The members of this school were concerned not so much with the origin
of things as with the principles of the world of things as it now is.
Their inquiries centered round the problem of change, and in their
solution of this problem they introduced the notions of Being and
Becoming, thus carrying speculation into regions strictly metaphysical.
The chief representatives of the school are Xenophanes the
theologian, Parmenides the metaphysician, Zeno the
dialectician, and Melissus, who shows a tendency to return to
the views of the Earlier Ionian students of nature.
Sources. The work entitled Concerning the Opinions, or
Concerning Xenphanes, Zeno, and Gorgias, which contains an
account of the doctrines of Xenophanes, Zeno, and others, and which was
at one time included among Aristotle's works, is now known to have been
written neither by Aristotle nor by Theophrastus, but by a later writer
of the Aristotelian school.  Our knowledge of the Eleatic philosophy
is derived from some fragments of the writings of the Eleatics
themselves, from Aristotle's account of them in his Metaphysics,
and from the works of Simplicius, who had access to a more complete
Eleatic literature than we now possess.
 Cf. Ritter and Preller, op. cit., p. 81.
Life. Xenophanes was born at Colophon, in Asia Minor, about the
year 570 B.C. According to Theophrastus, he was a disciple of
Anaximander. After wandering through Greece as a rhapsodist, he
settled at Elea in southern Italy; from this city is derived the name
of the school which he founded. The date of his death is unknown.
Sources. It is important to distinguish here (1) the fragments
of Xenophanes' didactic poem, and (2) the accounts given by our
secondary authorities. In the former we find merely a set of
theological opinions; in the latter Xenophanes is represented as
holding certain views on general metaphysical problems.
In his Didactic Poem Xenophanes opposes to the polytheistic belief of
the time the doctrine of the unity, eternity, unchangeableness,
sublimity, and spirituality of God. With the enthusiasm and fine frenzy
of a prophet, he inveighs against the notions commonly held concerning
the gods. "Each man," he says, "represents the gods as he himself is:
the negro as black and flat-nosed, the Thracian as red-haired and
blue-eyed; and if horses and oxen could paint, they, no doubt, would
depict the gods as horses and oxen" (frag. 6). So, also, he continues,
men ascribe to the gods mental characteristics which are human; they do
not understand that God is "all eye, all ear, all intellect."
According to our Authorities, -- and we have no right to challenge
their unanimous verdict in this matter, -- all that is said in the
sacred poem of Xenophanes is to be referred to the unity and eternity
of the totality of being. Plato  and Aristotle
 describe Xenophanes as
teaching the unity of all things. If this pantheism appears to us to be
irreconcilable with the monotheism of the poem, we must not conclude
that the contradiction was apparent to Xenophanes, who, though he
could rise above the popular concept of the gods, could not wholly free
himself from the notion, so deeply rooted in the Greek mind, that
nature is imbued with the divine.
 Sophis., 242 D.
 Met., I, 5, 986b, 21.
1. In his metaphysical inquiry Xenophanes seems, according to the
pseudo-Aristotelian treatise above mentioned, to have started with the
principle that "Nothing comes from nothing," whence he concluded that
there is no Becoming. Now, plurality depends on Becoming; if, then,
there is no Becoming, there is no plurality: "All is one, and one is
all." The authority, however, of this portion of the treatise is
doubtful, though it may with safety be said that if Xenophanes did not
develop this line of reasoning as Parmenides his disciple afterwards
did, the premises of these conclusions are implicitly contained in the
theological poem. For the same reason, it is uncertain whether
Xenophanes maintained the infinity or the finite nature of the Deity,
or whether he endowed the Deity with a certain spherical shape.
2. In physics, Xenophanes, in common with others of his school, forgets
the unity of being which, as a metaphysician, he had established, and
proceeds to an investigation of the plurality which he had denied. He
advocates empirical knowledge, though he holds it to be unworthy of
entire confidence, teaching (frag. 16) that truth is to be discovered
by degrees. According to some of our authorities he held that the
primitive substance was earth; according to others he held that
it was water and earth. A few attribute to him the doctrine of four
primitive elements. There is better foundation for the opinion that he
supposed the earth to have passed from a fluid to its present solid
condition,  basing his belief, according to Hippolytus, on the fact
that petrified marine animals are found on land and even on mountains.
Thus, although the one total is eternal, the world in its present form
is not eternal.
 Cf. frags. 9 and 10.
Historical Position. Xenophanes' system is, so far, the boldest
attempt to synthesize the phenomena of the universe. In
fact, it is one instance among many in which the desire to find the
one in the manifold -- a desire which is the inspiration of all
philosophical speculation -- is carried to the excess of monism. For,
if we are to accept any theory that will reconcile Xenophanes'
metaphysics with his theology, we must hold that he identified nature,
the one, immutable, eternal, with God, who likewise possesses these
Life. Parmenides, who was, perhaps, the greatest of all the
pre-Socratic philosophers, was born at Elea about 540 B.C. According
to Aristotle, he was a disciple of Xenophanes, whose doctrines he took
up and carried to their idealistic consequences. He had a more definite
grasp of principles than Xenophanes had, and developed them with
greater thoroughness than his master had done.
