THE ELEATIC SCHOOL

General Notions

The Eleatic School resumed discussion of the problem of being and becoming and attacked the opposition between sense knowledge and intellectual knowledge. The problem can be summed up: Reality in a logical manner appears to us under two different aspects -- accordingly as it is presented to our senses, or as it is presented to our mind.

Our senses perceive the multiplicity, the becoming, while our mind perceives the unity. Now the characteristics of unity are opposed to those of multiplicity. To which of the two must our consent be given for the ultimate reality? Heraclitus had answered that the only reality is becoming; the Eleatics say the opposite, that unity alone is being and that multiplicity is non-being, an illusion, considered both from the viewpoint of logic and metaphysics.

Xenophanes

The founder of the Eleatic School is Xenophanes, who was born at Colophon in Asia Minor about 580 B.C., and died at the age of more than ninety years. From his youth he was a soldier and had taken part in the defense of the Greek Ionian colonies against the Persian invasion. When these fell to the Persians, Xenophanes, in order not to submit to the conqueror, took up the life of a minstrel and went about singing the stories of the gods and heroes in the public squares. Finally he stopped in the Ionic colony of Elea in southern Italy, whence his school took its name.

Xenophanes, author of a poem of which only a few fragments remain, was a poet-philosopher who sought to draw the attention of men away from course anthropomorphism to the highest concept of divinity. "There is one God, sovereign alike over gods and men, unlike man either in appearance or in thought."

To represent the gods as men is to alter their nature in order to make them similar to us. These errors are due to the imaginations of men. If oxen or horses had a way of representing the gods, they would picture them as oxen or horses. Negroes represent their gods with black face and flat nose. But the "Optimus" is one, and bears resemblance to no one. "He sees all things entirely, hears all things entirely, and thinks all things entirely." Still it seems that Xenophanes confused God with space and with the universe taken it its totality.

Parmenides

The most noted thinker of the Eleatic School is Parmenides, who was born at Elea about 540 B.C. He was called "the Great" by Plato. He was author of a poem about nature which he divides into two parts: Voices of Truth and Voices of Opinion. A few fragments remain.

Xenophanes' criticism of popular religion and anthropomorphism was taken up and transferred by Parmenides to cosmic nature. Here also we find ourselves face to face with Unity, which is the totality of reality.

There is an extant fragment of Parmenides which summarizes his theory of knowledge. "Nothing can be but what can be thought." This statement indicates that Parmenides is the first philosopher to affirm the identity of being and intelligibility. According to his thought, however, intelligibility seems to mean a clear representation of the imagination.

Of far greater interest were Parmenides' metaphysical speculations, which upset Greek thought and influenced the subsequent development of metaphysics. The principle of Parmenides is: "Being is. Non-being is not." Let us try to grasp what this statement involves, for it is more difficult than it may seem at first glance.

Let us consider the first part of the principle: Being is. We know that Parmenides' predecessors, such men as Thales, Anaximander, Anaximenes, and Pythagoras, posed the question of what is the ultimate element or the source of the becoming and multiplicity of beings. Their answers varied and included water, fire, number, and other elements. Commenting on these solutions, Parmenides said that there can be doubt about what they meant by water, fire, and the life; but regardless of what they meant, each element they chose was being. Therefore: Being is. Whatever is not being does not exist and cannot be conceived. Thus he concludes: Being is. Non-being is not.

From this principle Parmenides drew some very interesting conclusions:

1. Being is one. Indeed, each being should distinguish itself from every other being. Now such a distinction should proceed either from being or from non-being. But neither is possible. The distinction cannot come from being because the second being, in so far as it is being, agrees with the first and cannot be distinguished from it. Moreover, such a distinction cannot come from non-being, for non-being does not exist and cannot be conceived. From nothing comes nothing. Therefore, being is one.
2. Becoming is also impossible. Nothing can become what it already is. For example, white cannot become white, for it is already white. But every becoming is nothing other than becoming a being. Thus, being becomes being by becoming, which is utterly inconceivable. Therefore, being is one and exists in its absolute immutability. Birth and death are illusions.
   

The One of Parmenides is not born; it is eternal, immutable, and always itself. Moreover, it is limited, since in Greek philosophy the unlimited is a sign of imperfection, and it is conceived as a finite sphere. It is the same One as that of Xenophanes but it is divested of all divine and religious attributes and reduced to one pure metaphysical and logical principle.

If the One is being and becoming is non-being, what then is all the cosmic becoming, including the life of man? Is it all a dream, an illusion? Parmenides leaves the problem unsolved. If he had solved it in conformity with his principles, the answer would have had to be affirmative and the life of the universe would appear a complete mystery.

Zeno

Zeno, chosen disciple of Parmenides, was born in Elea about the year 500 B.C. He is called by Aristotle the first dialectician because he assumed the task of proving with arguments (Sophistic) how much of paradox there was in the doctrine of his master.

Parmenides had reduced becoming to non-being and to illusion. Zeno attempted to prove just what exactly is becoming. To understand the arguments of Zeno it is necessary to remember that becoming signifies movement. If the movement were not real but illusory, it would follow that becoming also has no other consistency save that of illusion. This is the task which Zeno assumed.

His argument are four, but they follow the same pattern; for they all begin with the supposition that space (the line) is composed of infinite parts, and that it is impossible to cross these infinite parts of which space is composed. As a consequence, all that to us seems to move does not move in reality, for movement is an illusion.

Take, for example, the so-called argument of Achilles. The hero of the winged foot can never overtake the turtle -- symbol of slowness -- because the hero gives the turtle the handicap of space. Let us supposed that this interval between Achilles and the turtle is twenty feet, and while the hero runs twenty feet, the turtle advances one foot. Achilles cannot reach his running mate, because while he runs twenty feet the animal moves one foot, and while runs a foot, his rival will run one-twentieth of a foot, and successively, while Achilles run one-twentieth of a foot, the animal will have traveled one-twentieth of a twentieth of a foot, and so on, ad infinitum.

The same is to be said of the arrow which will never reach its target. Before striking the target, the arrow must traverse half the distance, and before it reaches half this space it must traverse one-half of this half, ad infinitum. Thus the arrow remains ever at the same place, no matter how much it may seem to be displaced. Such Sophistic arguments, as Aristotle noted well, are based on a false prejudgment that space is made up of an infinite number of parts.

Melissus

Among the Eleatics must be numbered Melissus, who was born at Samos and lived during the fifth century B.C. He accepts and defends Parmenides' doctrine of being, but unlike his master, he maintains that being is infinite, because it cannot be limited, neither by another being, in so far as being is one, nor by non-being, which does not exist. In agreement with Parmenides he maintains that change and motion do not exist in nature, for both imply an absurd transition from being to non-being.

The Eleatic School had the merit of calling the attention of philosophers to the concept of being and becoming, of motion, of time, of space, and of continuity. Its importance is such that all succeeding thought represented a victory over the one-sided and apparently contradictory conceptions held by Parmenides (unchanging being) and Heraclitus (successive becoming).