order to fill up the number ten, is also a sphere, and moves parallel to the earth. In the center of the universe is the central fire, around which the heavenly bodies, fixed in their spheres, revolve from west to east, while around all is the peripheral fire. This motion of the heavenly bodies is regulated as to velocity, and is therefore a harmony. We do not, however, perceive this harmony of the spheres, either because we are accustomed to it, or because the sound is too intense to affect our organs of hearing.

4. To psychology. It would seem that the early Pythagoreans taught nothing definite regarding the nature of the soul. In the Phaedo, [7] Plato introduces into the dialogue a disciple of Philolaus, who teaches that the soul is a harmony, while Aristotle [8] says: "Some of them (the Pythagoreans) say that the soul is identified with the corpuscles in the air, and others say that it is that which moves (to kinoun) the corpuscles." The idea, however, that the soul is a harmony seems to be part of the doctrine of the Pythagoreans. The transmigration of souls is, as has been said, traceable to the founder of the school, though it was probably held as a tradition, being derived from the mysteries without being scientifically connected with the idea of the soul or with the number theory.
[7] Phaedo, 85 E.

[8] De An., I, 2, 404, a, 26.
5. To theology. The Pythagoreans did not make extensive application of their number theory to their theological beliefs. They seem to have conformed, externally at least, to the popular religious notions, though there are indications of a system of purer religious concepts which were maintained esoterically.

6. To ethics. The ethical system of the Pythagoreans was thoroughly religious. The supreme good of man is to become godlike. This assimilation is to be accomplished by virtue. Now virtue is a harmony: it essentially consists in a harmonious equilibrium of the faculties, by which what is lower in man's nature is subordinated to what is higher. Knowledge, the practice of asceticism, music, and gymnastics are the means by which this harmony is attained. Finally, the Pythagoreans used numbers to define ethical notions. Thus, they said, justice is a number squared, arithmos isakis isos.

Historical Position. The chief importance of the Pythagorean movement lies in this, that it marks a deepening of the moral consciousness in Greece. The old-time buoyancy of religious feeling as seen in the Homeric poems has given way to a calmer and more reflective mood, in which the sense of guilt and the consequent need of atonement and purification assert themselves.

As a system of philosophy, the body of Pythagorean doctrine must, like all the pre-Socratic systems, be regarded as primarily intended to be a philosophy of nature, and this is how Aristotle describes it. [9] It is not concerned with the conditions of knowledge, and although the society which Pythagoras founded was ethical, the philosophy which is associated with that society treats of ethical problems only incidentally and in a superficial manner.
[9] Met., I, 8, 989 b, 29.
As an investigation of nature the Pythagorean philosophy must be pronounced a very decided advance on the speculative attempts of the Ionians. The Pythagoreans leave the concrete, sense-perceived basis of existence, and substitute for it the abstract notion of number, thus preparing the way for a still higher notion -- that of Being.


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