Religious Philosophy

"The Pythagoreans held, [Aristotle] tells us that there was "boundless breath" outside the heavens, and that it was inhaled by the world. In substance, this is the doctrine of Anaximenes, and... it was that of Pythagoras... Xenophanes denied it. ...[F]urther development of the idea is ...due to Pythagoras ...We are told that, after the first unit had been formed ...the nearest part of the Boundless was first drawn in and limited; and... the Boundless thus inhaled... keeps the units separate from each other. It represents the interval between them. This is a... primitive way of describing... discrete quantity."

"We know... Philolaos wrote on "numbers"; for Speusippos followed him in the account he gave of the Pythagorean theories on that subject. It is probable... he busied himself... with arithmetic, and... his geometry was... primitive... Eurytos was his disciple, and... his views were... crude."

"The Pythagoreans had... a great veneration for the... words of the Master... but... veneration is often accompanied by a singular licence of interpretation."

"[T]he most striking result of the Greeks' faith that the world could be understood in terms of rational principles was the invention of abstract mathematics. The most grandiose ambition they conceived was to explain all the properties of Nature in arithmetical terms alone. This was the aim of the Pythagoreans... [T]hey... knew that the phenomena of the Heavens recurred in a cyclical manner; and... discovered ...that the sound of a vibrating string ...is simply related to the length ...and its 'harmonics' always go with simple fractional lengths. ...[S]ince the Pythagoreans were a religious brotherhood... they thought that this search would lead to more than explanations alone. If one discovered the mathematical harmonies in things, one should... discover how to put oneself in harmony with Nature. ...[T]hey had ...positive grounds for thinking that both astronomy and acoustics were at the bottom arithmetical; and the study of simple fractions was called 'music' right down until the late Middle Ages."

"It is usually maintained that the Platonic or Socratic philosophy, like the rest of Greek speculation, was original, indigenous, owing very little to any outside influence. But the quest and life and faith of Socrates were as un-Greek as anything could possibly be: that was one of the reasons why the Greeks killed him: the essence of his life belonged to a world unknown to them, and therefore dangerous in their eyes […] There is only one “philosopher” whose doctrines, both practical and theoretical, appear to have resembled Plato’s in spirit and aim as well as in substance; and that one is Pythagoras. It is noteworthy that Pythagoras is the only great thinker of Greece whom Plato never criticises, but of whom he speaks with the greatest deference and respect […] instancing him as the great example of a teacher whose teaching had in it living truth enough to inspire a band of devoted disciples, and to transform their lives as well as their beliefs. And every one of those doctrines, which we know formed the “gospel” of Pythagoras and of the Pythagorean brotherhood at Crotona, was an almost exact reproduction of the cardinal doctrines of the Indian Vidya and the Indian Yoga—so much so that Indian Vedantists today do not hesitate to claim Pythagoras as one of themselves, one of their great expounders, whose very name was only the Greek form of the Indian title Pitta Guru, or Father-Teacher.’"

"It has been no easy task to revise this volume in such a way as to make it more worthy of the favour with which it has been received. Most of it has had to be rewritten in the light of certain discoveries made since the publication of the first edition, above all, that of the extracts from Menon’s Iατρικά, which have furnished, as I believe, a clue to the history of Pythagoreanism."

"The Pythagoreans knew some properties of s... how a plane can be filled by... regular triangles, squares, or regular hexagons, and space by cubes... [They] may also have known the regular oktahedron and dodekahedron—the latter figure because pyrite, found in Italy, crystallizes in dodekahedra, and models... date to Etruscan times."

