Pythagoras Essay - Critical Essays

Pythagoras

Introduction

Pythagoras c. 570 B.C.–c. 500 B.C.

Greek philosopher.

Although much of his life and thought has been obscured by spurious and often contradictory evidence, Pythagoras is nevertheless considered the most comprehensive of the Presocratic philosophers. A mysterious figure of near legendary status in Greek antiquity, Pythagoras is largely associated with the doctrines of reincarnation and the immortality of the soul. A proponent of Orphic mysticism, Pythagoras observed that the soul experiences continuous cycles of life and death, called transmigration or metempsychosis. He departed somewhat from the Orphies, however, in his belief that purification, or the redemption of the soul, and eventual release from this cycle was attainable through the pursuit of philosophy—the most noble goal of humanity, according to Pythagoras. Additionally, he is sometimes credited with coining the term philosopher, literally a "lover of wisdom," and considered among the first to follow this vocation. A religious leader and scientist as well, Pythagoras and his disciples are also typically associated with various discoveries in the fields of music, mathematics, and astronomy, as well as the conception of cosmic unity which has since become associated with a mathematical ideal of divine perfection—known in the Middle Ages as the musical "harmony of the spheres."

Biographical Information

Despite some critical dispute, Pythagoras is said to have been born on the Greek island of Samos in about 570 B.C., the son of a gem engraver named Mnesarchus. Ancient biographers record his youthful travels throughout the Mediterranean region, particularly in Egypt. Shortly after his return to Samos, however, Pythagoras fled his native island to avoid the political despotism of the tyrant Polycrates. By the time he had left Samos in 532 B.C., his reputation as a polymath had spread throughout Magna Graecia and preceded him when he arrived in the Italian city of Croton. Already several legends surrounding Pythagoras had come into common currency, including stories that he had appeared in two places simultaneously, that a river had spoken his name, and that he had a golden thigh. Despite the fantastic nature of these accounts, the fact remains that Pythagoras had earned an almost divine status and employed his considerable fame to establish a religious order and school in Croton. This highly secretive community eventually came to dominate political and social life not only in Croton but throughout southern Italy. The ascendancy of the exclusive Pythagorean sect in the political arena, however, precipitated a growing hostility over the next several decades. An uprising late in the sixth century B.C. forced Pythagoras into exile in Metapontum, where he died in approximately 500 B.C. Still, the Pythagorean order continued to flourish, despite continued clashes, well into the fifth century B.C.; although its political power steadily began to wane. While his school was no longer in existence by 400 B.C., the influence of Pythagoreanism nevertheless survived, appearing in many forms, particularly in the philosophy of Plato and the Neopythagorean philosophical movement which began in the first century A.D. and lasted for more than two centuries.

Major Works

Largely due to the secretive and mystic nature of the Pythagorean order, Pythagoras produced no written works, relying instead on the oral transmission of his teachings. While the authorship of certain works of poetry—particularly the Golden Verses, a poetic catechism of the order—have been attributed to him by some, these writings were likely drafted by his disciples and successors, many of whom adopted the practice of venerating their teacher by composing works in his name. Still, many of the basic tenets of Pythagorean thought may be discerned in the writings of later Pythagoreans and in the critical commentaries of Pythagoras's contemporaries. Among the most important aspects of Pythagorean thought is the interplay of dual forces, such as those of chaos and order, and the Limited and the Unlimited. According to the cosmology of Pythagoras, all things derive from the actions of the force of limitation on the so-called Unlimited—a chaotic mass that comprises the universe. From these forces arise the possibility of kosmos, or orderly arrangement, and harmonia, or harmony and balance—literally, "fitting together." Pythagoras defined these concepts in terms of mathematics and music, two fields to which he and his disciples made considerable contributions. Musical harmony, Pythagoras discovered, is based upon mathematical principles and proportions. Such practical observations are matched by the religious and mystical elements of Pythagoreanism, many of them concerned with the nature of the soul and the means by which it might achieve perfection. For Pythagoras the soul was immortal and fated to experience multiple lives as it traveled through cycles of life, death, and transmigration (or reincarnation). As a consequence of this belief, Pythagoras preached the kinship of all creatures, each of which possessed a soul. The Pythagorean religion thus prohibited the consumption of meat on the grounds that the animals might contain the souls of those who were once, or in the future would be, human. Release from the cycle of reincarnation could be achieved, however, by sustained contemplation—namely the pursuit of philosophy—which brought about purification of the soul.