Sources. The didactic poem peri phuse˘s, composed
by Parmenides and preserved by Sextus, Proclus, and others, consists of
three parts. The first is a sublimely conceived introduction, in which
the goddess of truth points out to the philosopher two paths of
knowledge, the one leading to a knowledge of truth, the other to a
knowledge of the opinions of men. The second part of the poem describes
the journey to truth, and contains the metaphysical doctrines of the
author. The third part, dealing with the opinions of men, contains a
hypothetical physics, a cosmology of the apparent.
Metaphysical Doctrines. Truth consists in the knowledge that
Being is, and that not-Being can neither exist nor be conceived to
exist. The greatest error lies in treating Being and not-Being as the
same. From this fundamental error arise the opinions of men. Truth
lies in thought, for "nothing can be but what can be thought." The
senses lead to error. Being, therefore, is, and since not-Being is not,
Being is one. It is consequently unchangeable and unproduced, despite
of the senses to the contrary. For how could Being be produced? Either
from not-Being, which does not exist, or from Being, in which case it
was before it began to be. Therefore it is unproduced, unchangeable,
undivided, whole, homogeneous, equally balanced on all sides, like a
perfect sphere. 
 Poem, lines 43 ff.
 Lines 97 ff.
From the comparison of Being to a sphere it appears that Being is not
incorporeal.  Ideas do not appear in philosophy ex abrupto.
They are gradually developed in the course of speculation. Thus,
Parmenides' idea of reality is not that of the Ionians, who spoke of a
crude material substratum of existence. Neither is it the highly
abstract notion of Being which we find in the philosophy of Plato and
Aristotle. It is a something intermediate between these extremes, and
is by some likened to our notion of space.
 Cf. Burnet, of. cit., p. 594.
Physical Doctrines. Though right reason (logos) maintains
that Being is one and immutable, the senses and common opinion
(doxa) are convinced of the plurality and change which
apparently exist around us. Placing himself, therefore, at this point
of view, Parmenides proceeds  to give us.
 Lines 110 ff.
1. A cosmology of the apparent. Here he is evidently influenced
by the Pythagorean doctrine of opposites. He maintains that all things
are composed of light, or warmth, and darkness, or cold; of these, the
former, according to Aristotle,  corresponds to Being, the latter to
not-Being. They are united by a Deity (daim˘n, he panta
kuberna). They are symbolically described as male and female, and
their union is said to be effected by Eros, the first creation of the
 Met., I, 5, 986 b, 31.
 Line 130.
2. An anthropology of the apparent. The life of the soul,
perception and reflection, depend on the blending of the lightwarm and
the dark-cold principles, each principle standing, as we should say, in
psychical relation to a corresponding principle in the physical world.
In his cosmology, as well as in his anthropology, Parmenides did not
abandon the metaphysical doctrine that Being is one and that change is
an illusion. The views just described are those which Parmenides would
have held had he believed in plurality and change.
Historical Position. Parmenides is the first Greek philosopher
to place reason in opposition to opinion. Though he makes no attempt at
determining the conditions of knowledge, he prepares the way for
subsequent thinkers and formulates the problem which Socrates was to
solve by his doctrine of concepts.
The doctrine of the unity of Being could not be further developed. It
was left for Zeno, the disciple of Parmenides, to give a more thorough
dialectical demonstration of the monistic idea.
ZENO OF ELEA
Life. Zeno of Elea, born about 490 B.C., was, according to
Plato,  the favorite pupil of Parmenides. He defended the doctrines
of his master, and showed, by the use of dialectics, the absurdity of
 Parm., 127 B.
Sources. Plato speaks of a work (apparently the only work) of
Zeno, which was a polemic against the common view that plurality and
change are realities. It consisted of several discourses
(logoi), in each of which were hupotheseis or
suppositions, made with the intention of reducing them ad
absurdum. The method is, therefore, indirect, and it is because of
the skill with which Zeno applied this method that Aristotle, if we are
to believe Diogenes and Sextus, regarded him as the founder of
The work, with the exception of a few extracts preserved by Simplicius,
is lost. We are obliged, consequently, to rely almost entirely on
secondary sources. Chief among these is the Physics of
Aristotle, in which we find Zeno's arguments against the reality of
 Phys., VI, 9, 239b, 9ff.
