The Eclectic Pythagorean

“There is geometry in the humming of the strings, there is music in the spacing of the spheres. ” -Pythagoras

Posts Tagged ‘Pythagorean’

Pythagorean Silence by Susan Howe

Posted by The Eclectic Pythagorean on October 23, 2008

A poem I just happen to like. I can’t recall where I found it.

Pythagorean Silence

[excerpt]

1.

age of earth and us all chattering

a sentence   or character
suddenly

steps out to seek for truth   fails
falls

into a stream of ink   Sequence
trails off

must go on

waving fables and faces   War
doings of the war

manoeuvering between points
between

any two points     which is
what we want   (issues at stake)

bearings and so

holes in a cloud   are minutes passing
which is

which
view   odds of images swept rag-tag

silver and grey
epitomes

seconds   forgeries engender
(are blue)   or blacker

flocks of words flying together   tense
as an order

cast off to crows

-Susan Howe

Advertisements

Posted in Poetry | Tagged: , , , , | 1 Comment »

THE GOLDEN SENTENCES OF DEMOCRATES

Posted by The Eclectic Pythagorean on October 21, 2008

1. If anyone will give his mind to these sentences, he will obtain many things worthy of a man, and be free from many things that are base.

2. The perfection of the soul will correct the depravity of the body; but the strength of the body without reasoning does not render the soul better.

3. He who loves the goods of the soul will love things more, divine; but he who loves the goods of its transient habitation will love things human.

4. It is beautiful to impede an unjust man; but, if this be not possible, it is beautiful not to act in conjunction with him.

5. It is necessary to be good, rather than to appear so.

6. The felicity of a man does not consist either in body or in riches, but in upright conduct and justice.

7. Sin should be abstained from, not through fear, but for the sake of the becoming.

8. It is a great thing to be wise where we ought in calamitous circumstances.

9. Repentance after base actions is the salvation of life.

10. It is necessary to be a speaker of the truth, and not to be loquacious.

11. He who does an injury is more unhappy than he who receives one.

12. It is the province of a magnanimous man to bear with mildness the errors of others.

13. It is comely not to oppose the law, nor a prince, nor one wiser than yourself.

14. A good man pays no attention to the reproofs of the depraved.

15. It is hard to be governed by these who are worse than ourselves.

16. He who is perfectly vanquished by riches, can never be just.

17. Reason is frequently more persuasive than gold itself.

18. He who admonishes a man that fancies he has intellect, labours in vain.

19. Many who have not learnt to argue rationally, still live according to reason.

20. Many who commit the basest actions often exercise the best discourse.

21. Fools frequently become wise under the pressure of misfortunes.

22. It is necessary to emulate the works and actions, and not the words of virtue.

23. Those who are naturally well disposed, know things beautiful, and are themselves emulous of them.

24. Vigour and strength of body are the nobility of cattle; but the rectitude of manners is the nobility of man.

25. Neither art nor wisdom can be acquired without preparatory learning.

26. It is better to reprove your own errors, than those of others.

27. Those whose manners are well ordered will also be orderly in their lives.

28. It is good not only to refrain from doing an injury, but even from the very wish.

29. It is proper to speak well of good works; for to do so of such as are base is the property of a fraudulent man and an impostor.

30, Many that have great learning have no intellect.

31. It is necessary to endeavour to obtain an abundance of intellect, and not pursue an abundance of erudition.

32. It is better that counsel should precede actions, than that repentance should follow them.

33. Put not confidence in all men, but in those that are worthy; for to do the former is the province of a stupid man, but the latter of a wise man.

34. A worthy and an unworthy man are to be judged not from their actions only, but also from their will.

35. To desire immoderately is the province of a boy, and not of a man.

36. Unseasonable pleasures bring forth pains.

37. Vehement desires about any one thing render the soul blind with respect to other things.

38. The love is just which, unattended with injury, aspires after things becoming.

39. Admit nothing as pleasant which is not advantageous.

40. It is better to be governed by, than to govern, the stupid.

41. Not argument but calamity is the preceptor to children.

42. Glory and wealth without wisdom are not secure possessions.

43. It is not indeed useless to procure wealth, but to procure it from injustice is the most pernicious of all things.

44. It is a dreadful thing to imitate the bad, and to be unwilling to imitate the good.

45. It is a shameful thing for a man to be employed about the affairs of others, but to be ignorant of his own.

46. To be always intending to act renders action imperfect.

47. Fraudulent men, and such as are only seemingly good, do all things in words and nothing in deeds.

48, He is a blessed man who has both property and intellect, for he will use them well in such things as are proper.