Critical Reception

Pythagoras seems to have elicited the awe and esteem of many in antiquity and the derision of a select few. A semi-divine figure to some, including Isocrates, who transmits many of the legends surrounding him in his Busiris, Pythagoras has been closely associated with the god Apollo, and tales of his incredible power and wisdom were common. Others, including his contemporary, Heracles, called him a charlatan and a deceiver. Negative assessments formed the minority opinion, however, excepting the weighty conclusions of Aristotle, who revealed many of the more absurd practices of Pythagoras, including his obsession with the spiritual qualities of numbers. Modern criticism has tended to focus on the mass of contradictory evidence concerning the philosopher and the question of his real influence on the development of Greek philosophy. Because of the lack of texts written by Pythagoras himself, scholars have been forced to rely on the documents of such later individuals as Philolaus, a Pythagorean who flourished in the fifth century B.C. and was the first to record the teachings of Pythagoras in written form. Twentieth-century critics have also undertaken the process of separating the scientific and mathematical discoveries that were likely made by later Pythagoreans from the largely spiritual and mystical thought of Pythagoras himself. Most now agree that the main contributions of the philosopher seem to have been in relation to his cosmology—particularly his synthesis of mathematical and musical forms into a theory of divine harmony—and his theory of the soul, which seems not to have existed in Greek thought prior to Pythagoras and which exerted a tremendous influence on later Platonic philosophy.

Criticism

B. A. G. Fuller (essay date 1923)

SOURCE: B. A. G. Fuller, "Pythagoras and the Pythagoreans," in History of Greek Philosophy: Thales to Democritus, Henry Holt and Company, 1923, pp. 103-17.

[In the following essay, Fuller summarizes the contributions of Pythagoras to the fields of music, mathematics, medicine, and astronomy. He notes the influence of the Pythagorean ideas of duality and their distinction between the concepts of "form" and "matter" on later philosophical thought.]

There is no figure in the history of philosophy so mysteriously shrouded in the phosphorescent mists of legend as the person of Pythagoras. Revered by his more immediate followers as a superior being, he acquired among later disciples the majesty of a demigod. He was variously reputed to be the son of Apollo in his present existence, and to have been the child of Hermes in a prior incarnation.

Like the Bodhisattvas on the threshold of Nirvana and Buddhahood, he was said to possess through the grace of his parent, Hermes, the memory of all his past existences. As for his teachings, they were derived straight from his other father, Apollo, through the lips of the Delphic oracle. And it was reported that in the flesh he had descended into Hades. He was also credited with other scarcely less distant but more mundane journeyings which had acquainted him at first hand with all the lore of the Phoenicians, the Chaldeans, the Magi, the Hindoos, the Arabians, and the Egyptians.

It is highly improbable that, even in an age when supernatural fathers were plentiful and direct confabulation with the divine was frequent, a commonplace personality could have attracted to itself so many and so flattering legends. It is true that Pythagoras' own adherence to mystical beliefs and rites like those of the Orphics and the votaries of the Delian Apollo, made his exaltation by his followers almost a bit of routine. In them transmigration, the partial incarnation of the divine in human nature, and ecstatic union with the deity through mystical sacrament and ritual, were a matter of course. Still, the myth suggests that Pythagoras was a remarkable and distinguished man, and such historic fact as we can gather goes to bear out this assumption.

He was born at Samos, probably in the last half of the Sixth Century. His dislike of the rule of Polycrates, who became tyrant of Samos in 532 B.C., caused him to emigrate to southern Italy, where at Croton he gathered about him a company of disciples and formed them into a religious order. This Order soon became powerful and influential and, like many later religious foundations of which history readily reminds us, tried to take a hand in politics and interfere in the government of the state. The School became a target for political abuse and disorder, so much so that the Master himself had to leave Croton, and take refuge in the city of Metapontium, where he died. By the middle of the Fifth Century the political activities of the Pythagoreans had become so obnoxious that the opposition rose, burned their lodge or monastery, killed many of them, and drove out the rest. Thus the Order became diffused through Magna Graecia and Greece proper.

