The Pythagorean school established at Crotona had perished in the Founder's lifetime, and the Brotherhood sworn to follow its principles was dispersed and absorbed into the flux of Mediterranean civilization. But the profound power of Pythagoras' ideas carried through Magna Graecia into Hellas and across the Aegean Sea to Anatolia. In showing that mathematics – especially integral harmonics and geometrical ratios – underlie metaphysics and ethics, epistemology and aesthetics, Pythagoras provided philosophy and science with a foundation that preserves the integrity of mythic intuition and of abstract reasoning. Thinkers striving to develop coherent concepts of matter, to understand the intricacies of social order, to learn the secrets of cosmogenesis and to pass beyond the threshold of mundane existence into the arcana of the human soul, could all draw from the storehouse of Pythagorean thought. A vast diversity of intellectual interests and a multiplicity of goals and intentions made inevitable a wide range of distortions and misunderstandings of the Master's teaching. Within the dizzying swirl of competing schools and conflicting systems, a few philosophers stood back and attempted to discern root ideas within the tangle of noisome thought. Heraclitus of Ephesus pointed to universal flux as the essential characteristic of the manifest cosmos. From the opposite pole of the Greek world, another voice spoke of that which is ontologically prior to change.

Parmenides was born in the Greek colony of Elea in southern Italy around 515 B.C., hardly twenty-five years after the city itself was established. According to Diogenes Laertius, Parmenides first became a pupil of Xenophanes of Colophon, who spent part of his life in Elea and who uncompromisingly excoriated anthropomorphic conceptions of deity and nature, ridiculing ethnocentric presuppositions of every kind. Parmenides was persuaded, however, to pursue the philosophical life by Ameinias, a poor but noble Pythagorean who had probably been a direct disciple of the Master. The depth of Parmenides' discipleship is evidenced by the tradition that upon the death of Ameinias, Parmenides built a shrine at Elea in honour of his teacher. Parmenides himself was highly respected and took a hand in legislating for Elea, a city noted for being well-governed. Zeno became his best-known disciple, defending his teacher's doctrines in a series of famous paradoxes which have fascinated, challenged and perplexed enquiring minds to the present day.

About 450 B.C. Parmenides and Zeno journeyed to Athens for the Great Panathenaea, a yearly festival – especially splendid every fourth year – held for twenty-eight days in Hekatombaion (July – August) and culminating in a torchlight procession on Athena's birthday. According to Plato, Parmenides was about sixty-five when he visited Athens, and still a man of distinguished appearance, while Zeno was tall, handsome and almost forty. Parmenides had retired from an active defense of his ideas, but Zeno had written a treatise elaborating the seminal thought of his teacher. Socrates, who was probably not more than twenty, heard Zeno read his treatise and boldly questioned its line of reasoning. Rather than being annoyed at his lack of reticence before elders, Parmenides praised Socrates for his budding insight. In the discussion which followed, Socrates discovered the depth and power of the philosophic mind, an event which seems to have influenced him throughout the remainder of his life. Whether or not the dialogue Parmenides actually records the conversation between Socrates and Parmenides is moot; the esteem in which Parmenides was held by Plato is undeniable, and the spirit of Parmenidean thought is carefully recorded.

Though it is the largest collection of fragments from a Greek philosopher before Plato, only one hundred fifty lines of dactylic hexameter have survived from Parmenides' writings. They belong to a treatise which discusses two modes of knowing – the Way of Truth and the Way of Seeming. The poem begins with an apocalyptic account of Parmenides' journey to a goddess who instructs him in the two ways. Like Orpheus descending into the underworld or Hesiod being taught by the Muses of Helicon, Parmenides found in the power of the reasoning mind truths akin to revelation. He was carried in a chariot to the luminous realm of the goddess.

On that way was I conveyed; for on it did the wise steeds convey me, drawing my chariot, and maidens led the way. The axle blazing in the socket – for it was urged round by well-turned wheels at each end – was making the boles in the naves sing, while the daughters of the Sun, hastening to convey me into the light, threw back the veils from off their faces and left the abode of night. There are the gates of the ways of Night and Day, fitted above with a lintel and below with a threshold of stone. They themselves, high in the air, are closed by mighty doors, and avenging Justice [dike] controls the double bolts. . . . When the doors were thrown back, they disclosed a wide opening, their brazen posts fitted with rivets and nails swinging in turn upon their hinges. Straight through them, on the broad way, did the maidens guide the horses and the chariot.

