Hegel’s History of Philosophy: Greek Philosophy

C. The Eleatic School.

The Pythagorean philosophy has not yet got the speculative form of expression for the Notion. Numbers are not pure Notion, but Notion in the form of ordinary idea or sensuous perception, and hence a mixture of both. This expression of absolute essence in what is a pure Notion or something thought, and the movement of the Notion or of Thought, is that which we find must come next and this we discover in the Eleatic school. In it we see thought becoming free for itself; and in that which the Eleatics express as absolute essence, we see Thought grasp itself in purity, and the movement of Thought in Notions In the physical philosophy we saw movement represented as an objective movement, as an origination and passing away. The Pythagoreans similarly did not reflect upon these Notions, and also treated their essence, Number, as fleeting. But since alteration is now grasped in its highest abstraction as Nothing, this objective movement changes into a subjective one, comes over to the side of consciousness, and existence becomes the unmoved. We here find the beginning of dialectic, i.e. simply the pure movement of thought in Notions; likewise we see the opposition of thought to outward appearance or sensuous Being, or of that which is implicit to the being-for-another of this implicitness, and in the objective existence we see the contradiction which it has in itself, or dialectic proper. When we reflect in anticipation on how the course of pure thought must be formed, we find (a) that pure thought (pure Being, the One) manifests itself immediately in its rigid isolation and self-identity, and everything else as null; (b) that the hitherto timid thought — which after it is strengthened, ascribes value to the “other” and constitutes itself therefrom — shows that it then grasps the other in it’s simplicity and even in so doing shows its nullity; (g) finally, Thought manifests the other in the manifold nature of its determinations. We shall see this in the development and culture of the Eleatics in history. These Eleatic propositions still have interest for Philosophy, and are moments which must necessarily there appear.

Xenophanes, Parmenides, Melissus and Zeno are to be reckoned as belonging to this school. Xenophanes may be regarded as the founder of it; Parmenides is supposed to have been his pupil, and Melissus, and especially Zeno, are called the pupils of Parmenides. In fact, they are to be taken together as forming the Eleatic school; later on it lost the name, being then called Sophistic, and its locality was transferred to Greece proper. What Xenophanes began, Parmenides and Melissus developed further, and similarly Zeno perfected what these two taught. Aristotle (Metaph. 1. 5) characterizes the first three thus: “Parmenides seems to comprehend the one as Notion (kata ton logon), Melissus as matter (kata thn ulhn); hence the former says that it is limited (peperasmenon) and the latter that it is unlimited (apeiron). But Xenophanes, who was the first of them to express the theory of the One, made the matter no plainer (diesaf hnisen), nor did he deal with either of these aspects (fusewς), but looking into the heavens” — as we say, into the blue — “said, God is the One. Xenophanes and Melissus are on the whole less civilized (mikron agroikoteroi) Parmenides, however, is more acute (mallon blepwn).” There is less to say of Xenophanes and Melissus, and what has come to us from the latter in particular — in fragments and derived from the sayings of others — is still in a state of ferment, and in his case there is least knowledge obtain. able. On the whole, philosophic utterances and Notions are still poor,. and it was in Zeno that Philosophy first attained to a purer expression of itself.

1. Xenophanes.

The period at which he lived is clear enough, and as this suffices, it is a matter of indifference that the year of his birth and of his death is unknown. According to Diogenes Laërtius (IX. 18), he was contemporary with Anaximander and Pythagoras. Of his circumstances further than this, it is only known that he, for reasons which are unknown. escaped from his native town, Colophon, in Asia Minor, to Magna Græcia, and resided for the most part at Zancle, (now Messina) and Catana (still called Catania) in Sicily. I find it nowhere said by the ancients that he lived at Elea, although all recent writers on the history of Philosophy repeat it, one after the other. Tennemann, in particular, says (Vol. I. pp. 151 and 414), that about the 61st Olympiad (536 B.C.), he repaired from Colophon to Elea. Diogenes Laërtius (IX. 20), however, only says that he flourished about the 60th Olympiad and that he made two thousand verses on the colonization of Elea, from which it might be easily concluded that he was also born at Elea. Strabo says this in the beginning of his sixth book — when describing Elea — of Parmenides and Zeno only, and these he called Pythagoreans; hence, according to Cicero (Acad. Quæst. IV. 42) the Eleatic school took its name from these two. Xenophanes was nearly a hundred years old, and lived to see the Median wars: it is said that he became so poor that he had not the means of having his children buried, and was obliged to do so with his own hands. Some say that he had no teacher; others name Archelaus, which is a chronological error.

He wrote a book “On Nature,” the general subject and title of Philosophy at that time; some verses have been preserved to us which so far show no powers of reasoning. Professor Brandis of Bonn collected them together, with the fragments of Parmenides and Melissus, under the title “Commentationum Eleaticarum, P. 1,” Altonæ 1813. The older philosophers wrote in verse, for prose comes much later on; on account of the awkward and confused mode of expression in Xenophanes’ poems, Cicero calls them (Acad. Quæst. IV. 23): minus boni versus.

As to his philosophy, Xenophanes in the first place maintained absolute existence to be the one, and likewise called this God. “The all is One and God is implanted in all things; He is unchangeable, without beginning, middle on end.” In some verses by Xenophanes found in Clemens of Alexandria (Strom. V. 14, p. 714, ed. Potter), it is said:

One God. is greatest amongst gods and men.
Neither like unto mortals in spirit or in form;

and in Sextus Empiricus (adv. Math. IX. 144):

“He sees everywhere, thinks everywhere, and hears everywhere,”

to which words Diogenes Laërtius (IX. 19) adds: “Thought and reason are everything and eternal.” By this Xenophanes denied the truth of the conceptions of origination and of passing away, of change, movement, &c., seeing that they merely belong to sensuous perception. “He found,” says Tennemann (Vol. I. p. 156) “all origination to be inconceivable:” the One as the immediate Product of pure thought, is, in its immediacy, Being.

For us the determination of Being is already known and trivial, but if we know about Being, the One, we place this, as a particular determination, in a line with all the rest. Here, on the contrary, it signifies that all else has no reality and is only a semblance. We must forget our own ideas; we know of God as Spirit. But, because the Greeks only had before them the sensuous world, these gods of their imagination, and found in them no satisfaction, they rejected all as being untrue, and thus came to pure thought. This is a, wonderful advance, and thought thus becomes for the first time free for itself in the Eleatic school. Being, the One of the Eleatic school, is just this immersion in the abyss of the abstract identity of the understanding. Just as this comes first, so it also comes last, as that to which the understanding comes back, and this is proved in recent times when God is grasped only as the highest Being. If we say of God that this the highest Being is outside of and over us, we can know nothing more of it but that it is, and thus it is the undetermined; for if we knew of determinations, this would be to possess knowledge. The truth then simply is that God is the One, not in the sense that there is one God (this is another determination), but only that He is identical with Himself; in this there is no other determination, any more than in the utterance of the Eleatic school. Modern thought has, indeed, passed through a longer path, not only through what is sensuous, but also through philosophic ideas and predicates of God, to this all negating abstraction; but the content, the result arrived at is the same.