"As a moral philosopher, many of his precepts relating to the conduct of life will be found in the verses which bear the name of the Golden Verses of Pythagoras. It is probable they were composed by some one of his school, and contain the substance of his moral teaching. The speculations of the early philosophers did not end in the investigation of the properties of number and space. The Pythagoreans attempted to find, and dreamed they had found, in the forms of geometrical figures and in certain numbers, the principles of all science and knowledge, whether physical or moral. The figures of Geometry were regarded as having reference to other truths besides the mere abstract properties of space. They regarded the unit, as the point; the duad, as the line; the triad, as the surface; and the tetractys, as the geometrical volume. They assumed the pentad as the physical body with its physical qualities. They seem to have been the first who reckoned the elements to be five in number, on the supposition of their derivation from the five regular solids. They made the cube, earth; the pyramid, fire; the octohedron, air; the icosahedron, water; and the dodecahedron, aether. The analogy of the five senses and the five elements was another favourite notion of the Pythagoreans."

"Almost all the theories, religious philosophical and mathematical, taught by the Pythagoreans, were known in India in the sixth century BCE, and the Pythagoreans, like the Jains and the Buddhists, refrained from the destruction of life and eating meat."

"[T]he authority of Anaximenes was so great that both Leukippos and Demokritos adhered to his theory of a disc-like earth. ...This, in spite of the fact that the spherical form of the earth was already a commonplace in circles affected by Pythagoreanism."

"While most s emphasized the reality of change — in particular, the Atomists, followers of and Democritus — the Pythagoreans stressed the study of the unchangeable elements in nature and society. In their search for the eternal laws of the universe they studied geometry, arithmetic, astronomy, and music (the '). Their most outstanding leader was Archytas of Tarentum...and to whose school, if we follow... E. [Eva] Frank, much of the Pythagorean brand of mathematics may be ascribed. ...Numbers were divided into classes: odd, even, even-times-even, odd-times-odd, prime and composite, perfect, friendly, triangular, square, pentagonal, etc. ...Of particular importance was the ratio of numbers (logos, Lat. ratio). Equality of ratio formed a proportion. They discriminated between an arithmetical (2b = a + c), geometrical (b^2 = ac), and a harmonical (\frac{2}{b} = \frac{1}{a} + \frac{1}{c}) proportion that they interpreted philosophically and socially."

"Nicomachus... mentions the customary Pythagorean divisions of quantum and the science that deals with each. Quantum is either discrete or continuous. Discrete quantum in itself considered, is the subject of Arithmetic; if in relation, the subject of Music. Continuous quantum, if immovable, is the subject of Geometry; if movable, of Spheric (Astronomy). These four sciences formed the of the Pythagoreans. With the (which Nicomachus does not mention) of Grammar, Logic, and Rhetoric, they composed the seven liberal arts taught in the schools of the Roman Empire."

"The Neo-Pythagoreans treated all the divisions of philosophy. In Metaphysics they held that the Unit and the (indeterminate) Two are the basis of all things. the Unit being the form, and the Two the matter. ...The Unit being the prior principle may be identified with Deity, and, as such, was thought of either as the former [creator] of indefinite matter into individual things, or, as in Neo-Platonism, as the transcendent origin of the derivative Unit and Two. Another mode of conception was to identify the numbers with the Platonic Ideas and then to think of the Unit as comprehending them in the same manner as the mind comprehends its thoughts and gives them form. In Logic the Neo-Pythagoreans were for the most part imitators of Aristotle. Their Physics was Aristotelian and Stoic. Their Anthropology was Platonic. In Ethics and Politics they merely reechoed the Academy and the Lyceum with Stoic additions. In all this Neo-Pythagoreanism has little originality."

"Those who dwelt in the common auditorium adopted this oath: "I swear by the discoverer of the Tetraktys, which is the spring of all our wisdom; The perennial fount and root of Nature.""

"The tetrad was called by the Pythagoreans every number, because it comprehends in itself all the numbers as far as to the decad, and the decad itself; for the sum of 1, 2, 3, and 4, is 10. Hence both the decad and the tetrad were said by them to be every number; the decad indeed in energy, but the tetrad in capacity. The sum likewise of these four numbers was said by them to constitute the tetractys, in which all harmonic ratios are included. For 4 to 1, which is a quadruple ratio, forms the symphony bisdiapason; the ratio of 3 to 2, which is sesquialter forms the symphony diapente; 4 to 3, which is sesquitertian, the symphony diatessaron; and 2 to 1, which is a duple ratio, forms the diapason."