49. The ignorance of what is excellent is the cause of error.

50. Prior to the performance of base things, a man should reverence himself.

51. A man given to contradiction, and very attentive to trifles, is naturally unadapted to learn what is proper.

52. Continually to speak without being willing to hear, is arrogance.

53. It is necessary to guard against a depraved man, lest he should take advantage of opportunity.

54. An envious man is the cause of molestation to himself, as to an enemy.

55. Not only he is an enemy who acts unjustly, but even he who deliberates about so acting.

56. The enmity of relations is far more bitter than that of strangers.

57. Conduct yourself to all men without suspicion; and be accommodating and cautious in your behaviour.

58. It is proper to receive favours, at the same time determining that the retribution shall surpass the gift.

59. When about to bestow a favour, previously consider him who is to receive it, lest being a fraudulent character he should return evil for good.

60. Small favours seasonably bestowed, become things of the greatest consequence to those who receive them.

61. Honours with wise men are capable of effecting the greatest things, if at the same time they understand that they are honoured.

62. The beneficent man is one who does not look to retribution, but who deliberately intends to do well.

63. Many that appear to be friends are not, and others, who do not appear to be friends, are so.

64. The friendship of one wise man is better than that of every fool,

65. He is unworthy to live who has not one worthy friend.

66. Many turn from their friends, if, from affluence, they fall into adversity.

67. The equal is beautiful in everything; but excess and defect to me do not appear to be so.

68. He who loves no one does not appear to me to be loved by any one.

69. He is an agreeable old man who is facetious, and abounds in interesting anecdote.

70. The beauty of the body is merely animal unless supported by intellect.

71. To find a friend in prosperity, is very easy; but in adversity, it is the most difficult of all things.

72. Not all relations are friends, but those who accord with what is mutually advantageous.

73. Since we are men, it is becoming, not to deride, but bewail, the calamities of men.

74. Good scarcely presents itself, even to those who investigate it; but evil is obvious without investigation.

75. Men who delight to blame others are not naturally adapted to friendship.

76. A woman should not be given to loquacity; for it is a dreadful thing.

77. To be governed by a woman is the extremity of insolence and unmanliness.

78. It is the property of a divine intellect to be always intently thinking about the beautiful.

79. He who believes that Divinity beholds all things, will not sin either secretly or openly.

80. Those who praise the unwise do them a great injury.

81. It is better to be praised by another than by oneself.

82. If you cannot reconcile to yourself the praises you receive, think that you are flattered.

83. The world is a scene; life is a transition. You came, you saw, you departed.

84. The world is a mutation: life a vain opinion.

Source:

The Golden Verses of Pythagoras And Other Pythagorean Fragments

Selected and Arranged by Florence M. Firth With an Introduction by Annie Besant[1904]

The Internet Sacred Text Archive

http://www.sacred-texts.com/cla/gvp/gvp05.htm

Posted in Pythagoreanism | Tagged: , , , | 1 Comment »

The Secret History of Pythagoras

Posted by The Eclectic Pythagorean on October 15, 2008

This is an odd one from 1751. It is claimed to be the true life of Pythagoras. Rather archaic English is used-so you’ve been duly warned. lol Enjoy.

secrethistoryofpythagoras.pdf

Posted in Greek philosophy, Philosophy, Pythagoreanism | Tagged: , , , , | 1 Comment »

Thomas Taylor, the Platonist

Posted by The Eclectic Pythagorean on October 15, 2008

Thomas Taylor the Platonist

Posted in Philosophy, Pythagoreanism | Tagged: , , , , , | Leave a Comment »

The First Philosophers of Greece

Posted by The Eclectic Pythagorean on October 4, 2008

the_first_philosophers_of_greece.pdf

Posted in Pythagoreanism | Tagged: , , | Leave a Comment »

Pythagoras and the Pythagorean School

Posted by The Eclectic Pythagorean on October 4, 2008

PYTHAGORAS


In developing a way of life which distinguishes the Pythagoreans from the rest of the world, Pythagoras clearly distinguishes himself from the Milesians and their nature philosophy, as K&R point out: but the distinction is not quite so clear-cut — Heraclitus too begins philosophy as a way of life, insofar as he includes a concern with a certain kind of wisdom.

