Pythagoreanism

“ At last, there arose a philosopher who cleared his imagination of the fallacies of kinds, as earth, air, fire, and water, and made the bold hypothesis that all things are ultimately founded, not on kind, but on its reciprocal, number, for Pythagoras was a mathematician. Then began the theories of reified abstractions, the theories by which the properties of bodies are unified as a foundation for monistic philosophy. ”

“ These four numbers which, united by addition produce the number 10, constituted the Being, as much universal as particular; so that the Quaternary, which is as its virtue, could become the emblem of all beings, since there is none which may not recognize the principles, and which does not manifest itself by faculties more or less perfect, and which may not enjoy an existence universal or relative; but the being to which Pythagoras applied it most commonly was Man. Man, as I have said, manifests himself as does the Universe, under the three principal modifications of body, soul, and spirit. ”

“ Pythagoras affirmed this to be a sacred quaternion, source of everlasting nature, [7] having, as it were, roots in itself; and that from this number all the numbers receive their originating principle. For eleven, and twelve, and the rest, partake of the origin of existence [8] from ten. Of this decade, the perfect number, there are termed four divisions,—namely, number, monad, [9] square, (and) cube. And the connections and blendings of these are performed, according to nature, for the generation of growth completing the productive number. ”

“ The mind that could conceive the world as a sphere and that interested itself in weights and measures was, obviously, a mind of the visualizing type. It is characteristic of this type of mind to be interested in the tangibilities of geometry, hence it is not surprising to be told that Pythagoras "carried that science to perfection." ”

“ Turning now to their philosophical teaching, the first thing that we have to understand is that we cannot speak of the philosophy of Pythagoras, but only of the philosophy of the Pythagoreans. For it is not known what share Pythagoras had in this philosophy or what share was contributed by his successors. Now we recognize objects in the universe by means of their qualities. But the majority of these qualities are not universal in their scope; some things possess some qualities; others possess others. A leaf, for example, is green, but not all things are green. ”

“ If one examines carefully the different cults which still dominate upon earth, one will see that they have not been animated by any other spirit. The knowledge of the Being of beings has been offered everywhere as the aim of wisdom; its similitude, as the crown of perfection; and its enjoyment, as the object of all desires and the goal of all efforts. The enumeration of its infinite faculties has varied; but when one has dared fix one’s attention upon the unity of its essence, one has always defined it as has Pythagoras: the principle and the end of all things. ”

“ I refer to the system of the Pythagoreans—one of the most remarkable instances of the invention of facts to fit and carry out a theory that can be found in the history of philosophy, although we are not without striking examples of this practice in modern speculations. It has already been seen that, during the whole period of Greek philosophy before the time of Plato, the problem was to find a primordial and universal agent by which the sensible universe was built up and produced; supplying, that is to say, the matter and force required for the generation of successive products. ”

“ The philosophy of Pythagoras, which was full of superstition, did first plant a monstrous imagination, which afterwards was, by the school of Plato and others, watered and nourished. It was, that the world was one entire, perfect, living creature; that the ebbing and flowing of the sea was the respiration of the world, drawing in water as breath, and putting it forth again. They went on and inferred, that if the world were a living creature, it had a soul and spirit. ”

“ Those of the Peripatetic school affirmed that in rhetoric and poetry, and in the popular music, any one may be an adept though he has gone through no process of study; but that in those pursuits properly called studies, [3] none can have any real knowledge unless he has first become a student of them. Hence they supposed that the theory of these things was called Mathematics, from μάθημα, study, science. And the followers of Pythagoras are said to have given this more distinctive name of mathematics to geometry, and arithmetic alone. ”

“ Numbers have their value in music, in gymnastics, in medicine, in morals, in politics, in all branches of science. The Pythagorean arithmetic is the bond and universal logic of the knowable. But at the same time Pythagoras and his school peopled the world with demons and genii, which were the causes of disease; they did not abandon the old mythical ideas of the incarnation of spirits and the transmigration of souls—theories and beliefs which recur in nearly all primitive and savage peoples. ”

“ In the seventeenth century, the birth of modern science required a new mathematics, more fully equipped for the purpose of analysing the characteristics of vibratory existence. And now in the twentieth century we find physicists largely engaged in analysing the periodicities of atoms. Truly, Pythagoras in founding European philosophy and European mathematics, endowed them with the luckiest of lucky guesses — or, was it a flash of divine genius, penetrating to the inmost nature of things? ”

“ We may gather from this, what is to be said of those who suppose that Pythagoras undoubtedly went too far, when he conceived the essence of things as mere number. It is true, they admit, that we can number things; but, they contend, things are far more than mere numbers. But in what respect are they more? The ordinary sensuous consciousness, from its own point of view, would not hesitate to answer the question by handing us over to sensuous perception, and remarking, that things are not merely numerable, but also visible, odorous, palpable, &c. ”

“ Pythagoras, like Empedocles, was a sort of magician or god. His doctrine was a religion, the respect with which he was surrounded was a cult, the observances he imposed on his family and on his disciples were rites. What he taught was that the true realities, which do not change, were numbers. The fundamental and supreme reality is one; the being who is one is God; from this number, which is one, are derived all the other numbers which are the foundation of beings, their inward cause, their essence; we are all more or less perfect numbers; each created thing is a more or less perfect number. ”

“ In his lectures, Pythagoras taught the mathematics, as a medium whereby to prove the existence of God from observation and by means of reason; grammar, rhetoric, and logic, to cultivate and improve that reason, arithmetic, because he conceived that the ultimate benefit of man consisted in the science of numbers, and geometry, music, and astronomy, because he conceived that man is indebted to them for a knowledge of what is really good and useful. ”