As we have said, the Pythagoreans were a religious community, drawing their inspiration and doctrine from the mystical side of Greek religion. Their interest centered in the purification and the redemption of the soul from the taint of the physical and the prison of the body, in her final release from the wheel of transmigration and rebirth, and her reunion with the Divine. To effect these ends the Pythagoreans offered the old mystical means of ceremonial purgations and abstinences, the avoidance of certain food and clothing, and the performance of certain ritual acts. Among them, as among the adherents of all religions, there were many doubtless who stopped with the dead letter of observance, but there were doubtless many also who reached the spirit which gave them a new and deeper life.

The exact source of the Pythagorean religious mysticism is somewhat in dispute. It has been argued that just as the Orphics reformed and purified the older cult of Dionysus out of which they sprang, so the Pythagorean Society might be regarded as essentially a reformed branch of Orphism, which sought to correct and supplement the tendency towards mere ritualism and formalism in the parent body by emphasizing the need of a real rule of life, not only in outward observances, but in thought and meditation.1 But it has also been suggested that the fountainhead of Pythagoras' religious beliefs lay not so much in Orphism as in the worship of the Delian Apollo, who had become, like Dionysus, the center of a "religion of redemption" with mystical rites of purification dating back it may be to Minoan Crete.2

However that may be, the Order, in addition to enjoying the practice of a formal ritual of purification, like the Orphics and the Apollonian worship, also divided the sheep from the goats on broader and more spiritual lines than that of mere church membership. They distinguished three types of men in general; the lovers of pleasure and gain, the lovers of practical activity, competition, worldly success, and honor, and, best of all, the lovers of contemplation and wisdom, who were devoted to the knowledge of the highest and deepest things of life. In fact, the term "philosophy" or "love of wisdom" is reported to have been first used by Pythagoras. And it was perhaps this third way of life, inspired and devoted to the philosophic interest, rather than any mere routine of ceremonial abstinences and participation in sacraments, which he regarded as religion pure and undefiled, making clean the heart within and preparing the spirit for mystical salvation and reunion with the Godhead. Such a view receives support from the fact that for Plato, as we shall soon see, who was much influenced by Pythagorean ideas, philosophy had precisely this high and solemn office.

But whether the interest in scientific and philosophical investigation and speculation had in the eyes of the Pythagorean this religious value and function, or was simply, like the modern Jesuit's occupation with similar interests, additional and subsidiary to a central and separate religious life and experience, the fact of that interest is undoubted. Like the most distinguished and learned of modern religious orders, the Pythagoreans, also, were preëminent in their application to the problems of science—particularly of music, mathematics, medicine, and astronomy—and of philosophy.

The philosophy of the Pythagoreans is largely indebted to the Milesian School. Pythagoras is said to have been in his youth, before he left Samos, a pupil of Anaximander, and he was a contemporary of Anaximenes. Like Anaximander he believed that the substratum of all things was the Unlimited, but he seems to have characterized this Unlimited as Air, and like Anaximenes to have conceived the world as supported and animated by the inbreathing of this Air in the midst of which it floated.

Pythagorean science was also in part sprung from Milesian sources. The so-called "Pythagorean" proposition in geometry had already been debated in Miletus, and some of the astronomical ideas of the Order suggest the influence of Anaximander's theories.

The important and original contribution to philosophy comes, however, in connection with the Pythagorean answer to what we have called the Second Commandment of philosophy to show by what means and process all the richness and variety of the manifold and parti-colored world arises from the simple and undifferentiated World-Substance. Anaximander had suggested a process of separation of pairs of opposites, Anaximenes, one of condensation and rarefaction. The Pythagoreans hold in a way to Anaximander's notion of opposites, but these opposites are not conceived by them as eventually and secondarily produced within and by the Unlimited, like successive or even simultaneous births of dissimilar and quarrelsome twins. On the contrary, the opposition is a fundamental and eternal one, of one primary World-Principle with another. From all eternity, so to speak, the Unlimited finds itself confronted and conjoined with another Principle, that of Limit and Determination, which exists outside and beside it. It is only through the action of this Principle upon the Unlimited that the interminable vacancy and monotony of the latter can be broken up, and mapped, and plotted, and specified out into a world of separate, distinct, individual things, each fenced within the bounds of its particular and specific self. The world, then, is the result of the interaction of these two factors. In a word, the Universe is a measuring out or off of the Unlimited by the Limited.

But this is very vague. It leaves two questions pressing for an answer. In the first place, is there any rule for determining how much of the Unlimited must be measured out in order to make definite objects? And secondly, how can different kinds of objects all be composed of one and the same indeterminate stuff? What is the difference, for instance, between a receipt for a cat and that for a dog?