In any case, Marias’ comment is also helpful here:

We have in the Pythagorean school a first clear example of philosophy understood as a way of life. The problem of the self-sufficient life issues in a special discipline consisting in contemplation. There appears here the theme of freedom, of self-reliance.

“The Mystical Side of Pythagoras’ Teaching”

Includes the notion of the transmigration of the soul; story of Pythagoras recognizing a soul in a whipped dog.

More generally establishes the kinship of all living things. This kinship follows from the notion that souls qua eternal can be reincarnated in a variety of living things: the suggestion is that the process is cyclical (–> source of Nietzsche‘s notion of eternal return). To put it still differently: the kinship of all living things is a “biological” expression of an emphasis on unity apparent in physical matters.

P. further established rules of abstinence and prohibitions, including a “philosophically-inspired vegetarianism.”

A Pythagorean vocabulary:

theoria (contemplation)kosmos (an orderliness found in the arrangement of the universe)

katharsis (purification)

[relatedly:

schole (“leisure” –> “school”)

mania (“orgy”) –> “enthusiasm” (en-theos) –> sophos

philosophia (includes notions of freedom and self-reliance)

mathematikos (fond of learning)

bios theoretikos (the theoretical life) — see above]

“By contemplating the principle of order revealed in the universe — and especially in the regular movements of the heavenly bodies — and by assimilating himself to that orderliness, man himself was progressively purified until he eventually escaped from the cycle of birth and attained immortality.”

In other words, what we might characterize as a religious sort of salvation is centrally dependent upon a “scientific” understanding of the central order of nature, and an “ethic” (from ethos, habit, rule or pattern of behavior) based on that “scientific” understanding which seeks to replicate the cosmic order in the life of the individual.

(This complementary attitude towards what we might call “faith” and “reason” will reappear in the early Middle Ages, and make possible both the recovery of the ancient Greek and Roman developments in science, mathematics, technology, and philosophy , especially as expanded and refined in the Muslim world – and the development of these knowledges and disciplines into the foundations of modern natural science.  The sense of opposition between “faith” and “reason” emerges in the West primarily post-Augustine (4th ct. C.E.) through the Dark Ages, and again with Cartesian dualism (17th ct. C.E.) and some strands of modern Protestantism [especially 19th ct. North American Fundamentalism].)

“Scientific” achievements:

1) establishes an ultimate dualism between Limit and the Unlimited;2) establishes the equation/identity of things with numbers.

More specifically, it is probable that Pythagoras discovered that the chief musical intervals are expressible in simple numerical ratios of the first four integers, i.e.:

Octave — 2:1Fifth — 3:2

Fourth — 4/3

This discovery, coupled with the discovery/invention of a mathematical order to the universe itself (familiar to us since Anaximander), leads to the venerable notion of “the harmony of the spheres.” As Julian Marias paraphrases it: since the distances of the planets correspond approximately to the musical intervals — then every/ star emits a note, all the notes together comprise the harmony of the spheres, a celestial music. We do not hear it because it is constant and without variation.

While we may be tempted to dismiss such a notion, note that this vision provided a foundation for such “modern” figures as:

a) Copernicus (who follows the Pythagorean astronomer Ecphantus in affirming the rotation of the earth), andb) Kepler (who diligently searched for over 10 years to find the Pythagorean harmonies — discovering the three laws of planetary motion in the process).  [We will also hear the computer realization of Kepler’s version of the Harmonia Mundi when we explore modern philosophy and natural science.]

More broadly, as K&R put it:

If the musical scale depends simply upon the imposition of definite proportions on the indefinite continuum of sound between high and low, might not the same principles, Limit and the Unlimited, underlie the whole universe? If numbers alone are sufficient to explain the “consonances,” might not everything else be likewise expressible as a number of a proportion?

Moreover, since the first four integers contain the whole secret of the musical scale, their sum, the number 10 or the Decad, might well “seem to embrace,” as Aristotle puts it, “the whole nature of number,” and so come to be regarded, as it certainly was, with veneration. As well, the first four integers generate the three maior figures beyond the point (cf. Speusippus, Kirk & Raven, pp. 253ff.).

