ELEATISM. - Philosophy of the school of Elea (a city of Magna Graecia, present-day Velia-Scavi, a station on the Naples-Reggio line) which includes Xenophanes, Parmenides, Zeno, Melissus.
XENOPHANES OF COLOPHON, b. ca. 570, d. 478 B.C., banished from his homeland, traveled as a rhapsode through Sicily and southern Italy, until he settled at Elea. In the most notable of the elegiac fragments that have come down to us, he ridicules the doctrine of metempsychosis, asserts the need for wisdom against the prevailing athleticism, condemns the introduction of Lydian luxury into Colophon and recommends the reasonable enjoyment of social pleasures.
Of the epic fragments the most important are those in which he attacks the anthropomorphic polytheism of his contemporaries. "There is one God... who resembles mortals neither in form nor in thought, he is all eyes, all ears, all mind" (οὔλος ὄρξ, οὔλος δὲ νοεῖ, οὔλος δὲ τ᾿ἀκούει), and without effort he governs all things with his understanding (νόου φρενί). Men have falsely conceived the gods in their own image and likeness, in particular Homer and Hesiod have attributed to the gods what is shameful and blameworthy, theft, adultery, mutual deception. It is uncertain, however, whether Xenophanes' conception of God should be understood in a monotheistic or a pantheistic sense.
PARMENIDES OF ELEA, b. ca. 530, d. 444 B.C., of a noble family, a politician and legislator, felt the influence of the Pythagoreans and transformed the theology of Xenophanes into a rigorously monistic metaphysics.
Of the 163 hexameters that have come down to us, some of them incomplete and a few others only in Latin translation, more than two thirds treat of truth, that is, of being as one and immutable, in which reality and thought are identified; the remaining third treats of opinion, of mutable appearance. The first part is by far the most important. Being is complete (οὔλον), unique in its kind (μονογενές), without beginning and without end (ἀναρχον, ἀπανάτων, ἀτέλεστων), it was not and will not be but is now (that is, at every instant) all at once, a continuous unity (οὐδὲ ποτ' ἦν, οὐδ' ἔστιν, ἐπεὶ νῦν ἔστιν ὁμοῦ πᾶν, ἕν, συνεχές). Thought and the object of thought are identical (παύτὸν δ' ἐστὶ νοεῖν τε καὶ οὐνεκὲν ἐστι νόημα). The world of appearance contains only opinions of mortals, which are not worthy of belief, to sem-
...to be explained by Parmenides through the opposition of light and darkness (φῶς and νῦς), which perhaps reproduce the hot and the cold (θερμὸν and ψυχρὸν) of Anaximander.
The attempts to explain how Parmenides, after having resolved the problem of being, sets himself that of illusory appearance, however ingenious, do not seem satisfactory. The conjecture of Wilamowitz and of Zeller that this is a probable hypothesis clashes with the rigid opposition between being and non-being which does not allow a more or a less; the attempt of Diels and of Burnet to discern in it an essay in doxography conflicts with the innovative spirit of the time, apart from other difficulties, and the idea of Joël, which would see in it a dialectical exercise, is no more fortunate. The unity of the two parts of the poem is saved, according to Reinhardt, by considering that the physical doctrine is an essential part of the theory of knowledge. The exposition of knowledge derived from pure conceptual thought must be followed by the description of the sensible world of appearance, and perhaps a much simpler explanation is that the philosopher could indeed devalue but not annul human experience.
ZENO OF ELEA flourished around 460 B.C.; a devoted and zealous disciple of Parmenides, replying to those who think that the master's doctrine implies contradictions, he tried to show that if one admits the plurality of things existing in space and time, one falls into far more serious contradictions.
If a plurality exists, it must consist of limited magnitudes; a limited magnitude will necessarily be infinitely large and infinitely small; infinitely large because, divisible to infinity, it is composed of an infinite number of parts; infinitely small, because parts without extension, even multiplied to infinity, could not compose an extension, a magnitude. Against the possibility of motion Zeno sets forth the famous argument known under the name of "Achilles and the tortoise," which can be reduced to this: for a moving body to traverse a given interval, it must first traverse half of it, and then half of the half, and so on without end. The arrow that flies is at rest: in fact the arrow must be at a given instant at a given point, and so throughout its entire course; now, since the instant is indivisible, the arrow will be at these points not in motion. The aporias of Zeno are resolved, as is well known, by the Aristotelian doctrine of the actual continuity of space and time.
MELISSUS OF SAMOS, the same person who as navarch defeated the Athenian fleet at Samos in 440 B.C., takes up again the direct demonstration of Parmenidean monism.
Being must be eternal and ungenerated, otherwise it would have arisen from nothing and would be resolved into nothing: it must be immutable, since every change is a coming into being and a perishing. Unlike Parmenides, who attributes to being the spherical form, Melissus affirms that it is infinite; in fact if it were limited, it would have a beginning and an end and would be limited by nothing, which is unthinkable both with respect to space and with respect to time.
The influence of the Eleatic school has been lasting and strong. In modern philosophy some of the Kantian antinomies, naturally through many intermediaries, go back to this source.
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Andrea Ferro