With this the dialectic reasoning of the Eleatics is closely connected in respect that they have also proved that nothing can originate or pass away. This deduction is to be found in Aristotle’s work, De Xenophane, Zenone et Gorgia, c. 3. “It is impossible, he says,[1] that if anything is, it arises (and he even applies this to the Godhead); for it must arise either from the like or from the unlike. But both are equally impossible: for it is no more probable that the like should be engendered from the like, than that it should engender it, for the like must have determinations identical with one another.” In acknowledging similarity, the distinction between begetting and begotten falls away. “Just as little can unlike arise from unlike, for if from the weaker the stronger takes its rise; or from the smaller, the greater; or from the worse, the better: or if, conversely the worse proceeds from the better, non-being would result from Being, this is impossible, and thus God is eternal.” The same thing has been expressed as Pantheism or Spinozaism, which rests on the proposition ex nihilo fit nihil. The unity of God is further proved by Xenophanes: “If God is the mightiest, He must be One; for wore He two or more, He would not have dominion over the others, but, not having dominion over the others, He could not be God. Thus were there several, they would be relatively more powerful or weaker, and thus they would not be gods, for God’s nature is to have nothing mightier than He. Were they equal, God would no longer possess the quality of being the mightiest, for the like is neither worse nor better than the like” — or it does not differ therefrom. “Hence if God is, and is such as this, He is only one; He could not, were there several, do what He willed. Since He is one, He is everywhere alike. He bears, sees and has also the other senses everywhere, for were this not the case, the parts of God would be one more powerful than the other, which is impossible. Since God is everywhere alike, He has a spherical form, for He is not here thus and elsewhere different, but is everywhere the same. Since He is eternal and one and spherical in form, He is neither unlimited nor limited. To be unlimited is non-being; for that has neither middle, beginning, end, nor part; and what is unlimited corresponds to this description. But whatever non-being is, Being is not. Mutual limitation would take place if there were several, but since there is only One, it is not limited. The one does not move itself, nor is it unmoved; to be unmoved is non-being. for to it none other comes, nor does it go into another; but to be moved must mean to be several, for one must move into another. Thus the One neither rests nor is it moved, for it is neither non-being nor is it many. In all this God is thus indicated; He is eternal and One, like Himself and spherical, neither unlimited nor limited, neither at rest nor moved.” From this result, that nothing can arise from the like or from the unlike, Aristotle (De Xenophane, Zenone et Gorgia c. 4) draws this conclusion that either there is nothing excepting God, or all else is eternal.”

We here see a dialectic which may be called metaphysical reasoning, in which the principle of identity is fundamental. “The nothing is like nothing and does not pass into Being or conversely; thus nothing can originate from like.” This, the oldest mode of argument, holds its place even to the present day, as, for example, in the so-called proof of the unity of God. This proceeding consists of making pre-suppositions such as the power of God, and from them drawing conclusions and denying the existence of predicates; that is the usual course in our mode of reasoning. In respect of determinations, it must be remarked that they, as being negative, are all kept apart from the positive and. merely real being. We reach this abstraction by a more ordinary way, and do not require a dialectic such as that of the Eleatic school: we say God is unchangeable. change concerns finite things alone (which we represent as an empirical proposition); on the one hand we thus have finite things and change, and on the other, unchangeableness in this abstract absolute unity with itself. It is the same separation, only that we also allow the finite to be Being, which the Eleatics deny. Or else we too proceed from finite thin” to kinds and genera, leaving the negative out bit by bit; and the highest order of all is God, who, as the highest Being is affirmative only, but devoid of any determination. Or we pass from what is finite to the infinite, for we say that the finite as limited must have its basis in the infinite. In all these different forms which are quite familiar to us, there is the same difficult question which exists in reference to the Eleatic thought. Whence comes determination and how is it to be grasped — how is it in the one, leaving the finite aside, and also how does the infinite pass out into the finite? The Eleatics in their reflections were distinguished from this our ordinary reflecting thought, in that they went speculatively to work (the speculative element being that change does not exist at all) and that they thus showed that, as Being was presupposed, change in itself is contradictory and inconceivable. For from the one, from Being, the determination of the negative, of the manifold, is withdrawn. Thus while we, in our conception, allow the actuality of the finite world, the Eleatics are more consistent, in that they proceeded to say that only the One exists and that the negative does not exist at all; — a consequence which, if it necessarily arouses in us surprise, still none the less remains a great abstraction.

Sceptics saw in this the point of view of the uncertainty of all things, and Sextus several times quotes verses such as these: —

“No man at any time knew clearly and truly; nor will he ever know
What of the gods I say, as also of the universe.
For what he thinks to speak most perfectly
He knows that not at all; his own opinions cleave to all.”

Sextus, generalizing, explains this in the first passage thus: “Let us imagine that in a house in which are many valuables, there were those who sought for gold by night; in such a case everyone would think that he had found the gold, but would not know certainly whether he actually had found it. Thus philosophers come into this world as into a great house to seek the truth, but were they to reach it, they could not tell whether they really had attained to it.” The indefinite expressions of Xenophanes might also merely mean that none knows that which he (Xenophanes) here makes known. In the second passage Sextus puts it thus: “Xenophanes does not make all knowledge void, but only the scientific and infallible; opinionative knowledge is, however, left. He expresses this in saying that opinion cleaves to all. So that with him the criterion is made to be opinion, i.e. the apparent, and not that which is firm and sure; Parmenides, on the contrary, condemns opinion.” But from his doctrine of the One, there follows the annihilation of ordinary ideas, which is what he did in the foregoing dialectic; it is evident, however, that nobody could know the truth which he hereby utters. If a thought such as this passed through one’s head, one could not tell that it was true, and in such a case it would only be an opinion.

We here find in Xenophanes a double consciousness; a pure consciousness and consciousness of Being, and a consciousness of opinion. The former was to him the consciousness of the divine, and it is the pure dialectic, which is negatively related to all that is determined and which annuls it. The manner in which he expresses himself towards the sensuous world and finite thought-determinations is seen most clearly in his allusions to the Greek mythological conceptions of the gods. He says, amongst other things, according to Brandis (Comment. Eleat. P. I. p. 68): —

“Did beasts and lions only have hands,
Works of art thereby to bring forth, as do men,
They would, in creating divine forms, give to them
What in image and size belongs to themselves.”

He also animadverts on the ideas of the gods held by Homer and Hesiod in verses which Sextus (adv. Math. IX. 193) has preserved to us: —

“Hesiod and Homer have attached to the gods
All that which brings shame and censure to men;
Stealing, adultery, and mutual deceit.”

As, on the one hand, he defined absolute Being to be simple, making that which is, however, break through and be immediately present in it, on the other hand he philosophizes on appearances; in reference to this certain fragments only are transmitted to us, and such physical opinions as these can have no great interest. They are meant to have no speculative significance any more than are those of our own physicists. When he says in this connection

“Out of the earth comes all, and returns to it again,
We all have come from earth and water alike,
Thus all that grows and takes its rise is only earth and water,”

this does not signify existence, physical principles, as did the water of Thales. For Aristotle expressly says, that no one regarded the earth as the absolute principle.

