Hegel's Lectures on the History of Philosophy · Georg Wilhelm Friedrich Hegel
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 Laertius, (IX. 25) Zeno was likewise 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.[58] 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 he 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.[59]
It has just been noticed that Zeno had the very important character of being the originator of the true objective dialectic. Xenophanes, Parmenides, and Melissus, 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 has 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 has 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 (_α_) external dialectic, in which this movement is different from the comprehension of the movement, or (_β_) 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 (_περὶ τοῦ προὔχοντος_), for it, too, has size, and in it there is what mutually differs (_προέξει αὐτοῦ τι_). 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 can 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.
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, 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 la matière est divisible à l’infini, elle contient un nombre infini de parties. Ce n’est donc point un infini en puissance, c’est un infini, qui existe réellement, actuellement. Mais quand-même on accorderait cet infini en puissance, qui deviendrait un infini par la 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 demi-pouces?
Il ne brise pas la table en demi-pouces, mais il y fait néanmoins une division, qui marque la distinction actuelle des parties; et je ne crois pas qu’Aristote eut voulu nier, que _si_ l’on tirait une infinité de lignes sur un pouce de matière, on n’y introduisît une division, qui réduirait en infini actuel ce qui n’était selon lui qu’un infini virtual.” 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.
Text from Project Gutenberg, public domain in the United States.