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Number, Flow, and BeingOur next trio of theorists may have been more or less aware of the Milesians. Pythagoras, Heraclitus, and Parmenides were variously separated by time and distance. Moreover, they were so concerned with a larger picture of the cosmos that the question of materiality seems almost incidental to their doctrines. Pythagoras mastered a temple of number, from which substance must be mystically manifest. Heraclitus promoted respect for a dynamic cosmos in which any material thing could be seen simply in flux. Parmenides preached that all Is, a permanent Being in which sensations of difference between this material and that are misleading.
PythagorasBorn on the Aegean island of Samos in 580 BCE, Pythagoras spent much of his youth traveling in the lands around the Mediterranean Sea. Visiting the places of wisdom, Pythagoras absorbed a variety of priestly teachings including those of the Eleusinian mysteries. While in Egypt, temple priests most likely imparted to the novice a sense of number, geometric figure, and celestial reckoning along with their myths. Pythagoras eventually settled in southern Italy at Crotona, a thriving Greek colony. The bustling port city was reknown for its medical school and had, presumably, a concomitant intellectual community. There Pythagoras founded a mystery school dedicated to number as the source of all things. Members lived under a regimen of disciplined thought, dress, exercise, diet, purification, and worship in a communal setting which maintained the equality of the sexes.
Figure 1.6 |
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Pythagorean initiates swore a vow of allegiance by the Oath of the Tetractys, a religious symbol which embodied the core teachings. The fourfold symbol was keyed on the unit-- a manifestation of Divine Unity-- and its generation of many units in orderly array. One unit begets two, two and one make three, then three and one make four. There are ten in all, the perfect number. Whether marked by grains of corn or points in the sand, when this sequence of units is arrayed in an equilateral triangle it generates the Tetractys. The triangle's base is delineated by four units, above which stand the three units spread horizontally above the base, then two units, then one at the apex of the triangle. The cult's Tetractys embodied the secret of material reality in several ways. Geometric figure, through which all objects are manifest, is developed progressively from the point, the line determined by two points, the plane from three, and the solid (represented by the tetrahedron) from four. The number One manifests its divinity through the principles of Two (feminine) and Three (masculine) based on Four (justice). Most importantly, the ratios 1:2, 2:3, and 3:4 were manifest as the musical harmonies.Pythagoras is on record as the first to discover the relationship between number and musical harmonies, which he no doubt demonstrated with divisions on vibrating string and the evenly spaced holes of a flute. Such physical evidence of manifest number was bolstered by mathematical prowess, best exemplified by the Pythagorean Theorem (that the square drawn upon the hypotenuse of a right triangle is equal to the sum of the two squares drawn upon the triangle's two remaining sides. While the theorem now bears his name, it was known in an earlier century by the Babylonian and Egyptian priests). Number theory and geometrical technique were presented as a rational path to universal understanding. Both fact and theory lent credence to the Master's teaching that the harmony of the cosmos is based on number.
Aristotle had this to say about the Pythagoreans in a review of the principles used by various philosophers in their explanations of the world:
"[They] consider that number is the principle both as matter for things and as forming both their modifications and their permanent states, and hold that the elements of number are the even and the odd, and that of these the latter is limited, and the former unlimited; and that the One proceeds from both of these (for it is both even and odd), and number from the One; and that the whole heaven [is] numbers.Those ten principles were known everafter as the Pythagorean Contraries and their associated numbers were said to embody the principles. Although not the first to promote the notion of a contrary as important for philosophy, the Pythogoreans certainly elevated its status by systematizing a complete set of contraries."Other members of this same school say there are ten principles, which they arrange in two columns of cognates-- limited and unlimited, odd and even, one and plurality, right and left, male and female, resting and moving, straight and curved, light and darkness, good and bad, square and oblong." (Metaphysics, I.5.986a15-26)
Born of number, all things exist in their proper ratio, and every substance, be it an element or compound, can be explained through number and geometric form. Masculine or feminine, cold and dry or hot and moist-- one way or another, qualitative difference was explained through number. Or so we, the uninitiated, may suppose. Pythagoras was said by some (but not all) ancient commentators to have left no writings but rather trusted his students to carry on the wisdom, the best of which was held in secret. The disciples were scattered abroad when the local folk of Crotona, not adept in the mysteries and fearful of the Pythagorean School's growing political power, set the buildings ablaze and murdered the Master. Even so, Pythagoreans kept the teachings alive among the Mediterranean intellectual elite during the next four centuries.