2. Parmenides.

Parmenides is a striking figure in the Eleatic school, and he arrives at more definite conceptions than does Xenophanes. He was, according to Diogenes (IX. 21), born at Elea of a rich and honourable race. Of his life, however, little is known; Aristotle only says (Met. 1. 5) from tradition that he was a scholar of Xenophanes. Sextus Empiricus (adv. Math. VII. III) calls him a friend (gnwrimoς) of Xenophanes. Diogenes Laërtius further states: “He beard Anaximander and Xenophanes also, but did not follow the latter” (which seems only to refer to his place of abode), “but he lived with Aminias and Diochartes the Pythagorean, attached himself to the latter. and by the former, and not by Xenophanes, was prevailed upon to lead a quiet life.” That the period in which his life falls comes between Xenophanes and Zeno — so that he is contemporaneous with them, though younger than the former and older than the latter — is ascertained. According to Diogenes (IX. 23) he flourished about the 69th Olympiad (504-501 B.C.). What is most important is his journey to Athens with Zeno, where Plato makes them talk with Socrates. This may be accepted generally, but what is strictly historical in it cannot be ascertained. In the Thætetus Plato makes Socrates reply to the invitation to examine the Eleatic system: “For Melissus and the others who assert the All to be One at rest, I have a certain respect; I have even more for Parmenides. For, to speak in Homeric language, he seems to me both venerable and strong. I knew him when he was an old man and I was ill quite young, and I heard wonderful things from him.” And in the Platonic Dialogue Parmenides (p. 127. Steph. p. 4. Bekk.) where, as is well known, the conversation is carried on by Parmenides and Socrates, the historic circumstances of this interview are related in detail. “Parmenides was very old, had hair which was quite grey, was beautiful in countenance, about sixty-five years old, and Zeno almost forty.” Tennemann (Vol. I. p. 415) places the journey in the 80th Olympiad (466-457B.C.). Thus Socrates, since he was born in Olympiad 77, 4 (469 B.C.), would seem to have been still too young to have carried on a dialogue such as Plato describes, and the principal matter of this dialogue, which is written in the spirit of the Eleatic school, belongs to Plato himself. Besides, we know from Parmenides’ life, that he stood in high respect with his fellow-citizens at Elea, whose prosperity must be chiefly ascribed to the laws which Parmenides gave them. We also find in the pinax of Cebes (towards the beginning) “a Parmenidian life” used synonymously with amoral life.

It must be remarked that here, where the Eleatic school is definitely treated of, Plato does not speak of Xenophanes at all, but only of Melissus and Parmenides. The fact that Plato, in one of his dialogues, likewise accords the chief part to Parmenides, and puts in his mouth the most lofty dialectic that ever was given, does not concern us here. If with Xenophanes, by the proposition that out of nothing nothing comes, origination and what depends upon or can be traced back to it is denied, the opposition between Being and non-being makes its appearance still more clearly with Parmenides, though still unconsciously. Sextus Empiricus and Simplicius have preserved to us the most important fragments from the poems of Parmenides; for Parmenides also propounded his philosophy as a poem. The first long fragment in Sextus (adv. Math. VII. III) is an allegorical preface to his poem on Nature. This preface is majestic; it is written after the manner of the times, and in it all there is an energetic, impetuous soul which strives with Being to grasp and to express it. We can show

Parmenides’ philosophy best in his own words. The introduction runs thus:

“Horses that bore me, impelled by their courage,
Brought me to the much-famed streets of the goddess
Who leads the wise man to every kind of knowledge.
Maidens point out the way.
The axle sings hot am the daughters of Helios quickly approach,
Leaving the dwelling of night, pressing on to the light,
With mighty hands raising the sheltering veil.”

The maidens are, according to Sextus (adv. Math. VII. 112, 113), the senses, and Helios? daughters are more especially the eyes: —

“These are the gates of the pathways of night and of day.
Now the heavenly maidens approach the great doors,
Whose lock double-turned the punishing Dice protects.
To this one soft words were by the maidens addressed
Subtly persuading her the barriers of oak from the gates,
Now to withdraw. Yet these,
Directly the yawning breadth of the doors was revealed,
Drove the horses and waggon, on through the gate.
The goddess received me in friendship, seized with her one hand my right,
And turning towards me, she said.
‘Oh, thou, who with guides all immortal and horses,
Camest here in my palace, — be welcome, young man.
For no evil fate has led thee into this path,
(Indeed it lies far from the ways of a man)
But Themis and Dice. Now shalt thou all things explore,
The heart never-flinching of the truth that persuades,
The transient opinions which are not to be trusted.
But from such paths keep the inquiring soul far away.
On this way let not the much followed custom
Cause thee to take the rash eye as thy guide,
Or the confused sounding ear and the tongue. Ponder considerately
With thy reason alone, the doctrine much and often examined,
Which I will proclaim. For there lacks but desire on your way.’”

The goddess develops everything from the double knowledge (a) of thought, of the truth, and (b) of opinion; these make up the two parts of the poem. In another fragment taken from Simplicius’ Commentary on Aristotle’s Physics (p. 25; l9 a) and from Proclus on the Timæus (p. 29 b), we have the principal part of what is here related preserved to us. “Understand,” says the goddess, “which are the two roads of knowledge. The one which is only Being, and which is not non-being, is the path of conviction, the truth is in it. The other that is not Being, and which is necessarily non-being, is, I must tell you, a path quite devoid of reason, for thou canst neither know, or attain to, or express, non-being.” The nothing, in fact, turns into something, since it is thought or is said: we say something, think something, if we wish to think and say the nothing. “It is necessary that saying and thinking should be. Being; for Being is, but nothing is not at all.” There the matter is stated in brief; and in this nothing, falls negation generally, or in more concrete form, limitation, the finite, restriction: determinatio est negatio is Spinoza’s great saying. Parmenides says, whatever form the negation may take, it does not exist at all. To consider the nothing as the true is “the way of error in which the ignorant and double-minded mortals wander. Perplexity of mind sways the erring sense. Those, who believe Being and non-being to be the same, and then again not the same, are like deaf and blind men surprised, like hordes confusedly driven.” The error is to confuse them and to ascribe the same value to each, or to distinguish them as if non-being were the limited generally. “Whichever way is taken, it leads back to the point from which it started.” It is a constantly self-contradictory and disintegrating movement. To human ideas, now this is held to be reality and now its opposite, and then again a mixture of both.

Simplicius quotes further, in writing on Aristotle’s Physics (p. 17 a; 31, 19): “But the truth is only the ‘is’; this is neither begotten of anything else, nor transient, entire, alone in its class (mounogeneς), unmoved and without end; it neither was, nor will be, but is at once the all. For what birth wouldst thou seek for it? How and whence should it be augmented? That it should be from that which is not, I shall allow thee neither to say nor to think, for neither can it be said or thought that the ‘is’ is not. What necessity had either later or earlier made it begin from the nothing? Thus must it throughout only be or not be; nor will any force of conviction ever make something else arise out of that which is not. Thus origination has disappeared, and decease is incredible. Being is not separable, for it is entirely like itself; it is nowhere more, else would it not hold together, nor is it less, for everything is full of Being. The all is one coherent whole, for Being flows into unison with Being: it is unchangeable and rests securely in itself; the force of necessity holds it within the bounds of limitation. It cannot hence be said that it is imperfect; for it is without defect, while non-existence is wanting in all.” This Being is not the undetermined (apeiron) for it is kept within the limits of necessity; we similarly find in Aristotle that limitation is ascribed to Parmenides. The sense in which the expression “limit” is to be taken is uncertain. According to Parmenides, however, this absolute limitation is as Dikh, absolute necessity clearly determined in itself; and it is an important fact that he went beyond the uncultured conception of the infinite. “Thought, and that on account of which thought is, are the same. For not without that which is, in which it expresses itself (en pefatismenon estin), wilt thou find Thought, seeing that it is nothing and will be nothing outside of that which is.” That is the main point. Thought produces itself, and what is produced is a Thought. Thought is thus identical with Being, for there is nothing beside Being, this great affirmation. Plotinus, in quoting (V. Ennead. 1. 8) this last fragment says: “Parmenides adopted this point of view, inasmuch as he did not place Being in sensuous things; identifying Being with Thought, he maintained it to be unchangeable.” The Sophists concluded from this: “All is truth; there is no error, for error is the non-existent, that which is not to be thought.”