“ Pythagoras studied science in Egypt and first became familiar with Egyptian and Babylonian mathematics and geometry. He also studied the Milesian cosmological philosophy. On his return to Greece from his foreign studies he sought to discover a principle of homogeneity in the universe more acceptable than any suggested by the earlier philosophers. He had noticed numerous relationships between numbers and natural phenomena, and believed that the true basis of philosophy was to be found in numbers. In seeking data to sustain this thesis, he discovered harmonic progression. ”

“ The method made use of by the moderns, in the new philosophy, recommends itself by its own excellence; for the spirit of analysis and geometry that pervades their manner of treating subjects, has contributed so much to the advancement of science, that it were to be wished they had never swerved from it. It is not, however, to be denied, that the noblest parts of that system of philosophy, received with so much applause in the three last centuries, were known and inculcated by Pythagoras, Plato, Aristotle, and Plutarch. ”

“ Pythagoras, by bringing up his scholars in the speculative knowledge of numbers, made their conceits therein so strong, that when they came to the contemplation of things natural, they imagined that in every particular thing they even beheld as it were with their eyes, how the elements of number gave essence and being to the works of nature: a thing in reason impossible ”

“ Moderatus Gaditanus, in relation to the numbers of Pythagoras, says, “Numbers are, so to speak, an assemblage of units, a progressive multitude which arises from unity, and finds there its ultimate cause.” And Hermias, expounding the doctrine of the Pythagoreans, says, that, according to them, “the unit, or simple essence, was the origin and principle of all things.”
Sextus Empiricus deems it unworthy of a philosopher to advance, that what falls under the notice of our senses, could be the principle of all things; for things sensible ought to be derived from what is not so. ”

“ There is harmony of numbers in all nature—in the force of gravity, in the planetary 47 movements, in the laws of heat, light, electricity and chemical affinity, in the forms of animals and plants, in the perceptions of the mind. Indeed, the direction of natural and physical science is towards a generalisation which shall express the fundamental laws of all by one simple numerical ratio. The mysticism of Pythagoras was vague only to the unlettered. It was a system of philosophy founded on existing mathematics which comprised more of the philosophy of numbers than our present. ”

“ The world also, which is composed from these tetractys, is perfect, being elegantly arranged in geometrical, harmonical, and arithmetical proportion; comprehending every power, all the nature of number, every magnitude, and every simple and composite body. But it is perfect, because all things are the parts of it, but it is not itself the part of any thing. Hence, the Pythagoreans are said to have first used the before-mentioned oath, and also the assertion that “all things are assimilated to number.” ”

“ Special emphasis was laid upon the mystery of numbers, and it is possible that the Neo-Pythagoreans had a far wider knowledge of the true teachings of Pythagoras than is available today. Even in the first century Pythagoras was regarded more as a god than a man, and the revival of his philosophy was resorted to apparently in the hope that his name would stimulate interest in the deeper systems of learning. But Greek philosophy had passed the zenith of its splendor; the mass of humanity was awakening to the importance of physical life and physical phenomena. ”

“ In this mysticism of numbers, that which alone has truth and value, is the thought, which lies at the ground of it all, that there prevails in the phenomena of nature a rational order, harmony and conformity to law, and that these laws of nature can be represented in measure and number. But this truth has the Pythagorean school hid under extravagant fancies, as vapid as they are unbridled.
The physics of the Pythagoreans possesses little scientific value, with the exception of the doctrine taught by Philolaus respecting the circular motion of the earth. Their ethics is also defective. ”

“ Pythagoras is said to have explained the conception of God in terms of mathematics and to have been willing to accept the personages of the popular polytheism on condition of finding their true mathematical equation.89.1 But this philosopher stands apart from the other leaders of this first period of Hellenic free thought. The mathematical mind is often a prey to mysticism. And Pythagoras was the most powerful champion and apostle of Orphism, the founder of those secret societies that threatened the secular and the intellectual freedom of Hellas. ”

“ Pythagoras, by his skill in mathematics, discovered that there can be no more than five regular solid figures, terminated by plane surfaces which are all similar and equal; to wit, the tetrahedron, the cube, the octahedron, the dodecahedron, and the eicosihedron. As nature works in the most simple and regular way, he thought that all elementary bodies must have one or other of those regular figures; and that the discovery of the properties and relations of the regular solids must be a key to open the mysteries of nature. ”

“ In making this extensive generalization, Pythagoras may, on his known principles, be supposed to have reasoned as follows: The mind of man perceives the relations of an eternal order in the proportions of space, and form, and number. That mind is, no doubt, a portion of the soul which animates and governs the universe; for on what other supposition shall we account 302 for its internal principle of activity--the very principle which characterizes the prime mover, and can scarce be ascribed to an inferior nature? ”

“ The Duad, for a contrary reason, was female, ever changing by addition, subtraction, or multiplication. It represents matter capable of form.
The union of the Monad and Duad produces the Triad, signifying the world formed by the creative principle out of matter. Pythagoras represented the world by the right-angled triangle, in which the squares of the two shortest sides are equal, added together, to the square of the longest one; as the world, as formed, is equal to the creative cause, and matter clothed with form. ”

“ I have often admired the mystical way of Pythagoras, and the secret Magick of numbers. Beware of Philosophy, is a precept not to be received in too large a sense; for in this Mass of Nature there is a set of things that carry in their Front, though not in Capital Letters, yet in Stenography and short Characters, something of Divinity, which to wiser Reasons serve as Luminaries in the Abyss of Knowledge, and to judicious beliefs as Scales and Roundles to mount the Pinacles and highest pieces of Divinity. ”