"Why was the Tetraktys so revered? Because to the eyes of the sixth century BC Pythagoreans, it seemed to outline the entire nature of the universe. In geometry — the springboard to the Greeks' epochal revolution in thought — the number 1 represented a point... 2 represented a line... 3 represented a surface... and 4 represented a three-dimensional tetrahedral solid... The Tetraktys, therefore appeared to encompass all the perceived dimensions of space."

"On the question whether mathematics was discovered or invented, Pythagoras and the Pythagoreans had no doubt — mathematics was real, immutable, omnipresent, and more sublime than anything that could conceivably emerge from the human mind. The Pythagoreans literally embedded the universe into mathematics. In fact, to the Pythagoreans, God was not a mathematician — mathematics was God! ...By setting the stage, and to some extent the agenda, for the next generation of philosophers — Plato in particular — the Pythagoreans established a commanding position in Western thought."

"The main purpose of the Orgia was to "purify" the believer’s soul, and so enable it to escape from the "wheel of birth," and it was for... this end that the Orphics were organised in communities. Religious associations must have been known to the Greeks from a fairly early date; but the oldest of these were based... in theory, on the tie of kindred blood. What was new was the institution of communities to which any one might be admitted by initiation. This was, in fact, the establishment of churches, though there is no evidence that these were connected... such... that we could rightly speak of them as a single church. The Pythagoreans came nearer to realising that."

"It is certain that the Theory of Numbers originated in the school of Pythagoras."

"None of Pythagoras' own work has survived, but the ideas fathered on him by his followers would be the most potent in modern history. Pure knowledge, the Pythagoreans argued, was the purification (catharsis) of the soul... rising above the data of the human senses. The pure essential reality... was found only in the realm of numbers. The simple, wonderful proportion if numbers would explain the harmonies of music... [T]hey introduced the musical terminology of the octave, the fifth, the fourth, expressed as 2:1, 3:1, and 4:3. ..."

"In Copernicus' time Pythagoreans still believed that the only way to truth was by mathematics."

"The Pythagorean mathematical concepts, abstracted from sense impressions of nature, were... projected into nature and considered to be the structural elements of the universe. [Pythagoreans] attempted to construct the whole heaven out of numbers, the stars being... material points. ...they identified the regular geometric solids... with the different sorts of substances in nature. ...This confusion of the abstract and the concrete, of rational conception and empirical description, which was characteristic of the whole Pythagorean school and of much later thought, will be found to bear significantly on the development of the concepts of calculus. It has often been inexactly described as mysticism, but such stigmatization appears to be somewhat unfair. Pythagorean deduction a priori having met with remarkable success in its field, an attempt (unwarranted...) was made to apply it to the description of the world of events, in which the Ionian hylozoistic interpretations a posteriori had made very little headway. This attack on the problem was highly rational and not entirely unsuccessful, even though it was an inversion of the scientific procedure, in that it made induction secondary to deduction."

"It has fallen to the lot of one people, the ancient Greeks, to endow human thought with two outlooks on the universe neither of which has blurred appreciably in more than two thousand years. ...The first was the explicit recognition that proof by deductive reasoning offers a foundation for the structure of number and form. The second was the daring conjecture that nature can be understood by human beings through mathematics, and that mathematics is the language most adequate for idealizing the complexity of nature into appreciable simplicity. Both are attributed by persistent Greek tradition to Pythagoras in the sixth century before Christ. ...there is an equally persistent tradition that it was Thales... who first proved a theorem in geometry. But there seems to be no claim that Thales... proposed the inerrant tactic of definitions, postulates, deductive proof, theorem as a universal method in mathematics. ...in attributing any specific advance to Pythagoras himself, it must be remembered that the Pythagorean brotherhood was one of the world's earliest unpriestly cooperative scientific societies, if not the first, and that its members assigned the common work of all by mutual consent to their master."