An answer to the first question was suggested to the Pythagoreans by their studies in music and medicine. They knew when they played the lyre that musical notes were vibrations imparted to the air by the quivering strings; and they were also familiar by experiment with the fact that those intervals in the scale which struck their ears as melodious and concordant were always associated with invariable arithmetical proportions in the length of one string to another. Further scrutiny showed them that the four perfectly concordant notes of which the lyre was capable were in such proportion that the two middle notes stood in the relation, also, of arithmetical means to the two extremes. The means, then, might be regarded as mixtures, according to an invariable arithmetical formula, of the extremes.

This notion of the mean as a balanced and harmonious mixture of opposites was reinforced by the Pythagoreans' medical theories. The body was obviously a combination of opposite qualities of dry here, and moist there, of heat in one place, and coolness in another. When these qualities were harmoniously balanced, when there was a "happy" mean of hot and cold, etc., the body was healthy and perfect and in a state of well-being. If there was a disturbance of the balance and one opposite upset the proportion by excess or deficiency, then there was disease.

The application of these studies in music and medicine to the philosophical situation was obvious enough. It was but a short, easy step to say that all sound, solid, clear-cut things owe, like healthy bodies, their definite and articulate nature to a harmony and balance of the factors which compose and sustain them. Every object was a correct and shapely mean between extremes of possible lopsidedness and deformity in one direction or another. The Universe, then, was the stable and well ordered, the neatly mapped and plotted and fenced affair it was, because to each of its component parts, to each cat, and dog, and tree, and blade of grass, "just enough" for that particular kind of thing, and not "too much" or "too little" had been allotted.

We should by this time be almost prepared for the answer which the Pythagoreans gave to the second question—the question which asks by what principle that balanced and happy "middle term" which means the lithe and purring cat, is differentiated from that golden mean which manifests itself in the faithful, barking watch-dog. The reply might almost rise to our lips unprompted. The measure of the one is different from the measure of the other. Each thing is a specific number, a specific amount, of the Indeterminate. Every kind of object has its own particular, mathematically expressible receipt or formula. The differences between things are then essentially differences in amount and number. In a word, the Limited, the Principle of Determination which divides up and lays out the Unlimited as an ordered and definite Universe is Number, and different things are, if one looks beyond their faces into their hearts, really nothing but different Numbers.

Before relegating this doctrine to the realm of fantastic and incomprehensible theories, let us stop and ponder it a moment. When we think of a number we generally have in mind simply the Roman or Arabic numeral by which we sum it up and symbolize it. For instance, if we think of the number "eight" there comes before our eyes simply the figure 8, or VIII. But this figure is nothing in itself. It stands for something, for eight something, or at least for eight anything. It means among other things the ability to point your finger at a line of objects and count them out. This line may be a line of all sorts of things, or, if one is abstractedly minded, it may be simply a line of plots or positions in empty space which things might occupy. But in any case the plot of space occupied by the series is the sum, so to speak, of the plots occupied by each member of the line.

Or, again, any one of the plots occupied by any member of the series may be subdivided into smaller plots that shrink eventually into...

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W. K. C. Guthrie (essay date 1962)

SOURCE: W. K. C. Guthrie, "Pythagoras and the Pythagoreans," in A History of Greek Philosophy, Vol. I, Cambridge at the University Press, 1962, pp. 146-340.

[In the following excerpt, Guthrie highlights evidence of Pythagoras's teachings and life in the works of his contemporaries and other important figures in the history of ancient Greece.]

The history of Pythagoreanism is perhaps the most controversial subject in all Greek philosophy, and much about it must remain obscure. For this there are several good reasons, which are themselves not without interest. The subject is not only obscure but highly complex, and its complexity demands above all a clear statement at...

(The entire section is 12589 words.)

C. J. De Vogel (essay date 1966)

SOURCE: C. J. De Vogel, in an introduction to Pythagoras and Early Pythagoreanism: An Interpretation of Neglected Evidence on the Philosopher Pythagoras, Van Gorcum & Comp. N.V., 1966, pp. 1-19.

[In the following excerpt, De Vogel surveys modern criticism of Pythagoras, especially of his presumed dual role as a religious leader and as a scientist-philosopher.]