Since in this an advance into the region of the ideal is observable, Parmenides began Philosophy proper. A man now constitutes himself free from all ideas and opinions, denies their truth, and says necessity alone, Being, is the truth. This beginning is certainly still dim and indefinite, and we cannot say much of what it involves; but to take up this position certainly its to develop Philosophy proper, which has not hitherto existed. The dialectic that the transient has no truth, is implied in it, for if these determinations are taken as they are usually understood, contradictions ensue. In Simplicius (in Arist. Phys. p. 27 b.; 31 b.) we have further metaphorical images from Parmenides. “Since the utmost limit of Being is perfect, it resembles on every side the form of a well rounded sphere, which from its centre extends in all directions equally, for it can be neither larger or smaller in one part or another. There is no non-being which prevents it from attaining to the like” — from coming into unity with itself — “and there is no Being where it was devoid of Being, here more and there less. Because the all is without defect, it is in all places in the same way like itself in its determinations.” Plotinus in the passage quoted says: “He compares Being with the spherical form, because it comprehends — all in itself, and Thought is not outside of this, but is contained in it.” And Simplicius says: “We must not wonder at him, for on account of the, poetic form, he adopts a mythological fiction (plasmatoς).” It immediately strikes us that the sphere is limited, and furthermore in space, and hence another must be above it; but then the Notion of the sphere is the similarity of withholding the different, notwithstanding that even the undifferentiated must be expressed; hence this image is inconsistent.

Parmenides adds to this doctrine of the truth, the doctrine of human opinions, the illusive system of the world. Simplicius, writing on Aristotle’s Physics (p. 7 b; 39 a), tells us that he says: “Men have two forms of opinion, one of which should not be, and in it they are mistaken; they set them in opposition to one another in form and symbol. The one, the ethereal fire of the flame, is quite fine, identical with itself throughout, but not identical with the other, for that is also for itself; on the other hand there is what belongs to night, or thick and ponderous existence.” By the former, warmth, softness, lightness is expressed, and by the latter, cold. “But since everything is called light and night, and their qualities are suited both to the one kind of things and the other, everything alike is filled with light and dark night; both are alike since nothing exists without both.” Aristotle (Met. 1. 3 and 5), and the other historians, likewise unanimously attribute to Parmenides the fact that he sets forth two principles for the system of manifest things, warmth and cold, through the union of which everything is. Light, fire, is the active and animate; night, cold, is called the passive.

Parmenides also speaks like a Pythagorean — he was called anhr Puqagoreioς by Strabo — in the following, and likewise mythologic al conception: “There are circlets wound round one another, one of which is of the rare element and the other of the dense, between which others are to be found, composed of light and darkness mingled. Those which are less are of impure fire, but those over them of night, through which proceed the forces of the flames. That which holds this all together, however, is something fixed, like a wall, under which there is a fiery wreath, and the most central of the rare spheres again is fiery. The most central of those mixed is the goddess that reigns over all, the Divider (klho oucoς), Dice and Necessity. For she is the principle of all earthly produce and intermingling, which impels the male to mix with the female, and conversely; she took Love to help her, creating him first amongst the gods. The air is an exhalation (anapnoh) of the earth; the sun and the milky way, the breath of fire; and the moon is air and fire mingled, &c.

It still remains to us to explain the manner in which Parmenides regarded sensation and thought, which may undoubtedly at first sight seem to be materialistic. Theophrastus, for example, remarks in this regard: “Parmenides said nothing more than that there are two elements. Knowledge is determined according to the preponderance of the one or of the other; for, according as warmth or cold predominate, thought varies; it becomes better and purer through warmth, and yet it requires also a certain balance.

“For as in each man there still is in his dispersive limbs an intermingling,
So is the understanding of man; for that
Which is thought by men, is the nature of the limbs,
Both in one and all; for thought is indeed the most.” [2]

He thus takes sensation and thought to be the same, and makes remembrance and oblivion to arise from these through mingling them, but whether in the intermingling they take an equal place, whether this is thought or not, and what condition this is, he leaves quite undetermined. But that he ascribes sensation to the opposites in and for themselves is clear, because he says: “The dead do not feel light or warmth or hear voices, because the fire is out of them; they feel cold, stillness and the opposite, however, and, speaking generally, each existence has a certain knowledge.” In fact, this view of Parmenides is really the opposite of materialism, for materialism consists in putting together the soul from parts, or independent forces (the wooden horse of the senses).

3. Melissus.

There is little to tell about the life of Melissus. Diogenes Laërtius (IX. 24) calls him a disciple of Parmenides, but the discipleship is uncertain; it is also said of him that he associated with Heraclitus. He was born in Samos, like Pythagoras, and was besides a distinguished statesman amongst his people. It is said by Plutarch (in Pericle, 26) that, as admiral of the Samians, he gained in battle a victory over the Athenians. He flourished about the 84th Olympiad (444 B.C.).

In regard to his philosophy, too, there is little to say. Aristotle, where he mentions him, places him always with Parmenides, as resembling him in mode of thought. Simplicius, writing on Aristotle’s Physics (p. 7 sqq.), has preserved several fragments of his prose writings on Nature, which show the same kind of thoughts and arguments as we find in Parmenides, but, in part, somewhat more developed. It was a question whether the reasoning in which it is shown that change does not exist, or contradicts itself, which, by Aristotle in his incomplete, and, in some parts, most corrupt work on Xenophanes, Zeno, and Gorgias (c. I.), was ascribed to Xenophanes, did not really belong to Melissus.[3]

Since the beginning, in which we are told whose reasoning it is, is wanting, conjecture only applies it to Xenophanes. The writing begins with the words “He says,” without any name being given. It thus depends on the superscription alone whether Aristotle speaks of the philosophy of Xenophanes or not, and it must be noticed that different hands have put different superscriptions. Indeed, there is in this work (c. 2) an opinion of Xenophanes mentioned in such a way that it appears as though had what was previously quoted by Aristotle been by him ascribed to Xenophanes, the expression would have been different. It is possible that Zeno is meant, as the internal evidence abundantly shows. There is in it a dialectic more developed in form, more real reflexion, than from the verses could be expected, not from Xenophanes alone, but even from Parmenides. For Aristotle expressly says that Xenophanes does not yet determine with precision; thus the cultured reasoning contained in Aristotle must certainly be denied to Xenophanes; at least, it is so far certain that Xenophanes himself did not know how to express his thoughts in a manner so orderly and precise as that found here. We find it said: —

“If anything is, it is eternal (aidion).” Eternity is an awkward word, for it immediately makes us think of time and mingle past and future as an infinite length of time; but what is meant is that aidion is the self-identical, supersensuous, unchangeable, pure present, which is without any time-conception. It is, origination and change are shut out; if it commences, it does so out of nothing or out of Being. “It is impossible that anything should arise from the nothing. If everything could have arisen, or could it merely not have been everything eternally, it would equally have arisen out of nothing. For, if everything had arisen, nothing would once have existed. If some were alone the existent out of which the rest sprang, the one would be more and greater. But the more and greater would thus have arisen out of the nothing of itself, for in the less there is not its more, nor in the smaller its greater.”

Simplicius makes this note to the Physics of Aristotle (p. 22 b): “No more can anything arise out of the existent, for the existent already is, and thus does not first arise from the existent.”