"They [the Pythagoreans] say the things themselves are Numbers and do not place the objects of mathematics between forms and sensible things. ...Since again, they saw that the modifications and the ratios of the musical scales were expressible in numbers—since, then, all other things seemed in their whole nature to be modelled on numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number... and the whole arrangement of the heavens they collected and fitted into their scheme; and if there was a gap anywhere, they readily made additions so as to make their whole theory coherent."

"These thinkers seem to consider that number is the principle both as matter for things and as constituting their attributes and permanent states."

"Ionian philosophers... had sought to identify a first principle for all things. Thales had thought to find this in water, but others preferred to think of air or fire as the basic element. The Pythagoreans had taken a more abstract direction, postulating that number... was the basic stuff behind phenomena; this numerical atomism... had come under attack by the followers of Parmenides of Elea... The fundamental tenet of the was the unity and permanence of being... contrasted with the Pythagorean ideas of multiplicity and change. Of Parmenides' disciples the best known was Zeno the Eleatic... who propounded arguments to prove the inconsistency in the concepts of multiplicity and divisibility."

"They thought they found in numbers, more than in fire, earth, or water, many resemblances to things which are and become; thus such and such an attribute of numbers is justice, another is soul and mind, another is opportunity, and so on; and again they saw in numbers the attributes and ratios of the musical scales. Since, then, all other things seemed in their whole nature to be assimilated to numbers, while numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number."

"We may... go to our... statement from Aristotle's treatise on the Pythagoreans, that according to them the universe draws in from the Unlimited time and breath and the void. The cosmic nucleus starts from the unit-seed, which generates mathematically the number-series and physically the distinct forms of matter. ...it feeds on the Unlimited outside and imposes form or limit on it. Physically speaking this Unlimited is [potential or] unformed matter... mathematically it is extension not yet delimited by number or figure. ...As apeiron in the full sense, it was... duration without beginning, end, or internal division—not time, in Plutarch's words, but only the shapeless and unformed raw material of time... As soon... as it had been drawn or breathed in by the unit, or limiting principle, number is imposed on it and at once it is time in the proper sense. ...the Limit, that is the growing cosmos, breathed in... imposed form on sheer extension, and by developing the heavenly bodies to swing in regular, repetitive circular motion... it took in the raw material of time and turned it into time itself."

"If someone associates with a true Pythagorean, what will he will get from him, and in what quantity? I would say: statesmanship, geometry, astronomy, arithmetic, harmonics, music, medicine, complete and god-given prophecy, and also the higher rewards — greatness of mind, of soul, and of manner, steadiness, piety, knowledge of the gods and not just supposition, familiarity with blessed spirits and not just faith, friendship with both gods and spirits, self-sufficiency, persistence, frugality, reduction of essential needs, ease of perception, of movement, and of breath, good color, health, cheerfulness, and immortality."

"[T]he religious revival... suggested the view that philosophy was above all a "way of life." Science too was a "purification," a means of escape from the "wheel." This is the view expressed so strongly in Plato’s Phaedo, which was written under the influence of Pythagorean ideas."

"Aristotle is... decided in his opinion that Pythagoreanism was intended to be a cosmological system like the others. "Though the Pythagoreans... made use of less obvious s and elements than the rest, seeing that they did not derive them from sensible objects, yet all their discussions and studies had reference to nature alone. They describe the origin of the heavens, and they observe the phenomena of its parts, all that happens to it and all it does." They apply their first principles entirely to these things, "agreeing... with the other natural philosophers in holding that reality was just what could be perceived by the senses, and is contained within the compass of the heavens," though "the first principles and causes of which they made use were... adequate to explain realities of a higher order than the sensible.""

"[P]revailing tradition gives the high note of the octave to the heaven of the fixed stars... [I]t follows that all the heavenly bodies revolve in the same direction, and... their velocity increases in proportion to their distance from the centre."

"It seems to me that they do well to study mathematics, and it is not at all strange that they have correct knowledge about each thing, what it is. For if they knew rightly the nature of the whole, they were also likely to see well what is the nature of the parts. About geometry, indeed, and arithmetic and astronomy, they have handed us down a clear understanding, and not least also about music. For these seem to be sister sciences; for they deal with sister subjects, the first two forms of being."