Also attributed to Pythagoras – the Pythagorean theorem, with its corrollary, the incommensurability of the diagonal and the side of a square. Revealing this secret cost one poor student his life, it is said.

[For those who are really with it: the experience and conception of a harmony (=connection in the face of difference) avoids the conflict implicitly raised by Anaximander (dualism) and Anaximenes (monism) — and between Parmenides (dualism) and Heraclitus (monism)]

http://www.drury.edu/Ess/History/Ancient/pythagoras1.html

The Pythagoreans


Because of the Persian domination, philosophy moves from Ionia to the coasts of Magna Graeca, southern Italy and Sicily — to form what Aristotle calls the Italian school.

Pythagoras is a highly obscure figure. He apparently came from the island of Samos, settled in Croton (Magna Graeca). Several journeys are attributed to him, including one to Persia where he is said to have met the Magus Zaratas [= Zoroaster/Zarathustra].

He is further associated with the Orphics and the revival of the worship of Dionysus.

[CE] Indeed, it should be emphasized that the insights gained in this “philosophy” qua “theory” of the physical order are not designed so much for manipulating the environment as for saving one’s soul.

The Pythagoreans settled in a number of cities on the Italian mainland and Sicily, and from thence to Greece proper.

They formed a league or a sect. They did not eat meat or beans; the could not wear clothes made of wool; the could not pick up anything that had fallen, stir a fire with iron, etc.

The sect was divided between the akousmatikoi (hearers) and the mathematikoi (learned). The local democrats frowned on this aristocracy, if not on the sect as such, and many were killed.

The Pythagoreans formed the first “school” (from schole, “leisure”), defined as a way of life. And, perhaps because of their situation as foreigners, they understood themselves as following the spectator’s way of life (in contrast with those who buy and sell, and those who run in the stadium). This is the bios theoretikos, the contemplative or theoretic life.

The main difficulty to overcome: the body and its necessities which subdue man. It is necessary to free oneself from these. The body is a tomb — one must triumph over it, but not lose it. To so so requires that one attain the state of enthusiasm (en- theos). (This seems to suggest a connection with the Orphics and their rites, founded on mania, “orgy” — though the Pythagoreans apparently moderated this somewhat.)

In this way, one attains a self-sufficient, theoretic life — a life not tied to the necessities of the body, a divine life.

Such a man is a wise man, a sophos.

(The term philosophia, “love of wisdom,” is first used in Pythagorean circles.)

MATHEMATICS

Greek mathematics began in the Milesian school (cf. Thales, Anaximander), inheriting the knowledge of Egypt and Asia Minor (Babylonia). The Pythagoreans transform it into an autonomous and rigorous science.

In mathematics, the Pythagoreans discovered a type of entity — numbers and geometric figures — which is not corporeal, but which seems to have non-arbitrary features of its own (in contrast with the arbitrary, changing whim of fancy, imagination, dream). Marias suggests that this discovery perhaps leads to the further claim that Being is not simply corporeal, material being — in which case, we would now have a problem. A development of the concept of being is called for[?].

In any case, for the Pythagoreans, Being means the being of mathematical objects:

Numbers and figures are the essence of things;Entities which exist are imitations of mathematical forms

[anticipates Plato’s alleged theory of forms]

Pythagorean mathematics is not an operative technique: it is the discovery and construction of new entities, which are changeless, eternal — in contrast with things which are variable and transitory.

Aristotle gives this account – and critique – of the Pythagoreans:

Since of these principles numbers are by nature the first, and in numbers they seemed to see many resemblances to the things that exist and come into being – more than in fire and earth and water (such and such a modification of numbers being justice, another being soul and reason, another being opportunity – and similarly almost all other things being numerically expressible); since again they saw that the attributes and the ratios of the musical scales were expressible in numbers; since, then, all other things seemed in their whole nature to be modelled after 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 all the properties of numbers and scales which they could show to agree with the attributes and parts and the whole arrangment 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. E.g. as the number 10 is thought to be perfect and to comprise the whole nature of numbers, they say that the bodies which move through the heavens are ten, but as the visible bodies are only nine, to meet this they invent a tenth the ‘counter-earth.’ (Metaphysics A5, 985b23)