The details of this mystic journey intimate a fundamental distinction between the region of day and night, where the pairs of opposites reign in the harmony of the spheres, and the realm of Truth beyond all contrasts and distinctions. Justice (dike) stands at the threshold of the two worlds, for its perfect harmony reflects eternal Truth and is the ordering principle of the world of change. The image of the chariot which carries Parmenides to the goddess is reminiscent of analogies in the Upanishads, the Bhagavad Gita and in Plato's Phaedrus, as well as Shelley's account in The Daimon of the World.

The goddess greeted me kindly, and took my right hand in hers, and spake to me these words: 'Welcome, O youth, that comest to my abode on the car that bears thee, tended by immortal charioteers. It is no ill chance, but right and justice, that has sent thee forth to travel on this way. Far indeed does it lie from the beaten track of men. Meet it is that thou shouldst learn all things, as well the unshaken heart of well-rounded truth, as the opinions of mortals in which is no true belief at all. Yet nonetheless shalt thou learn these things also – how the things that seem, as they all pass through everything, must gain the semblance of being.'

Truth is well-rounded, being complete in itself, and each attribute of reality may be derived from any other, like the permutations of syllables in the chant of a Vedic mantram. "It is all one to me where I begin; for I shall come back there again in time." The Way of Seeming to which mortals cling should likewise be known, if only for contrast, so that the two are never confused as in the thinking of human beings.

Come now, and I will tell thee – and do thou hearken and carry my word away – the only ways of enquiry that exist for thinking: the one way, that it is and cannot not be, is the path of persuasion, for it attends upon Truth [aletheia]; the other, that is is not and needs must not be, that I tell thee is a path altogether unthinkable. For thou couldst not know that which is not (for that is impossible) nor utter it; for the same thing exists for thinking and for being.

Knowledge is possible because the order of pure meditative thought is resonant and isomorphic with the spiritual order or reality. While in the world of seeming what is apparently true at one moment may not be apparently true at another, in the realm of changeless Being all truth is necessary and eternal. Thus the basic ontological premise that is the beginning of the Way of Truth 15: estin e ouk estin, 'It is or it is not.' Greek verbs – in this case esti – carry pronouns with them implicitly, but Parmenides avoided any hint of an antecedent. 'It' can neither be plenum nor void, for Being is beyond all the pairs of opposites. One must assert that it is, but one cannot say that it is not, for one cannot assert that which is absolutely nothing. The psychological via negativa can withdraw putative attributions from that which is attributeless, providing nothing that can be an object of thought but releasing thought from its objects. Negations in the world of seeming are significant just because what is denied could exist contingently; in the realm of eternal Being, existence is necessary and such negation is therefore impossible.

That which can be spoken and thought needs must be for it is possible for it, but not for nothing, to be; that is what I bid thee ponder.

In the world of seeming, 'is' has distinct existential and predicative functions, but in the sphere of changeless reality these functions cannot be sharply distinguished. Since existence and attribute are ultimately both aspects of necessity, they mutually entail one another. In Beings, negation is impossible because it is ontologically empty.

When the two possibilities – 'it is' and 'it is not' – are understood, the first is seen to be necessary. They are falsely conceived if taken as alternatives within the Way of Truth. The Way of Seeming does not deal with Being, but rather with what Plato called Becoming, and there the alternatives are combined in the affirmation, 'It is and it is not.' This is because "two-headed" mortals, "carried along, deaf and blind at once, altogether dazed", are victims of time, or serial consciousness, and believe that a thing can be at one time and not at another, confusing the possibility of predicative change over time with existential alteration. If there were no necessary Being, there could be no Becoming, for the latter can be understood only in terms of the former. Thus the distinction between the Ways of Truth and Seeming is that between reality and illusion. Not recognizing an invisible, incorporeal realm of Being, people mistake illusion for reality and thus give false ontological status to aggregates of attributes which appear to change because of the illusion of time. When one discerns Being beyond Becoming, one will refuse to assign reality to that which can never be more than illusion.

Having established esti as the only premise which can be true of Being, Parmenides proceeded to derive its attributes.