"I realized it perfectly. But however sincere, these feelings are too deeply covered by a thick crust of self sufficiency and egoistical stubbornness to awaken in me anything like sympathy."

"We cannot alter Karma my "good friend" or we might lift the present cloud from your path. But we do all that is possible in such material matters. No darkness can stay for ever. Have hope and faith and we may disperse it. There are not many left true to the original programme! And you have been taught much and have much that is and will be useful."

"For centuries we have had in Tibet a moral, pure hearted, simple people, unblest with civilization, hence—untainted by its vices. For ages has been Tiibet the last corner of the globe not so entirely corrupted as to preclude the mingling together of the two atmospheres—the physical and the spiritual. And he would have us exchange this for his ideal of civilization and Govt.! This is pure self peroration, an intense passion for hearing himself discuss, and for imposing his ideas upon every one."

"All things being are in mystery; we expound mysteries by mysteries"—you may perhaps say. Well, well; to you as to one forewarned it will not be one; since, for several reasons—one more plausible than the other—I take you into my confidence. One of them is,—to save you a feeling of involuntary envy (the word is queer isn't it?) when you hear of it. As he will see somebody quite different from the real K.H., though it will still be K.H.— you need not feel like one wronged by your trans-himalayan friend. Another reason is, to save the poor fellow from the suspicion of boasting; the third and chiefest, though neither least nor last, is, that theosophy and its adherents have to be vindicated at last."

"Common people, are the masses as different from those who are distinguished. Your methods were not abandoned, it was only sought to show the drift of cyclic change no doubt that is helped by you too. Are you not man of the world enough to bear the small defects of young disciples. In their way they also help—and do greatly. In you is also concealed a power to help from your side for the poor Society will even yet need all the care it can get. It is good that you have seen the work of a noble woman, who has left all for the cause. Other ways and times will appear for your help. For you are a single witness and well knowing the facts that will be challenged by traitors."

"Now really, Mr. H. ought to be sent by an international Committee of Philanthropists, as a Friend of Perishing Humanity to teach our Dalai Lamas—wisdom. Why he does not straightway sit down and frame a plan for something like Plato's Ideal Republic with a new scheme for everything under the Sun and moon—passes my poor comprehension!"

"Good friend, I will not, in sending forth the letter, reiterate again the many remarks that might be made respecting the various objections which we have the right to raise against Spiritual phenomena and its mediums. We have done our duty; and, because the voice of truth came through a channel which few liked, it was pronounced as false, and along with it—Occultism. The time has gone by to argue, and the hour when it will be proved to the world that Occult Science instead of being... a superstition itself, as they may be disposed to think it, will be found the explanation and the extinguisher of all superstitions—is nearby."

"It is not politic that H. S. Olcott should be exclusively your guest during his whole stay in Britain; his time should be divided between yourself and others of various opinions—should they wish to invite him for a short time."

"Every Western Theosophist should learn and remember, especially those of them who would be our followers—that in our Brotherhood, all personalities sink into one idea—abstract right and absolute practical justice for all. And that, though we may not say with the Christians, return good for evil—we repeat with Confucius— return good for good, for evil—justice."

"My desire is that you should be gathering together all the reserve forces of your being so that you may rise to the dignity and importance of the crisis. However little you may seem to achieve—psychically—in this birth, remember that your interior growth proceeds every instant, and that toward the end of your life as in your next birth your accumulated merit shall bring you all you aspire to."

"This is indeed benevolent in him to go so far out of his way to teach us. Of course, this is pure kindness and not a desire to over-top the rest of humanity. It is his latest acquisition of mental evolution, which, let us hope, will not turn in—dissolution....Now just listen to the man jabbering about what he knows nothing. No men living are freer than we when we have once passed outside of the stage of pupilage. Docile and obedient but never slaves during that time we must be; otherwise, and if we pass our time in arguing we never would learn anything at all."