PreParmenidean Pythagoreanism

Beyond the insight first articulated by Pythagoras — that the universe, on analogy with the lyre, is built out of numbers and a harmony expressible in numbers — the dualism of Limit and Unlimited is expanded:

Limit Unlimited
odd even
one plurality
right left
male female
resting moving
straight curved
light darkness
good bad
square oblong

(see Jones)

Aristotle further reports that the Pythagoreans — evidently in contrast with all other Greeks — regarded the unit to have spatial magnitude (thus confusing “the point of geometry with the unit of arithmetic.”)

It is against such an assumption that Zeno’s paradoxes have their greatest force.

These unit-points functioned also as the basis of physical matter: they were regarded in fact as a primitive form of atom. Concrete objects are literally composed of aggregations of unit-point-atoms

Hence Aristotle:

Further, how are we to combine the belief that the modifications of number, and number itself, are causes of what exists and happens in the heavens both from the beginning and now, and that there is no other number than this number out of which the world is composed? (Met. A8, 990al8)

But the Pythagoreans, because they saw many attributes of numbers belonging to sensible bodies, supposed real things to be numbers – not separable numbers, however, but numbers of which real things consist. (Met.. N3, lO9Oa20)

While this may seem bizarre to us, Plato seems to have been the first Greek to have consciouslv thought that anything could exist otherwise than in space, and he was followed in this respect by Aristotle.

COSMOGONY

“When the one had been constructed, either out of planes or of surface or of seed or of elements which they cannot express, immediately the nearest part of the unlimited began to be drawn in and limited by limit.”

Cf. modern accounts of the “Big Bang,” etc.

This is apparently a biologically-based conception, one which

(a) further recalls the basic similarity between the mythopoetic and philosophical/scientific structures of explanation, and(b) jibes with placing the male principle under limit and the female under unlimited in the table of opposites:

“The early Pythagoreans may well, therefore, have initiated the cosmogonical process by representing the male principle of Limit as somehow implanting in the midst of the surrounding Unlimited the seed which, by progressive growth, was to develop into the visible universe.” (K&R 251)

In this process, the void exists and functions to differentiate things:

Apparently the first unit, like other living things, began at once to grow, and somehow as the result of its growth burst asunder into two; whereupon the void, fulfilling its proper function, keeps the two units apart, and thus, owing to the confusion of the units of arithmetic with the points of geometry, brings into existence not only the number 2 but also the line. So the process is begun which, continuing indefinitely, is to result in the visible universe as we know it.

Notice here as well that the leap from the lyre to the conception of the entire universe as number and the harmony of the spheres rests on the Milesian tendency to draw analogies between the human and the natural — a tendency in keeping with the attempt to uncover an original unity which accounts for both the human and the physical orders.

Indeed, as already noted above, Aristotle chastizes the Pythagoreans in regard to their theory of a counter-earth (so as to complete the nine bodies in the heavens with a perfect 10th) this way “In all this they are not seeking for theories and causes to account for observed facts, but rather forcing their observations and trying to accomodate them to certain theories and opinions of their own.” (see K&R, pp. 257ff.)


Student Comments on the Pythagoreans

The pythagoreans “… infused all nature with mathematical concepts.” Mathematics became abstract and deductive. “The early Pythagorean community was a mystical, religious group; researches into the science of mathematics were part of a larger philosophy.” An idea that was very important to the Pythagoreans was an idea of a natural harmony in the universe. Janet L.

I found that Alioto had an interesting quote about the Pythagoreans: “In other words, with Thales, mathematics became deductive and therfore abstract. The Pythagoreans extended this process of abstraction and in turn infused all of nature with mathematical concepts. It seems that they were the first to stress the idea of number and geometry underlying diverse natural phenomena. The result, adapted and enshrined in Plato’s later philosophy along with an ethical, transcendental corollary, was the important recognition that numbers are abstractions, mental concepts, suggested by material things but independent of them. For the early Pythagoreans, however, the physical world was actually constructed from numbers.” (36). This, I believe, was a major step for philosophy because of the use of abstraction to relate to reality.  – Robert

Posted in Pythagoreanism | Tagged: , | Leave a Comment »