The Arguments against Motion are as follows. First
argument : A body, in order to move from one point to another, must
move tbrough an infinite number of spaces; for magnitude
is divisible ad infinitum. But the infinite cannot be
traversed; therefore motion is impossible. Second argument: The
problem of Achilles and the tortoise. Third argument: A body
which is in one place is certainly at rest. Now, the arrow in its
flight is at each successive moment in one place; therefore it is at
rest. Fourth argument: This is based on the fact that two bodies
of equal size move past each other twice as fast (if they move with
equal velocities in opposite directions) as one would move past the
other if this latter were stationary. Motion, therefore, is an
illusion, because one of its fundamental laws -- that bodies with
equal velocities traverse a certain space in equal times -- is not
Aristotle meets these arguments by defining the true nature of time,
and by pointing out the difference between actual and potential
 Loc. cit., 241 a.
Similarly, Zeno, according to our secondary sources, argued against
Plurality and Space. (1) Zeno argued directly against the
testimony of the senses: If a measure of corn produces a sound,
each grain ought to produce a sound.  (2) Against space: if
Being exists in space, space itself must exist in space, and so ad
infinitum. This argument is contained in one of the extracts
preserved by Simplicius. (3) If the manifold exists, it must be
at once infinitely great and infinitesimally small, because it has an
infinitude of parts which are indivisible. Therefore the existence of
the manifold involves a contradiction. 
Historical Position. Zeno's contribution to the philosophy of
the Eleatic school consists in what must have been considered an
irrefutable indirect proof of the twofold principle on which the school
was founded, namely, that Being is one and that change is an illusion.
Life. Melissus was, according to Diogenes Laertius, a native of
Samos. We have no reason for doubting that he was, as Plutarch says,
the commander of the Samian fleet which defeated the Athenians off the
coast of Samos in the year 442 B.C.  He was, therefore, a younger
contemporary of Zeno, and it is possible that, like Zeno, he was a
pupil of Parmenides. He wrote a work, peri tou ontos or peri
 Percl., Chap. 26.
Sources. Of the work just mentioned, Simplicius has preserved
some fragments. These fragments agree with the accounts given of the
doctrines of Melissus in the first part of the pseudo-Aristotelian
treatise Concerning Xenophanes, etc.
Method. Melissus undertook, as Zeno had done, to defend the
doctrines of Parmenides. But while Zeno's method of argumentation was
indirect, Melissus employed the direct method. He took up the
principles of the Ionians and tried to show points of union between the
Ionian and Eleatic schools.
Metaphysical Doctrine. All that we know of Melissus' doctrine
concerning Being may be summed up in the four propositions: (1) Being
is eternal; (2) Being is infinite; (3) Being is one; (4) Being is
unchangeable. His metaphysical doctrine is, therefore, identical with
that of Parmenides, save in one respect. Parmenides did not pronounce
Being infinite, while according to Melissus infinity is one of the
attributes of Being. But, as appears from frag. 5, Melissus must not be
understood to maintain the true infinity of Being. Evidently he had in
mind infinite magnitude. Again, when he says s˘ma mŕ
echei, we must not imagine that Melissus had attained a precise
notion of the incorporeal. His metaphysics was a blending of the Ionian
with the Eleatic doctrines, and we may suppose that there were many
points of contradiction.
 Frag. 16.
The Physical Doctrines attributed to Melissus by Stobaeus and
Philoponus cannot safely be said to have been held by him.
Historical Position. Melissus does not represent a development
of Eleatic philosophy. His task was one of synthesis, or
reconciliation, and in accomplishing this task he did not wholly escape
the danger to which such an undertaking is always exposed: he admitted
into Eleatic doctrines notions and definitions which were antagonistic
to Eleatic principles.
Retrospect. With Melissus the Eleatic school ends. What was left
of Eleaticism drifted into Sophism, for which Zeno had prepared the way
by his abuse of dialectical reasoning. But, though the school
disappeared, its influence continued, and may be traced through
Heraclitus, Anaxagoras, and the Atomists down to Plato and Aristotle.
The Eleatics were the first to formulate the problems of Being and
Becoming -- problems which are always the center of metaphysical
speculation. These were the problems that Plato and Aristotle were to
solve by the theory of Ideas and the doctrine of matter and form.
Pre-Socratic philosophy is throughout objective in spirit and aim; it
is a philosophy of nature. To this, Eleatic philosophy forms no
exception. It is true that the Eleatics give to physics merely a
hypothetical value, and that they decry sense-received knowledge,
contrasting it with reason. Yet on closer examination it will be seen
that all their inquiry is concerned with the origin and explanation of
nature, and that the Being which they maintain to be the only reality
is a something extended in space, or, as Aristotle  describes it, the
substrate of sensible things. Zeno, indeed, introduced dialectic into
philosophy, but he treated it merely as an instrument of proof,
unaccompanied by any inquiry into the nature and conditions of
knowledge. The founder of the philosophy of the concept is Socrates,
and Aristotle  is right when he looks for the germ of Socratic
philosophy, not in the Eleatic doctrine, but in the teachings of
Democritus and the Pythagoreans.
 Cf.Met., IV, 5, 1010 a, and De Coelo, III,
298 b, 21.