“As eternal, the existent also is unlimited, since it has no beginning from. which it came, nor end in which it ceases. The infinite all is one, for, if there were two or more, they would limit one another,” and thus have a beginning and end. The one would be the nothing of the other and come forth from this nothing. “This one is like itself; for if it were unlike it would no longer be the one that was posited, but many. This one is likewise immovable, inasmuch as it does not move itself, since it does not pass out into anything. In passing out, it would require to do so into what is full or what is empty; it could not be into the full, for that is an impossibility, and just as little could it be into what is empty, for that is the nothing. The one, therefore, is in this way devoid of pain or suffering, not changing in position or form, or mingling with what is different. For all these determinations involve the origination of non-being and passing away of Being, which is impossible.” Thus here again the contradiction which takes place when origination and passing away are spoken of, is revealed.

Now Melissus places opinion in opposition to this truth. The change and multiplicity extinguished in Being appears on the other side, in consciousness, as in what is opinionative; it is necessary to say this if only the negative side, the removal of these moments, the Absolute as destitute of predicate, is laid. hold of. “In sensuous perception the opposite is present for us; that is to say, a number of things, their change, their origination and passing away, and their intermingling. Thus that first knowledge must take its place beside this second, which has as much certainty for ordinary consciousness as the first.” Melissus does not seem to have decided for the one or the other, but, oscillating between both, to have limited the knowledge of the truth to the statement that, speaking generally, between two opposite modes of presentation, the more probable opinion is to be preferred, but that what is so preferred is only to be regarded as the stronger opinion, and not as truth. This is what Aristotle says of him.

Since Aristotle, in distinguishing his philosophy from the philosophy of Parmenides, maintains that in the first place Parmenides seems to understand the One as the principle of thought, and Melissus as matter, we must remark that this distinction falls away in pure existence, Being, or the One. Pure matter, as also pure thought (if I am to speak of such a distinction), are not present to Parmenides and Melissus, since they are abrogated; and it must only be in the manner of his expression that one of them — according to Aristotle (Phys. 1. 2), on account of his clumsier mode of treatment (mallon fortikoς) — could seem to have conceived of the other sense. If the difference consisted secondly in the fact that Parmenides regarded the one as limited and Melissus as unlimited, this limitation of the one would, in effect, immediately contradict the philosophy of Parmenides; for since limit is the non-being of Being, non-being would thus be posited. But when Parmenides speaks of limit, we see that his poetic language is not altogether exact; limit, however, as pure limit, is just simple Being and absolute negativity, in which all else said and set forth is sublated. Necessity, as this pure negativity and movement within itself, although impassive thought, is absolutely bound to its opposite. In the third place it may be said that Parmenides set forth a concomitant philosophy of opinion or reality, to which Being as existence for thought was thus more opposed than was the case with Melissus.

4. Zeno.

What specially characterizes Zeno is the dialectic which, properly speaking, begins with him; he is the master of the Eleatic school in whom its pure thought arrives at the movement of the Notion in itself and becomes the pure soul of science. That is to say, in the Eleatics hitherto considered, we only have the proposition: “The nothing has no reality and is not at all, and thus what is called origin and decease disappears.” With Zeno, on the contrary, we certainly see just such an assertion of the one and removal of what contradicts it, but we also see that this assertion is not made the starting point; for reason begins by calmly demonstrating in that which is established as existent, its negation. Parmenides asserts that “The all is immutable, for, in change, the non-being of that which is would be asserted, but Being only is; in saying that “non-being is, the subject and the predicate contradict themselves.” Zeno, on the other hand, says: “Assert your change; in it as change there is the negation to it, or it is nothing.” To the former change existed as motion, definite and complete. Zeno protested against motion as such, or pure motion.

Pure Being is not motion; it is rather the negation of motion.” We find it specially interesting that there is in Zeno the higher consciousness, the consciousness that when one determination is denied, this negation is itself again a determination, and then in the absolute negation not one determination, but both the opposites must be negated. Zeno anticipated this, and because he foresaw that Being is the opposite of nothing, he denied of the One what must be said of the nothing. But the same thing must occur with all the rest. We find this higher dialectic in Plato’s Parmenides; here it only breaks forth in respect to some determinations, and not to the determination of the One and of Being. The higher consciousness is the consciousness of the nullity of Being as of what is determined as against the nothing, partly found in Heraclitus and then in the Sophists; with them it never has any truth, it has no existence in itself, but is only the for-another, or the assurance of the individual consciousness, and assurance as refutation, i.e. the negative side, of dialectic.

According to Diogenes Laërtius, (IX. 25) Zeno was like wise an Eleat; he is the youngest, and lived most in company with Parmenides. The latter became very fond of him and adopted him as a son; his own father was called Telentagoras. Not in his State alone was his conduct held in high respect, for his fame was universal, and he was esteemed particularly as a teacher. Plato mentions that men came to him from Athens and other places, in order to profit from his learning. Proud self-sufficiency is ascribed to him by Diogenes (IX. 28) because he — with the exception of a journey made to Athens — continued to reside in Elea, and did not stay a longer time in the great, mighty Athens, and there attain to fame. In very various narratives his death was made for ever celebrated for the strength of his mind evinced in it; it was said that he freed a State (whether his own home at Elea or in Sicily, is not known) from its Tyrant (the name is given differently, but an exact historical account has not been recorded) in the following way, and by the sacrifice of his life. He entered into a plot to overthrow the Tyrant, but this was betrayed. When the Tyrant now, in face of the people, caused him to be tortured in every possible way to get from him an avowal of his confederates, and when he questioned him about the enemies of the State, Zeno first named to the Tyrant all his friends as participators in the plot, and then spoke of the Tyrant himself as the pest of the State. The powerful remonstrances or the horrible tortures and death of Zeno aroused the citizens, inspired them with courage to fall upon the Tyrant, kill him, and liberate themselves. The manner of the end, and his violent and furious state of mind, is very variously depicted. He is said to have pretended to wish to say something into the Tyrant’s ear, and then to have bitten his ear, and thus held him fast until lie was slain by the others. Others say that he seized him by the nose between his teeth; others that as on his reply great tortures were applied, he bit off his tongue and spat it into the Tyrant’s face, to show him that he could get nothing from him, and that he then was pounded in a mortar.

It has just been noticed that Zeno had the very important character of being the originator of the true objective dialectic. Xenophanes, Parmenides, and Melisibus, start with the proposition: “Nothing is nothing; the nothing does not exist at all, or the like is real existence,” that is, they make one of the opposed predicates to be existence. Now when they encounter the opposite in a determination, they demolish this determination, but it is only demolished through another, through my assertion, through the distinction that I form, by which one side is made to be the true, and the other the null. We have proceeded from a definite proposition; the nullity of the opposite does not appear in itself; it is not that it abrogates itself, i.e. that it contains a contradiction in itself. For instance, I assert of something that it is the null; then I show this by hypothesis in motion, and it follows that it is the null. But another consciousness does not assert this I declare one thing to be directly true; another has the right of asserting something else as directly true, that is to say, motion. Similarly what seems to be the case when one philosophic system contradicts another, is that the first is pre-established, and that men starting from this point of view, combat the other. The matter is thus easily settled by saying: “The other has no truth, because it does not agree with me,” and the other bas the right to say the same. It does not help if I prove my system or my proposition and then conclude that thus the opposite is false; to this other proposition the first always seems to be foreign and external. Falsity must not be demonstrated through another, and as untrue because the opposite is true, but in itself; we find this rational perception in Zeno.

