History of the Intellectual Development of Europe, Volume I (of 2) / Revised Edition

by John William Draper

The approval of the doctrines of Pythagoras so generally expressed was doubtless very much due to the fact that they supplied an intellectual void. Those who had been in the foremost ranks of philosophy had come to the conclusion that, as regard external things, and even ourselves, we have no criterion of truth; but in the properties of numbers and their relations, such a criterion does exist.

Pythagorean philosophy.

It would scarcely repay the reader to pursue this system in its details; a very superficial representation of it is all that is necessary for our purpose. It recognizes two species of numbers, the odd and even; and since one, or unity, must be at once both odd and even, it must be the very essence of number, and the ground of all other numbers; hence the meaning of the Pythagorean expression, "All comes from one;" which also took form in the mystical allusion, "God embraces all and actuates all, and is but one." To the number ten extraordinary importance was imputed, since it contains in itself, or arises from the addition of, 1, 2, 3, 4—that is, of even and odd numbers together; hence it received the name of the grand tetractys, because it so contains the first four numbers. Some, however, assert that that designation was imposed on the number thirty-six. To the triad the Pythagoreans likewise attached much significance, since it has a beginning, a middle, and an end. To unity, or one, they gave the designation of the even-odd, asserting that it contained the property both of the even and odd, as is plain from the fact that if one be added to an even number it becomes odd, but if to an odd number it becomes even. They arranged the primary elements of nature in a table of ten contraries, of which the odd and even are one, and light and darkness another. They said that "the nature and energy of number may be traced not only in divine and dæmonish things, but in human works and words everywhere, and in all works of art and in music." They even linked their arithmetical views to morality, through the observation that numbers never lie; that they are hostile to falsehood; and that, therefore, truth belongs to their family: their fanciful speculations led them to infer that in the limitless or infinite, falsehood and envy must reign. From similar reasoning, they concluded that the number one contained not only the perfect, but also the imperfect; hence it follows that the most good, most beautiful, and most true are not at the beginning, but that they are in the process of time evolved. They held that whatever we know must have had a beginning, a middle, and an end, of which the beginning and end are the boundaries or limits; but the middle is unlimited, and, as a consequence, may be subdivided ad infinitum. They therefore resolved corporeal existence into points, as is set forth in their maxim that "all is composed of points or spacial units, which, taken together, constitute a number." Such being their ideas of the limiting which constitutes the extreme, they understood by the unlimited the intermediate space or interval. By the aid of these intervals they obtained a conception of space; for, since the units, or monads, as they were also called, are merely geometrical points, no number of them could produce a line, but by the union of monads and intervals conjointly a line can arise, and also a surface, and also a solid. As to the interval thus existing between monads, some considered it as being mere aërial breath, but the orthodox regarded it as a vacuum; hence we perceive the meaning of their absurd affirmation that all things are produced by a vacuum. As it is not to be overlooked that the monads are merely mathematical points, and have no dimensions or size, substances actually contain no matter, and are nothing more than forms.

Pythagorean cosmogony.