Heraclitus |
Figure 1.7 |
Thirty miles north of Miletus in the generation after Anaximenes, the city-state of Ephesus was home to Heraclitus, the man remembered over the millenia for his aphorism: "You cannot step twice in the same river (for other waters and yet others go ever flowing on)". Dozens of such pithy wisdoms attributed to Heraclitus spice the annals of philosophy. Although he left behind a sketchy treatise-- On Nature-- before he died (circa 490-80 BCE), we only know fragments of his teaching as quoted by later writers. Easy access is not to be expected from a man who taught: "It should be understood that war is the common condition, that strife is justice, and that all things come to pass through the compulsion of strife." Holding Pythagoras in low opinion, Heraclitus saw harmony as a mere phase in the ebb and flow of strife, arguing that the cosmos without strife would stop dead. He considered fire as the primal element, seen in the thunderbolt as a fleeting manifestation of the Logos which flows evermore through the cosmos. He taught that, by paying attention to detail and attaining self-control, a man may realise the Logos and participate in its flow. (We suppose his meaning for Logos was something akin to Divine Speech, the words continually manifest as reality.)Heraclitus theorized a common source from which the flow of Logos generates all things. He reportedly employed a mercantile metaphor to illustrate the principle. Like gold in the marketplace, fire is the universal medium of exchange. All the wares of this world are sooner or later exchanged for fire-- everything burns-- and the fire in its turn is converted into other wares. The value of fire circulates through all the elements quite tangibly: "Fire lives in the death of earth, air in the death of fire, water in the death of air, and earth in the death of water." Behind the details of such theory, Heraclitus advocated a style of inquiry:
In other words, according to Heraclitus we can trust what we learn through the senses and integrate with reason (our portion of the Logos)-- insofar as both are shared in common with other knowledgeable men. On the other hand, knowledge claimed from a private source-- whether from a prophet's hallucinated sensations or insular rational prowess-- is suspect.
- "My own method is to distinguish each thing according to its nature, and to specify how it behaves..."
- "The things of which there can be sight, hearing, and learning-- these are what I especially prize."
- "We should let ourselves be guided by what is common to all. Yet, although the Logos is common to all, most men live as if each of them had a private intelligence of his own."
- "The waking have one world in common, whereas the sleeper turns away to a private world of his own."
- "One should not act or speak as if he were asleep."
Parmenides
A decade or two after the death of Heraclitus, a remarkable poem in epic meter was published (circa 460-70 BCE). Parmenides, a Greek in the colonial city of Elea along the coast in southwestern Italy, chose the epic style to underline his thesis. The poem, On Nature, describes his enlightenment through a meeting with the Goddess of Truth which was granted him only after a long pilgrimage. "It is needful that you should learn of all matters," she advises him, "both the unshaken heart of well-rounded truth and the opinions of mortals which lack true belief. For it is needful that by passing everything under review you should learn this also-- how to judge of mere seeming."
| The Goddess presents a "trustworthy
rational discourse concerning truth" which argues against those who "wander
ignorantly, with divided minds and scattered thoughts, so befuddled and
helpless as to resemble the deaf and blind. There are crowds of them, without
discernment, maintaining that to be and not to be are the same and not
the same, and that everything is in a state of movement and countermovement."
Upon hearing this, a contemporary might first of all consider the helpless
wanderers as dupes of Heraclitus, perhaps also befuddled by the several
options offered by the Milesians. A Phythagorean, however, need not be
among the ignorant. There is some evidence that Parmenides had been an
initiate in his youth and his doctrine is easily construed as a larger
sphere which included the sphere of number within it.