In Plato’s Parmenides (pp. 127, 128, Steph., pp. 6, 7, Bekk.) this dialectic is very well described, for Plato makes Socrates say of it: “Zeno in his writings asserts fundamentally the same as does Parmenides, that All is One, but he would feign delude us into believing that he was telling something new. Parmenides thus shows in his poems that All is One; Zeno, on the contrary, shows that the Many cannot be.” Zeno replies, that “He wrote thus really against those who try to make Parmenides’ position ridiculous, for they try to show what absurdities and self-contradictions can be derived from his statements; he thus combats those who deduce Being from the many, in order to show that far more absurdities arise from this than from the statements of Parmenides.” That is the special aim of objective dialectic, in which we no longer maintain simple thought for itself, but see the battle fought with new vigour within the enemy’s camp. Dialectic has in Zeno this negative side, but it bas also to be considered from its positive side.

According to the ordinary ideas of science, where propositions result from proof, proof is the movement of intelligence, a connection brought about by mediation. Dialectic is either (a) external dialectic, in which this movement is different from the comprehension of the movement, or (b) not a movement of our intelligence only, but what proceeds from the nature of the thing itself, i.e. from the pure Notion of the content. The former is a manner of regarding. objects in such a way that reasons are revealed and new light thrown, by means of which all that was supposed to be firmly fixed, is made to totter; there may be reasons which are altogether external too, and we shall speak further of this dialectic when dealing with the Sophists. The other dialectic, however, is the immanent contemplation of the object; it is taken for itself, without previous hypothesis, idea or obligation, not under any outward conditions, laws or causes; we have to put ourselves right into the thing, to consider the object in itself, and to take it in the determinations which it has. In regarding it thus, it shows from itself that it contains opposed determinations, and thus breaks up; this dialectic we more especially find in the ancients. The subjective dialectic, which reasons from external grounds, is moderate, for it grants that: “In the right there is what is not right, and in the false the true.” True dialectic leaves nothing whatever to its object, as if the latter were deficient on one side only; for it disintegrates itself in the entirety of its nature. The result of this dialectic is null, the negative; the affirmative in it does not yet appear. This true dialectic may be associated with the work of the Eleatics. But in their case the real meaning and quality of philosophic understanding was not great, for they got no further than the fact that through contradiction the object is a nothing.

Zeno’s dialectic of matter has not been refuted to the present day; even now we have not got beyond it, and the matter is left in uncertainty. Simplicius, writing on the Physics of Aristotle (p. 30), says: “Zeno proves that if the many is, it must be great and small; if great, the many must be infinite in number” (it must have gone beyond the manifold, as indifferent limit, into the infinite; but what is infinite is no longer large. and no longer many, for it is the negation of the many). “If small, it must be so small as to have no size,” like atoms. “Here he shows that what has neither size, thickness nor mass, cannot be. For if it were added to another, it would not cause its increase; were it, that is to say, to have no size and be added thereto, it could not supplement the size of the other and consequently that which is added is nothing. Similarly were it taken away, the other would not be made less, and thus it is nothing. If what has being is, each existence necessarily has size and thickness, is outside of one another, and one is separate from the other; the same applies to all else (peri tou proucontoς), for it, too, has size, and in it there is what mutually differs (proexei autou ti). But it is the same thing to say something once and to say it over and over again; in it nothing can be a last, nor will there not be another to the other. Thus if many are, they are small and great; small, so that they have no size; great, so that they are infinite.”

Aristotle (Phys. VI. 9) explains this dialectic further; Zeno’s treatment of motion was above all objectively dialectical. But the particulars which we find in the Parmenides of Plato are not his. For Zeno’s consciousness we see simple unmoved thought disappear, but become thinking movement; in that he combats sensuous movement, he concedes it. The reason that dialectic first fell on movement is that the dialectic is itself this movement, or movement itself the dialectic of all that is. The thing, as self-moving, has its dialectic in itself, and movement is the becoming another, self-abrogation. If Aristotle says that Zeno denied movement because it contains an inner contradiction, it is not to be understood to mean that movement did. not exist at all. The point is not that there is movement and that this phenomenon exists; the fact that there is movement is as sensuously certain as that there are elephants; it is not in this sense that Zeno meant to deny movement. The point in question concerns its truth. Movement, however, is held to be untrue, because the conception of it involves a contradiction; by that he meant to say that no true Being eau be predicated of it.

Zeno’s utterances are to be looked at from this point of view, not as being directed against the reality of motion, as would at first appear, but as pointing out how movement must necessarily be determined, and showing the course which must be taken. Zeno now brings forward four different arguments against motion; the proofs rest on the infinite divisibility of space and time.

(a) This is his first form of argument: — “Movement has no truth, because what is in motion must first reach the middle of the space before arriving at the end.” Aristotle expresses this thus shortly, because he had earlier treated of and worked out the subject at length. This is to be taken as indicating generally that the continuity of space is pre-supposed. What moves itself must reach a certain, end, this way is a whole. In order to traverse the whole, what is in motion must first pass over the half, and now the end of this half is considered as being the end; but this half of space is again a whole, that which also has a half, and the half of this half must first have been reached, and so on into infinity. Zeno here arrives at the infinite divisibility of space; because space and time are absolutely continuous, there is no point at which the division can stop. Every dimension (and every time and space always have a dimension) is again divisible into two halves, which must be measured off; and however small a space we have, the same conditions reappear. Movement would be the act of passing through these infinite moments, and would therefore never end 4 thus what is in motion cannot reach its end. It is known how Diogenes of Sinope, the Cynic, quite simply refuted these arguments against movement; without speaking he rose and walked about, contradicting them by action. But when reasons are disputed, the only valid refutation is one derived from reasons; men have not merely to satisfy themselves by sensuous assurance, but also to understand. To refute objections is to prove their non-existence, as when they are made to fall away and can hence be adduced no longer; but it is necessary to think of motion as Zeno thought of it, and yet to carry this theory of motion further still.

We have here the spurious infinite or pure appearance, whose simple principle Philosophy demonstrates as universal Notion, for the first time making its appearance as developed in its contradiction; in the history of Philosophy a consciousness of this contradiction is also attained. Movement, this pure phenomenon, appears as something thought and shown forth in its real being — that is, in its distinction of pure self-identity and pure negativity, the point as distinguished from continuity. To us there is no contradiction in the idea that the here of space and the now of time are considered as a continuity and length; but their Notion is self-contradictory. Self-identity or continuity is absolute cohesion, the destruction of all difference, of all negation, of being for self; the point, on the contrary, is pure being-for-self, absolute self-distinction and the destruction of all identity and all connection with what is different. Both of these, however, are, in space and time, placed in one; space and time are thus the contradiction; it is necessary, first of all, to show the contradiction in movement, for in movement that which is opposed is, to ordinary conceptions, inevitably manifested. Movement is just the reality of time and space, and because this appears and is made manifest, the apparent contradiction is demonstrated, a and it is this contradiction that Zeno notices. The limitation of bisection which is involved in the continuity of space, is not absolute limitation, for that which is limited is again continuity; however, this continuity is again not absolute, for the opposite has to be exhibited in it, the limitation of bisection; but the limitation of continuity is still not thereby established, the half is still continuous, and so on into infinity. In that we say “into infinity,” we place before ourselves a beyond, outside of the ordinary conception, which cannot reach so far. It is certainly an endless going forth, but in the Notion it is present, it is a progression from one opposed determination to others, from continuity to negativity, from negativity to continuity; but both of these are before us. Of these moments one in the process may be called the true one; Zeno first asserts continuous progression in such a way that no limited space can be arrived at as ultimate, or Zeno upholds progression in this limitation.

