Eleaticism

Eleaticism, one of the principal schools of ancient pre-Socratic philosophy, so called from its seat in the Greek colony of Elea (or Velia) in southern Italy. This school, which flourished in the 5th century bce, was distinguished by its radical monism—i.e., its doctrine of the One, according to which all that exists (or is really true) is a static plenum of Being as such, and nothing exists that stands either in contrast or in contradiction to Being. Thus, all differentiation, motion, and change must be illusory. This monism is also reflected in its view that existence, thought, and expression coalesce into one.

The sources for the study of Eleaticism are both archaeological and literary. Archaeologists have ascertained that, at the time of Parmenides, the founder of the school, Elea was a large town with many temples, a harbour, and a girdle of walls several miles long. They have also unearthed a site presumed to be that of the medical school that Parmenides established and an inscription bearing Parmenides’ name.

The literary sources consist of fragments preserved by later classical authors. (The fragments are collected in their conventional numerical order in Die Fragmente der Vorsokratiker [1903], edited by Hermann Diels.) Of these passages, 19 are from Parmenides, 4 from his pupil Zeno, renowned for his paradoxes of motion, and 10 from another pupil, Melissus, an admiral of Sámos; all but 3 from Parmenides and 2 from Melissus are 10 lines or fewer in length. Naturally, any interpretation of the fragments must give due consideration to the biases of the citing authors. Parmenideans of the second generation, for example, saw their master, simplistically, only as the prophet of immobility; and the ancient Skeptic Sextus Empiricus distorted Parmenides’ thinking into problems of epistemology (theory of knowledge), because this is what his Skeptical eye saw in Parmenides’ writings.

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The Eleatic school vis-à-vis rival movements

Each member of the Eleatic school espoused a distinctive variety of Eleaticism: Parmenides pursued a direct and logical course of thought and viewed Being as finite and timeless; Zeno concurred in Parmenides’ doctrines but employed the indirect methods of reductio ad absurdum and infinite regress (see below The paradoxes of Zeno); and Melissus modified the doctrines, viewing Being as infinitely extensive and eternally temporal. A fourth thinker, the Sicilian Sophist Gorgias of Leontini, though not an adherent of Eleaticism, employed the methods of the Eleatic Zeno to defend its opposite—a nihilism that affirmed Not-Being instead of Being.

Eleaticism represents a reaction against several tendencies of thought. Methodologically, it spurned the empirical (observational) approach taken by earlier cosmologists, such as the 6th-century Milesians Thales and Anaximenes, who discerned ultimate reality in water and in air (or breath), respectively, for these substances are materializations of Being—analogous to the materialization that occurs in Pythagoreanism in passing from an abstract line or plane or three-dimensional form to a solid perceptible body—rather than Being itself; or, at best (as some scholars have held), the substances are mythological representations of Being. The Eleatics, on the contrary, ignoring perceptual appearances, pursued a rationalistic—i.e., a strictly abstract and logical—approach and thus found reality in the all-encompassing, static unity and fullness of Being and in this alone. Thus, Parmenides was the father of pure ontology.

Ontologically—in its view of the nature of Being—the Eleatic school, holding to what Parmenides called the “way of truth” (“what is”), stood opposed to two other “ways of research” that were then current: first, to the “way of opinion” (or seeming; later developed at length by Plato in the Sophist), which held that a being comprises or is defined by not only what it is but also what it is not—i.e., by its contrast with other things; and, second, to a way recognizable as that of Heracleitus, a caustic and often cryptic philosopher then living in Ephesus, who maintained—still more radically—that the essence of a being lies in part in its involvement in, or even its identity with, its opposite. Finally, as an aspect of Parmenides’ opposition to the way of opinion, he was in reaction also against Anaximander, another Milesian scientist and philosopher. Though Anaximander’s basic principle, the apeiron (“boundless”), was duly abstract and not a part of the world itself (as were water and air), his philosophy depended, nonetheless, upon the world’s contrast with the infinite apeiron, from which all things come and to which they return “in accordance with the ordinance of Time.” This contrast—which, in a Pythagorean version, envisioned the world as breathing in voidness from the infinite outer breath in order to keep things apart or discrete—thus spawned a “many” that contradicts the Eleatic One.

The rigorous ontologism of Parmenides and Melissus

For a long time Xenophanes of Colophon, a religious thinker and rhapsode of the 6th–5th century bce, was considered the founder of the Eleatic school and Parmenides’ mentor. This ancient claim, however, was successfully criticized by the 20th-century German philosopher Karl Reinhardt. It is even possible that, on the contrary, Xenophanes was an older pupil of Parmenides. In any case, his monistic view of a cosmic God, whom he may have equated pantheistically with Being itself, was Eleatic in its contention that God is one and ungenerated, that his seeing, thinking, and hearing are equally all-pervading (i.e., he is not a composite), and that he “always remains in the same place, not moving at all.”

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Parmenides’ poem Peri physeōs (On Nature) is divided into three parts: (1) a proem (preface), in which his chariot ride through the heavens to the very seat of the goddess Alētheia (Truth) is described and their initial conversation is related, in which she announces that he is “to learn all things, both the unshaken heart of well-rounded truth and also what seems to mortals, in which is no true conviction”; (2) the “Way of Truth,” the main part, in which the real and unique Being is depicted; and (3) the “Way of Opinion” (or Seeming), in which the empirical world—i.e., the single things as they appear every day to every human—is presented.