"My good friend—it is very easy for us to give phenomental proofs when we have necessary conditions. For instance— Olcott's magnetism after six years of purification is intensely sympathetic with ours—physically and morally is constantly becoming more and more so. Damodar and Bhavani Rao being congenitally sympathetic their auras help —instead of repelling and impeding phenomenal experiments. After a time you may become so—it depends on yourself. To force phenomena in the presence of difficulties magnetic and other is forbidden. As strictly as for a bank cashier to disburse money which is only entrusted to him. Mr. Hume cannot comprehend this. And therefore is "indignant" that the various tests he has secretly prepared for us have all failed. They demanded a tenfold expenditure of power since he surrounded them with an aura not of the purest—that of mistrust, anger, and anticipated mockery. Even to do this much for you so far from the Headquarters would be impossible but for the magnetisms O. and B. R. have brought with them—and I could do no more."

"The recent occurrences in which you have borne a part not altogether pleasant, may be distressing to some and tiresome to others, yet it is better so than that the old paralytic calm should have continued. An outbreak of fever in the human body is nature's evidence that she is trying to expel the seeds of disease and perhaps death anteriorily absorbed. As things were, the London Branch was but vegetating and the vast possibilities of psychic evolution in Britain were completely untried. Karma evidently required that the repose should be broken by the agency of the one most responsible for it"

"If you care anything about our future relations, then, you better try to make your friend and colleague Mr. Hume give up his insane idea of going to Tibet. Does he really think that unless we allow it, he, or an army of Pelings will be enabled to hunt us out, or bring back news, that we are, after all, but a "moonshine" as she calls it. Madman is that man who imagines that even the British Govt: is strong and rich enough and powerful enough to help him in carrying out his insane plan ! Those whom we desire to know us will find us at the very frontiers. Those who have set against themselves the Chohans as he has—would not find us were they to go L'hassa with an army. His carrying out the plan will be the signal for an absolute separation between your world and ours. His idea of applying to the Govt : for permission to go to Tibet is ridiculous. He will encounter dangers at every step and will not even hear the remotest tidings about ourselves or our whereabouts."

"Let the eyes of the most intellectual among the public be opened to the foul conspiracy against theosophy that is going on in the missionary circles and in one year's time you will have gained your footing. In India it is: "either Christ or the Founders (! !) Let us stone them to death!" They have nearly finished killing one—they are now attacking the other victim—Olcott. The padris are as busy as bees."

"My dear friend :—do not accuse me—after having started it myself—of indiiference to, or oblivion of, our little speculation. The Chohan is not to be consulted every day on such worldly matters, and that is my excuse for the unavoidable delay. And now, I am permitted by my venerated Chief to convey to you a memorandum of His views and ideas upon the fortune and destinies of a certain paper upon which his foresight was asked by your humble friend and his servant. Putting them into business shape I have noted his views as follows. I. The establishment of a new journal of the kind described is desirable, and very feasible—with proper effort. II. That effort must be made by your friends in the world, and every Hindu theosophist who has the good of his country at heart, and not very afraid to spend energy and his time. It has to be made by outsiders—i.e. those who do not belong to our Order irretrievably ; as for ourselves. III. We can direct and guide their efforts and the movement, in general. Tho' separated from your world of action we are not yet entirely severed from it so long as the Theosophical Society exists. Hence, while we cannot inaugurate it publicly and to the knowledge of all theosophists and those concerned, we may, and will so far as practicable, aid the enterprise. In fact, we have begun already to do so."

"The fifth round has not commenced on our earth and the races and sub-races of one round must not be confounded with those of another round. The fifth round mankind may be said to have commenced when there shall not be left on the planet which precedes ours a single man of that round and on our earth not one of the fourth round. You should know also that the casual fifth round men (and very few and scarce they are) who come in upon us as avant couriers do not beget on earth fifth round progeny. Plato and Confucius were fifth round men and our Lord a sixth round man (the mystery of his avatar is spoken of in my forthcoming letter) not even Gautama Buddha's son was anything but a fourth round man."