1. The problem

We have all grown up with the idea that very little was to be known about Pythagoras. From contemporary evidence, we saw, he appears as a kind of 'shaman'. And can a shaman be a man of science?

Whatever one might be inclined to say in reply to this...

(The entire section is 6536 words.)

Edward Hussey (essay date 1972)

SOURCE: Edward Hussey, "Pythagoras and the Greek West," in The Presocratics, Duckworth, 1972, pp. 60-77.

[In the following excerpt, Hussey examines evidence of the life of Pythagoras and the immediate impact of his thought on Graeco-Roman medicine, mathematics, astronomy, music, and philosophy.

'The Greek West' is a convenient name for what came to be called in antiquity 'Great Greece' [Magna Graecia): the area of Greek settlement in the Western Mediterranean, above all in Sicily and southern Italy. Most of the Greek cities there had been founded in the last half of the seventh century, but they received fresh waves of emigrants from old Greece throughout the...

(The entire section is 5989 words.)

S. K. Heninger, Jr. (essay date 1974)

SOURCE: S. K. Heninger, Jr., "Pythagoras' School and Biography," in Touches of Sweet Harmony: Pythagorean, Cosmology, and Renaissance Poetics, The Huntington Library, 1974, pp. 19-44.

[In the following essay, Heninger recounts perceptions of Pythagoras and his thought from the Renaissance.]

In the development of Western philosophy as the renaissance saw it the sect of Pythagoras had played a definite and important role, a role much more important than is generally conceded today. For Ralph Cudworth, in fact, "Pythagoras was the most eminent of all the ancient Philosophers." While such praise might be excessively generous—the myopic view of a Cambridge...

(The entire section is 5351 words.)

Charles H. Kahn (essay date 1974)

SOURCE: Charles H. Kahn, "Pythagorean Philosophy Before Plato," in The Pre-Socratics: A Collection of Critical Essays, edited by Alexander P. D. Mourelatos, Anchor Books, 1974, pp. 161-85.

[In the following essay, Kahn outlines the critical debate surrounding Pythagoras and his contributions to ancient Greek philosophy, examining the doctrines generally attributed to him and the evidence that might substantiate these attributions.]

The name of Pythagoras is not only the most famous, it is also the most controversial in the history of Greek thought before Socrates and Plato. Since antiquity it has been a name to conjure with: There is such a wealth of conflicting...

(The entire section is 10380 words.)

Jonathan Barnes (essay date 1979)

SOURCE: Jonathan Barnes, "Pythagoras and the Soul," in The Presocratic Philosophers, Vol. 1, Routledge & Kegan Paul, 1979, pp. 100-20.

[In the following essay, Barnes analyzes Pythagorean arguments for the immortality and transmigration of the soul.]

(a) Ipse dixit

The ancient historians of philosophy distinguished between the Ionian and the Italian tradition in Presocratic thought. … Although the Italian 'school' was founded by émigrés from Ionia, it quickly took on a character of its own: if the Ionians followed up Thaïes' cosmological speculations, the Italians, I judge, had more sympathy for his inquiry into...

(The entire section is 9545 words.)

David R. Fideler (essay date 1987)

SOURCE: David R. Fideler, in an introduction to The Pythagorean Sourcebook and Library, edited and translated by Kenneth Sylvan Guthrie, Phanes Press, 1987, pp. 19-54.

[In the following excerpt, Fideler discusses the significant elements of Pythagoras's thought and assesses the influence of these ideas in the present era.]

It has been suggested, by Alfred North Whitehead, that "the safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato." If such be the case, what might then be said of Pythagoras, to whose philosophy Plato was so greatly indebted? While no definitive answer will be attempted here, it...

(The entire section is 16510 words.)

Richard D. McKirahan, Jr. (essay date 1994)

SOURCE: Richard D. McKirahan, Jr., "Pythagoras of Samos and the Pythagoreans," in Philosophy before Socrates: An Introduction with Texts and Commentary, Hackett Publishing Company, Inc., 1994, pp. 79-115.

[In the following essay, McKirahan presents an overview of Pythagorean thought on issues of religion, mathematics, number theory, and cosmology, citing contemporaneous sources as evidence for his statements.]

Pythagoras' Life and the Pythagorean Movement

Although details of Pythagoras' life and work are unclear, even mysterious, the following brief account is widely accepted. Born on the island of Samos c. 570, he left c. 530 on account of...

(The entire section is 14879 words.)