While the crowds wander lost on the wrong road through life, the rational journey of Parmenides toward truth is rightly mapped by the Goddess. As her teaching procedes, we learn there is "but one word by which to express the [true] road: Is. And on this road there are many signs that What Is has no beginning and never will be destroyed: it is whole, still, and without end. It neither was nor will be, it simply is-- now, altogether, one continuous." In other words, the Is of Being is unchanging, immovable and "fixed where it is. For strong Necessity holds it in bonds of limit, which constrain it on all sides; Natural Law forbids that Being should be other than perfectly complete." Lest the mortal mind lack a visual image of such perfection, the Goddess adds: "Since there has to be limit, Being is complete on every side, like the mass of a well-rounded sphere, equally balanced in every direction from the center." |
Figure 1.8 |
This cosmos which includes our being must be timeless. "How could you go about investigating its birth? How and whence could it have grown? I shall not allow you to say or think of it as coming from not-being, for it is impossible to say or think that not-being is. Besides, what could have stirred up activity so that it should arise from not-being later rather than earlier." The maxim that Being cannot arise from non-being proved to be the most durable element of Parmenides' teaching and, centuries later, was codified in the latin catchphrase: ex nihilo nihil fit (from nothing, nothing is made). But such nihilism interrupts the flow of the Goddess' speech:"Necessarily therefore, either it simply Is or it simply Is Not. Strong conviction will not let us think that anything springs from Being except itself. Justice does not loosen her fetters to let Being be born or destroyed, but holds them fast. Thus our decision must be made in these terms: Is or Is Not. Surely by now we agree that it is necessary to reject the unthinkable unsayable path as untrue and to affirm the alternative as the path of reality and truth."
Mayhaps the Goddess' initial claim to "rational discourse" is betrayed by her recourse here to rhetorical adjuration. Surely some must agree and, while Parmenides was no Buddha to bequeath a perpetual monastic tradition of pure contemplation living the Is-ness, his doctrine-- the permanence of Being-- did inspire a few disciples. Among those remembered are Zeno and Melissus, known collectively with their master and subsequent disciples as the Eleatics. Above all, it was Zeno who left his mark on reasonable thought in perpetuity.
Parmenides had asserted that the unity of Being is such that any thing is like every other thing, simply Being. Apparent difference is simply an illusion and all true difference is logically impossible. As the Goddess explains, "all the usual notions that mortals accept and rely on as if true-- coming-to-be and perishing, being and not-being, change of place and variegated shades of color-- these are nothing more than names." Thus motion is impossible, according to Parmenides, since Being in one place implies not-Being in another place. Since not-Being is impossible, then no empty place or void can exist and thus there is no place for any thing of Being to move. Pushing such logic to its extreme, Zeno articulated a plethora of paradox for every occasion-- motion, plurality, place, and even sound. The most famous logical paradox pits the fastest runner in Greece against the slowest to illustrate the contradiction inherent in motion. Achilles' race with the logical tortoise was doomed, once the latter was given a head-start, since even as the fleet-footed runner covered half the distance between them, the slow tortoise had advanced. Half again, advance again. Forever only halfway towards overtaking his logical opponent, the sensuous Achilles fell victim to a trick of reason.
In a bizarre sense of the word 'monism', Parmenides' doctrine was the culmination of the Greek quest for a monistic explanation of substance. Successive sages had offered water, aperion, air, number, and fiery dynamic as the singular universal substrate. These nouns of materiality appeared to be trumped by a verb: Is. While a hyper-rational doctrine of the permanence of Being attracted few adherents in a tumultuous life-or-death world, fewer still had any doubt that a race is won by the swift. Nevertheless, to serious philosophers after Parmenides and Zeno, evidence from the senses was tainted with suspicion and subject to a bruising rational interrogation. Contrary to Heraclitus and within two generations of the Eleatics, the suspicion of sensory evidence would be elevated to an art form by the master of dialectic reasoning, Plato.
Who are we to say which of these has turned "away to a private world of his own" and which is attuned to the shared Logos?
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