The Pythagoreans applied these principles to account for the origin of the world, saying that, since its very existence is an illusion, it could not have any origin in time, but only seemingly so to human thought. As to time itself, they regarded it as "existing only by the distinction of a series of different moments, which, however, are again restored to unity by the limiting moments." The diversity of relations we find in the world they supposed to be occasioned by the bond of harmony. "Since the principles of things are neither similar nor congenerous, it is impossible for them to be brought into order except by the intervention of harmony, whatever may have been the manner in which it took place. Like and homogeneous things, indeed, would not have required harmony; but, as to the dissimilar and unsymmetrical, such must necessarily be held together by harmony if they are to be contained in a world of order." In this manner they confused together the ideas of number and harmony, regarding the world not only as a combination of contraries, but as an orderly and harmonical combination thereof. To particular numbers they therefore imputed great significance, asserting that "there are seven chords or harmonies, seven pleiads, seven vowels, and that certain parts of the bodies of animals change in the course of seven years." They carried to an extreme the numerical doctrine, assigning certain numbers as the representatives of a bird, a horse, a man. This doctrine may be illustrated Modern Pythagorisms in chemistry. by facts familiar to chemists, who, in like manner, attach significant numbers to the names of things. Taking hydrogen as unity, 6 belongs to carbon, 8 to oxygen, 16 to sulphur. Carrying those principles out, there is no substance, elementary or compound, inorganic or organic, to which an expressive number does not belong. Nay, even an archetypal form, as of man or any other such composite structure, may thus possess a typical number, the sum of the numbers of its constituent parts. It signifies nothing what interpretation we give to these numbers, whether we regarded them as atomic weights, or, declining the idea of atoms, consider them as the representatives of force. As in the ancient philosophical doctrine, so in modern science, the number is invariably connected with the name of a thing, of whatever description the thing may be.

The grand standard of harmonical relation among the Pythagoreans was the musical octave. Physical qualities, such as colour and tone, were supposed to appertain to the surface of bodies. Of the elements they enumerated five—earth, air, fire, water, and ether, connecting therewith the fact that man has five organs of sense. Of the planets they numbered five, which, together with the sun, moon, and earth, are placed apart at distances determined by a musical law, and in their movements through space give rise to a sound, the harmony of the spheres, unnoticed by us because we habitually hear it. They place the sun Pythagorean physics and psychology. in the centre of the system, round which, with the other planets, the earth revolves. At this point the geocentric doctrine is being abandoned and the heliocentric takes its place. As the circle is the most perfect of forms, the movements of the planets are circular. They maintained that the moon is inhabited, and like the earth, but the people there are taller than men, in the proportion as the moon's periodic rotation is greater than that of the earth. They explained the Milky Way as having been occasioned by the fall of a star, or as having been formerly the path of the sun. They asserted that the world is eternal, but the earth is transitory and liable to change, the universe being in the shape of a sphere. They held that the soul of man is merely an efflux of the universal soul, and that it comes into the body from without. From dreams and the events of sickness they inferred the existence of good and evil dæmons. They supposed that souls can exist without the body, leading a kind of dream-life, and identified the motes in the sunbeam with them. Their heroes and dæmons were souls not yet become embodied, or who had ceased to be so. The doctrine of transmigration which they had adopted was in harmony with such views, and, if it does not imply the absolute immortality of the soul, at least asserts its existence after the death of the body, for the disembodied spirit becomes incarnate again as soon as it finds a tenement which fits it. To their life after death the Pythagoreans added a doctrine of retributive rewards and punishments, and, in this respect, what has been said of animals forming a penitential mechanism in the theology of India and Egypt, holds good for the Pythagoreans too.

Of their system of politics nothing can now with certainty be affirmed beyond the fact that its prime element was an aristocracy; of their rule of private life, but little beyond its including a recommendation of moderation in all things, the cultivation of friendship, the observance of faith, and the practice of self-denial, promoted by ascetic exercises. It was a maxim with them that a right education is not only of importance to the individual, but also to the interests of the state. Pythagoras himself, as is well known, paid much attention to the determination of extension and gravity, the ratios of musical tones, astronomy, and medicine. He directed his disciples, in their orgies or secret worship, to practise gymnastics, dancing, music. In correspondence with his principle of imparting to men only such knowledge as they were fitted to receive, he communicated to those who were less perfectly prepared exoteric doctrines, reserving the esoteric for the privileged few who had passed five years in silence, had endured humiliation, and been purged by self-denial and sacrifice.

The Eleatic philosophy.

We have now reached the consideration of the Eleatic philosophy. It differs from the preceding in its neglect of material things, and its devotion to the supra-sensible. It derives its name from Elea, a Greek colonial city of Italy, its chief authors being Xenophanes, Parmenides, and Zeno.

Xenophanes represents a great philosophical advance.