The general explanation which Aristotle gives to this contradiction, is that space and time are not infinitely divided, but are only divisible. But it now appears that, because they are divisible — that is, in potentiality — they must actually be infinitely divided, for else they could not be divided into infinity. That is the general answer of the ordinary man in endeavouring to refute the explanation of Aristotle. Bayle (Tom. IV. art. Zénon, not. E.) hence says of Aristotle’s answer that it is “pitoyable: C’est se moquer du monde que de se servir de cette doctrine; car si Ia matière est divisible à l’infini, elle contient un nombre infini de parties. Ce n’est done point un infini en puissance, c’est un infini, qui existe réellement, actuellement. Mais quandmême on accorderait cet infini en puissance, qui deviendrait un infini par Ia division actuelle de ses parties, on ne perdrait pas ses avantages; car le mouvement est une chose, qui a la même vertu, que la division. Il touche une partie de l’espace sans toucher l’autre, et il les touche toutes les unes après les autres. N’est-ce pas les distinguer actuellement? N’est-ce pas faire ce que ferait un géomètre sur une table en tirant des lignes, qui désignassent tous les demiponces? II ne brise pas Ia table en demi-pouces, mais il y fait néanmoins une division, qui marque Ia distinction actuelle des parties; et ie ne crois pas qu’Aristote ent voulu nier, que si l’on tirait une infinité de lignes sur un pouce de matière, on n’y introduisit une division, qui reduirait en infini actuel ce qui n’etait selon lui qu’un infini virtuel.” This si is good! Divisibility is, as potentiality, the universal; there is continuity as well as negativity or the point posited in it — but posited as moment, and not as existent in and for itself. I can divide matter into infinitude, but I only can do so; I do not really divide it into infinitude. This is the infinite, that no one of its moments has reality. It never does happen that, in itself, one or other — that absolute limitation or absolute continuity — actually comes into existence in such a way that the other moment disappears. There are two absolute opposites, but they are moments, i.e. in the simple Notion or in the universal, in thought, if you will; for in thought, in ordinary conception, what is set forth both is and is not at the same time. What is represented either as such. or as an image of the conception, is not a thing; it has no Being, and yet it is not nothing.

Space and time furthermore, as quantum, form a limited extension, and thus can be measured off; just as I do not actually divide space, neither does the body which is in motion. The partition of space as divided, is not absolute discontinuity [Punktualität], nor is pure continuity the undivided and indivisible; likewise time is not pure negativity or discontinuity, but also continuity. Both are manifested in motion, in which the Notions have their reality for ordinary conception — pure negativity as time, continuity as space. Motion itself is just this actual unity in the opposition, and the sequence of both moments in this unity. To comprehend motion is to express its essence in the form of Notion, i.e., as unity of negativity and continuity; but in them neither continuity nor discreteness can be exhibited as the true existence. If we represent space or time to ourselves as infinitely divided, we have an infinitude of points, but continuity is present therein as a space which comprehends them; as Notion, however, continuity is the fact that all these are alike, and thus in reality they do not appear one out of the other like points. But both these moments make their appearance as existent; if they are manifested indifferently, their Notion is no longer posited, but their existence. In.them as existent, negativity is a limited size, and they exist as limited space and time; actual motion is progression through a limited space — and a limited time and not through infinite space and infinite time.

That what is in motion must reach the half is the assertion of continuity, i.e. the possibility of division as mere possibility; it is thus always possible in every space, however small. It is said that it is plain that the half must be reached, but in so saying, everything is allowed, including the fact that it never will be reached; for to say so in one case, is the same as saying it an infinite number of times. We mean, on the contrary, that in a larger space the half can be allowed, but we conceive that we must somewhere attain to a space so small that no halving is possible, or an indivisible, non-continuous space which is no space. This, however, is false, for continuity is a necessary determination; there is undoubtedly a smallest in space, i.e. a negation of continuity, but the negation is something quite abstract. Abstract adherence to the subdivision indicated, that is, to continuous bisection into infinitude, is likewise false, for in the conception of a half, the interruption of continuity is involved. We must say that there is no half of space, for space is continuous; a piece of wood may be broken into two halves, but not space, and space only exists in movement. It might equally be said that space consists of an endless number of points, i.e. of infinitely many limits and thus cannot be traversed. Men think themselves able to go from one indivisible point to another, but they do not thereby get any further, for of these there is an unlimited number. Continuity is split up into its opposite, a number which is indefinite; that is to say, if continuity is not admitted, there is no motion. It is false to assert that it is possible when one is reached, or that which is not continuous; for motion is connection. Thus when it was said that continuity is the presupposed possibility of infinite division, continuity is only the hypothesis; but what is exhibited in this continuity is the being of infinitely many, abstractly absolute limits.

(b) The second proof, which is also the presupposition of continuity and the manifestation of division, is called “Achilles, the Swift.” The ancients loved to clothe difficulties in sensuous representations. Of two bodies moving in one direction, one of which is in front and the other following at a fixed distance and moving quicker than the first, we know that the second will overtake the first. But Zeno says, “The slower can never be overtaken by the quicker.” And he proves it thus: “The second one requires a certain space of time to reach the place from which the one pursued started at the beginning of the given period.” Thus during the time in which the second reached the point where the first was, the latter went over a new space which the second has again to pass through in a part of this period; and in this way it goes into infinity.

         c       d    e   f   g
         B       A     

B, for instance, traverses two miles (c d) in an hour, A in the same time, one mile (d e); if they are two miles (c d) removed from one another, B has in one hour come to where A was at the beginning of the hour. While B, in the next half hour, goes over the distance crossed by A of one mile (d e), A has got half a mile (e f) further, and so on into infinity. Quicker motion does not help the second body at all in passing over the interval of space by which he is behind: the time which he requires, the slower body always has at its avail in order to accomplish some, although an ever shorter advance; and this, because of the continual division, never quite disappears.

Aristotle, in speaking of this, puts it shortly thus: “This proof asserts the same endless divisibility, but it is untrue, for the quick will overtake the slow body if the limits to be traversed be granted to it.” This answer is correct and contains all that can be said; that is, there are in this representation two periods of time and two distances, which are separated from one another, i.e. they are limited in relation to one another; when, on the contrary, we admit that time and space are continuous, so that two periods of time or points of space are related to one another as continuous, they are, while being two, not two, but identical. In ordinary language we solve the matter in the easiest, way, for we say: “Because the second is quicker, it covers a greater distance in the same time as the slow; it can therefore come to the place from which the first started and get further still.” After B, at the end of the first hour, arrives at d and A at e, A in one and the same period, that is, in the second hour, goes over the distance e g, and B the distance d g. But this period of time which should be one, is divisible into that in which B accomplishes d e and that in which B passes through e g. A has a start of the first, by which it gets over the distance e f, so that A is at f at the same period as B is at e. The limitation which, according to Aristotle, is to be overcome, which must be penetrated, is thus that of time; since it is continuous, it must, for the solution of the difficulty, be said that what is divisible into two spaces of time is to be conceived of as one, in which B gets from d to e and from e to g, while A passes over the distance c g. In motion two periods, as well as two points in space, are indeed one.