The paradoxes of Zeno

The position of the other great pupil of Parmenides, Zeno of Elea, was clearly stated in the first part of Plato’s dialogue Parmenides. There Zeno himself accepted the definition of Socrates, according to which he did not really propose a philosophy different from that of Parmenides but only tried to support it by the demonstration that the difficulties resulting from the pluralistic presupposition of the polla (the multiple beings of daily experience) were far more severe than those that seemed to be produced by the Parmenidean reduction of all reality to the single and universal Being.

The arguments by which Zeno upheld his master’s theory of the unique real Being were aimed at discrediting the opposite beliefs in plurality and motion (see paradoxes of Zeno). There are several arguments against plurality. First, if things are really many, everything must be infinitely small and infinitely great—infinitely small because its least parts must be indivisible and therefore without extension and infinitely great because any part having extension, in order to be separated from any other part, needs the intervention of a third part; but this happens to such a third part, too, and so on ad infinitum.

Very similar is the second argument against plurality: If things are more than one, they must be numerically both finite and infinite—numerically finite because they are as many things as they are, neither more nor less, and numerically infinite because, for any two things to be separate, the intervention of a third thing is necessary, ad infinitum. In other words, in order to be two, things must be three, and in order to be three, they must be five, and so on. The third argument says: If all-that-is is in space, then space itself must be in space, and so on ad infinitum. And the fourth argument says: If a bushel of corn emptied upon the floor makes a noise, each grain must likewise make a noise, but in fact this does not happen.

Zeno also developed four arguments against the reality of motion. These arguments may also be understood (probably more correctly) as proofs per absurdum of the inconsistency of any presupposed multiplicity of things, insofar as these things may be proved to be both in motion and not in motion. The first argument states that a body in motion can reach a given point only after having traversed half of the distance. But before traversing half, it must traverse half of this half, and so on ad infinitum. Consequently, the goal can never be reached.

The second argument is known as “Achilles and the tortoise,” or the Achilles paradox. If in a race the tortoise has a start on Achilles, Achilles can never reach the tortoise; for while Achilles traverses the distance from his starting point to that of the tortoise, the tortoise will have gone a certain distance, and while Achilles traverses this distance, the tortoise will have gone still farther, ad infinitum. Consequently, Achilles may run indefinitely without overtaking the tortoise. This argument is fundamentally identical to the previous one, with the only difference being that here two bodies instead of one are moving.

The third argument is the strongest of them all. It says the following: So long as anything is in a space equal to itself, it is at rest. Now, an arrow is in a space equal to itself at every moment of its flight; therefore, even the flying arrow is at rest all of the time. And the final argument says: Two bodies moving at equal speed traverse equal spaces in an equal time. But when two bodies move at equal speed in opposite directions, one passes the other in half of the time that a moving body needs to pass a body that is at rest.

The difficulty with all these arguments is that of really understanding them in their historical frame, which neither Aristotle—who was mainly concerned to confute Zeno—nor many modern scholars—who are concerned with developing new theories for the calculation of infinitesimal quantities—have really tried to do. Moreover, the role of the author of the paradoxes in the history of Greek philosophy is itself paradoxical, for many of the same arguments by which Zeno proved the self-contradictory nature of the unity considered as the smallest element of a pluralistic reality (the Many) were later similarly used by Gorgias and Plato to demolish the Parmenidean One-Totality itself.

The decline of Eleaticism

This problem is also connected with that of the correct interpretation of the second part of Plato’s Parmenides. Here the discussion to which Parmenides submits the young Socrates is meant as a serious exemplification of the logical training that Socrates still needs if he wants to make progress in philosophy. But the result is simply comic—a “fatiguing joke”—because Parmenides always starts from the mere principles of the pure Being or the One and arrives at absurd conclusions: everything is shown to be true as well as false and deducible and not deducible from everything else.

Such dialectical futility had been anticipated by the nihilism of Gorgias, presented in a work ironically entitled Peri tou mē ontos ē peri physeōs (On That Which Is Not, or On Nature), in which he said (1) that nothing exists; (2) that if anything exists, it is incomprehensible; and (3) that if it is comprehensible, it is incommunicable—and in so doing he applied Parmenides’ coalescence of Being and thought and expression to Not-Being instead of to Being and thus signalled the decline of Eleaticism.

The serious discussion and criticism of the Eleatic philosophy, however, and the positive interpretation of every Not-Being as a heteron (i.e., as a being characterized only by its difference from “another” being) is neither in Gorgias nor in the Parmenides but in the Sophist of Plato. There Plato argued that the antinomy between on and mē-on (Being and Not-Being) does not really exist, the only real antinomy being that of tauton and heteron—i.e., only that of a single object of consciousness in its present determination and all other things from which it is distinguished.

The real story of ancient Eleaticism thus ends with Plato and with Democritus, who said that Being exists no more than Not-Being, the thing no more than the no-thing. But many thinkers, and great thinkers at that—from Aristotle to Immanuel Kant and from G.W.F. Hegel to Martin Heidegger—have continued to work or to fight with the antinomy of Being and Not-Being.