One way only is left to be spoken of, that it is; and on this way are full many signs that what is is uncreated and imperishable, for it is entire, immovable and without end. It was not in the past, nor shall it be, since it is now, all at once, one, continuous; for what creation wilt thou seek for it? How and whence did it grow? Nor shall I allow thee to say or to think 'from that which is not'; for it is not to be said or thought that it is not. And what need would have driven it on to grow, starting from nothing, at a later time rather than an earlier? Thus it must either completely be or be not. Nor will the force of true belief allow that, beside what is, there could also arise anything from what is not. . . . For if it came into being, it is not, nor if it is going to be in the future. So coming into being is extinguished and perishing unimaginable.

Since esti is true, Being is eternal. Time cannot exist sub specie aeternitatis, and so Being is eternally present. Since no relations between parts can be derived from this premise, Being is continuous. Having no parts, it is neither created nor destroyed; having no origin, there can be no empty void from which it arises. "Nor is it divisible, since it is all alike; nor is there more here and less there, which would prevent it from cleaving together, but it is all full of what is." Being is homogeneous and indivisible.

Parmenides rigorously refused to allow a hint of duality to enter Being. Therefore, little can be predicated, but everything affirmed, of reality. Motion cannot be ascribed to it, nor can expansion, for that would presuppose a time at which it is incomplete. In this sense it might be thought of as finite, like a sphere extending equally in all directions. The analogy would be misleading, however, if one forgets that this 'sphere' has its centre everywhere. And thus its surface nowhere. The Way of Truth is chaste, without delusion or falsity, affirming only what is true by the strictest canons of pure reason.

The only thing that exists for thinking is the thought that it is. For you will not find thought without what is; in relation to what is uttered; for there is not, nor shall be, anything else besides what is, since Fate fettered it to be entire and immovable. Wherefore all these are mere names which mortals laid down believing them to be true – coming into being and perishing, being and not being, change of place and variation of bright colour.

With the utterance of the false predicates which human beings believe to be true, Parmenides leaves the Way of Truth and begins his return journey from the realm of the goddess on the Way of Seeming. The goddess warns, "Here I end my trustworthy discourse and thought concerning truth; henceforth learn the beliefs of mortal men, listening to the deceitful ordering of my words." The transition is from the exercise of pure reason to sensory experience as ordered by consciousness bound to the senses. Having explored the realm of Being, Parmenides was willing to outline a cosmogony in the false terms of ordinary experience, but he warns against confusing the objects of sense with the objects of reason, nor generalizations of experience with propositions of logic. The Way of Truth is marked by a choice between two ultimate opposites – it is or it is not, Being or non-being. The Way of Seeming is characterized by the fact that affirmation of one of a pair of opposites requires acceptance of the other. Heat implies cold, large points to small, bright to dark, life to death. Parmenides began by passing back through the portal of Justice and took day and night as the first pair of mutually dependent opposites. "These two, light and darkness, are the world's eternal ways", the Bhagavad Gita teaches. The Tao te ching holds that the first principles of manifestation are yang and yin, often represented as light and darkness.

To tread the Way of Seeming, one must be willing to equate thought and perception. Once this great error is accommodated in the human psyche, 'knowledge' of the world of illusion is possible. Light and darkness, day and night, are the governing principles of the cosmos. Physically, they become lightness and density, the contrary and mutually interacting qualities of matter. Biologically, they become male and female, the qualities of all living beings. The descent to the opaque world of mortals is complete. Although the Way of Seeming is utterly false or mayavic, Parmenides felt that struggling human beings caught in the twilight world of opinions need a relatively coherent cosmology, for even in illusion there are relatively superior and inferior accounts of the nature of things.

In his journey from ignorance to enlightenment, from deluded sense-experience to pristine thought, Parmenides displayed a cool logic which stripped away every quality and attribute unworthy of eternal Being. He showed the intimate connection between reason and reality, consciousness and logic, being and saying. By distinguishing clearly between ultimate reality and illusion, he presaged Plato's explanation of degrees of Becoming ascending ever closer to the Agathon, Being Itself. The realm of archetypal ideas, the forms which cluster about the gate which Justice throws open to him who would see beyond, represent the degrees of increasing reality implicit in the world of Becoming. They establish the foundation for ethics through the virtues which, when cultivated, enable one to ascend the stairway to Being, and show how any human being can embark on the glorious journey which Parmenides took. That pilgrimage culminates in a vision outside all time and limiting conditions, yet circles back into this world of delusion. One who tread the whole Way of Truth will return with that clarity of insight and depth of knowledge which marks those who are in the world but not of it.