If we wish to make motion clear to ourselves, we say that,,the body is in one place and then it goes to another; because it moves, it is no longer in the first, but yet not in the second; were it in either it would be at rest. Where then is it? If we say that it is between both, this is to convey nothing at all, for were it between both, it would be in a place, and this presents the same difficulty. But movement means to be in this place and not to be in it, and thus to be in both alike; this is the continuity of space and time which first makes motion possible. Zeno, in the deduction made by him, brought both these points into forcible opposition. The discretion of space and time we also uphold, but there must also be granted to them the over-stepping of limits, i.e. the exhibition of limits as not being, or as being divided periods of time, which are also not divided. In our ordinary ideas we find the same determinations as those on which the dialectic of Zeno rests; we arrive at saying, though unwillingly, that in one period two distances of space are traversed, but we do not say that the quicker comprehends two moments of time in one; for that we fix a definite space. But in order that the slower may lose its precedence, it must be said that it loses its advantage of a moment of time, and indirectly the moment of space.

Zeno makes limit. division, the moment of discretion in space and time, the only element which is enforced in the whole of his conclusions, and hence results the contradiction. The difficulty is to overcome thought. for what makes the difficulty is always thought alone, since it keeps apart the moments of an object which in their separation are really united. It brought about the Fall, for man ate of the tree of the knowledge of good and evil; but it also remedies these evils.

(c) The third form, according to Aristotle, is as follows: — Zeno says. “I The flying arrow rests, and for the reason that what is in motion is always in the self-same Now and the self-same Here, in the indistinguishable;” it is here and here and here. It can be said of the arrow that it is always the same, for it is always in the same space and the same time; it does not get beyond its space. does not take in another, that is, a greater or smaller space. That, however, is what we call rest and not motion. In the Here and Now, the becoming “other” is abrogated, limitation indeed being established, but only as moment; since in the Here and Now as such, there is no difference, continuity is here made to prevail against the mere belief in diversity. Each place is a different place, and thus the same; true, objective difference does not come forth in these sensuous relations, but in the spiritual.

This is also apparent in mechanics; of two bodies the question as to which moves presents itself before us. It requires more than two places — three at least — to determine which of them moves. But it is correct to say this, that motion is plainly relative; whether in absolute space the eye, for instance, rests, or whether it moves, is all the same. Or, according to a proposition brought forward by Newton, if two bodies move round. one another in a circle, it may be asked whether the one rests or both move. Newton tries to decide this by means of an external circumstance, the strain on the string. When I walk on a ship in a direction opposed to the motion of the ship, this is in relation to the ship, motion, and in relation to all else, rest.

In both the first proofs, continuity in progression has the predominance; there is no absolute limit, but an overstepping of all limits. Here the opposite is established; absolute limitation, the interruption of continuity, without however passing into something else; while discretion is pre-supposed, continuity is maintained. Aristotle says of this proof: “It arises from the fact that it is taken for granted that time consists of the Now; for if this is not conceded, the conclusions will not follow.”

(d) “The fourth proof,” Aristotle continues, “is derived from similar bodies which move in opposite directions in the space beside a similar body, and with equal velocity, one from one end of the space, the other from the middle. It necessarily results from this that half the time is equal to the double of it. The fallacy rests in this, that Zeno supposes that what is beside the moving body, and what is beside the body at rest, move through an equal distance in equal time with equal velocity, which, however, is untrue.”

             k    i   m 
             g n h 

In a definite space such as a table (A B) let us suppose two bodies of equal length with it and with one another, one of which (C D) lies with one end (C) on the middle (g) of the table, and the other (B F), being in the same direction, has the point (B) only touching the end of the table (h); and supposing they move in opposite directions, and the former (C D) reaches in an hour the end (h) of the table; we have the result ensuing that the one (E F) passes in the half of the time through the same space (1 k) which the other does in the double (g h); hence the half is equal to the double. That is to say, this second passes (let us say, in the point 1) by the whole of the first C D. In the first half-hour 1 goes from m to i, while k only goes from g to n.

                   k o i   m   
                   g n h 

In the second half-hour 1 goes past o to k, and altogether passes from m to k, or the double of the distance.

                       k  o i   m 
                   g n h 

This fourth form deals with the contradiction presented in opposite motion; that which is common is given entirely to one body, while it only does part for itself. Here the distance travelled by one body is the sum of the distance travelled by both, just as when I go two feet east, and from the same point another goes two feet west, we are four feet removed from one another; in the distance moved both are positive, and hence have to be added together. Or if I have gone two feet forwards and two feet backwards, although I have walked four feet, I have not moved from the spot; the motion is then nil, for by going forwards and backwards an opposition ensues which annuls itself.

This is the dialectic of Zeno; he had a knowledge of the determinations which our ideas of space and time contain, and showed in them their contradiction; Kant’s antinomies do no more than Zeno did here. The general result of the Eleatic dialectic has thus become, “the truth is the one, all else is untrue,” just as the Kantian philosophy resulted in “we know appearances only.” On the whole the principle is the same; “the content of knowledge is only an appearance and not truth,” but there is also a great difference present. That is to say, Zeno and the Eleatics in their proposition signified “that the sensuous world, with its multitudinous forms, is in itself appearance only, and has no truth.” But Kant does not mean this, for he asserts: “Because we apply the activity of our thought to the outer world, we constitute it appearance; what is without, first becomes an untruth by the fact that we put therein a mass of determinations. Only our knowledge, the spiritual, is thus appearance; the world is in itself absolute truth; it is our action alone that ruins it, our work is good for nothing.” It shows excessive humility of mind to believe that knowledge has no value; but Christ says, “Are ye not better than the sparrows?” and we are so inasmuch as we are thinking; as sensuous we are as good or as bad as sparrows. Zeno’s dialectic has greater objectivity than this modern dialectic.

Zeno’s dialectic is limited to Metaphysics; later, with the Sophists, it became general. We here leave the Eleatic school. which perpetuates itself in Leucippus and, on the other side, in the Sophists, in such a way that these last extended the Eleatic conceptions to all reality, and gave to it the relation of consciousness; the former, however, as one who later on worked out the Notion in its abstraction, makes a physical application of it, and one which is opposed to consciousness. There are several other Eleatics mentioned, to Tennemann’s surprise, who, however, cannot interest us. “It is so unexpected,” he says (Vol. I., p. 190), “that the Eleatic system should find disciples; and yet Sextus mentions a certain Xeniades.”

Editor’s Notes

1. That Xenophanes is here meant is shown from the titles of the collected Becker manuscripts, as also from comparing this passage with the verses remaining to us, which are by Xenophanes, though they were earlier ascribed to Zeno; this was done by Hegel when he did not, as in many lectures, take the Eleatic passages together. The editor found a justification in this for placing the passage in its proper place.

2. This obscure clause has been differently interpreted. Dr. Hutchison Stirling, in his annotations on Schwegler’s “History of Philosophy,” says: “Zeller accepts (and Hegel, by quoting and translating the whole passage, already countenanced him in advance) the equivalent of Theophrastus for to pleon, to uperballon namely, and interprets the clause itself thus: — ‘The preponderating element of the two is thought occasions and determines the ideas;’ that is as is the preponderating element (the warm or the cold) so is the state of mind. In short, the more is the thought is the linguistic equivalent of the time for according to the more is the thought.

3. As a matter of fact, since a comparison of this reasoning with the fragments of Melissus which Simplicius (in Arist. Physica and De Coelo) has retained, places this conjecture beyond doubt, the editor is constrained to place it here, although Hegel, when he dealt with the Eleatics separately, put it under the heading of Xenophanes.


Translated by E.S. Haldane and Frances H. Simson, published by K. Paul Trench, Trübner in 1894.

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