Z E N Z E N 779 on the supposition that his speed is ten times that of the tortoise, must traverse an infinite number of spaces, 1000 feet, 100 feet, 10 feet, &c., and the tortoise must traverse an infinite number of spaces, 100 feet, 10 feet, 1 foot, &c., before they reach the point, distant from their starting-points 1111J feet and 11 1J feet respect ively, at which the tortoise is overtaken. In a word, 1000, 100, 10, &c. , in (6) and J, |, ^, &c., in (5) are convergent series, and 1111J and 1 are the limits to which they respectively approximate.] (7) So long as anything is in one and the same space, it is at rest. Hence an arrow is at rest during every moment of its flight, and therefore also during the whole of its flight. (8) Two bodies mov ing with equal speed traverse equal spaces in equal times. But, when two bodies move with equal speed in opposite directions, the one passes the other in half the time in which it passes it when at rest. These propositions appeared to Zeno to be irreconcilable. In short, the ordinary belief in plurality and motion seemed to him to involve fatal inconsistencies, whence he inferred that Par- menides was justified in distinguishing the mutable movable Many from the immutable immovable One, which alone is really existent. In other words, Zeno re-affirmed the dogma, "The Ent is, the Xon- ent is not." It may seem strange that a reasoner so acute should confound that which is infinitely divisible with that which is in finitely great, as in (1), (2), (5), and (6) ; that he should identify space and magnitude, as in (3) ; that he should neglect the imper fection of the organs of sense, as in (4) ; that he should resolve motion into a series of states of rest, and on the strength of this analysis deny the reality of motion, as in (7); and that he should ignore the relativity of speed, as in (8). But Zeno s perplexity was genuine, and his end was positive. He was neither an eristic seeking an argumentative victory, nor a sceptic despairing of truth, but an honest thinker, breaking ground in a new field with indiffer ent success. Great as was the importance of these paradoxes of plurality and motion in stimulating speculation about space and time, their direct influence upon Greek thought was less considerable than that of another paradox, strangely neglected by historians of philosophy, the paradox of predication. We learn from Plato (Parmenides, 127 D) that "the first hypothesis of the first argument" of Zeno s book above mentioned ran as follows : "If ex istences are many, they must be both like and unlike [unlike, inasmuch as they are not one and the same, and like, inasmuch as they agree in not being one and the same, Proclus, On the Parmenides, ii. 143]. But this is impossible ; for unlike things cannot be like, nor like things unlike. Therefore existences are not many." That is to say, not perceiving that the same thing may be at once like and unlike in different relations, Zeno regarded the attribution to the same thing of likeness and unlike- ness as a violation of what was afterwards known as the principle of contradiction ; and, finding that plurality entailed these attributions, he inferred its unreality. Now, when without qualification he affirmed that the unlike thing cannot be like, nor the like thing unlike, he was on the high road to the doctrine maintained three-quarters of a century later by the Cynics, that no predication which is not identical is legitimate. He was not indeed aware how deeply he had committed himself ; otherwise he would have observed that his argument, if valid against the Many of the vulgar, was valid also against the One of Parmenides, with its plurality of attributes, as well as that, in the absence of a theory of predication, it was useless to specu late about knowledge and being. But others were not slow to draw the obvious conclusions ; and it may be con jectured that Gorgias s sceptical development of the Zeno- nian logic contributed, not less than Protagoras s sceptical development of the Ionian physics, to the diversion of the intellectual energies of Greece from the pursuit of truth to the pursuit of culture. For three-quarters of a century, then, philosophy was at a standstill ; and, when in the second decade of the 4th century the pursuit of truth was resumed, it was plain that the difficulty raised by Zeno must be met before the problems which had occupied the earlier thinkers the problem of knowledge and the problem of being could be so much as attempted. Accordingly, in the seventh book of the Republic, where Plato propounds his scheme of Academic education, he directs the attention of studious youth primarily, if not exclusively, to the concurrence of inconsistent attributes; and in the Ph&do, 102B-103A, taking as an instance the tallness and the shortness simul taneously discoverable in Simmias, he offers his own theory of the immanent idea as the solution of the paradox. Simmias, he says, has in him the ideas of tall and short. Again, when it presently appeared that the theory of the immanent idea was inconsistent with itself, and moreover inapplicable to explain predication except where the sub ject was a sensible thing, so that reconstruction became necessary, the Zenonian difficulty continued to demand and to receive Plato s best attention. Thus, in the Par menides, with the paradox of likeness and unlikeness for his text, he inquires how far the current theories of being (his own included) are capable of providing, not only for knowledge, but also for predication, and in the concluding sentence lie suggests that, as likeness and unlikeness, greatness and smallness, &c., are relations, the initial paradox is no longer paradoxical ; while in the Sophist, Zeno s doctrine having been shown to be fatal to reason, thought, speech, and utterance, the principle which in the Parmenides is applied to avra K.a.6 avra ft8t] and to sensible particulars is extended to include the case of eiS?; which are not avra KaO avrd. It would seem then that, not to Antisthenes only, but to Plato also, Zeno s paradox of predication was a substantial difficulty ; and we shall be disposed to give Zeno credit accordingly for his percep tion of its importance. In all probability Zeno did not observe that in his controversial defence of Eleaticism he was interpreting Parmenides s teaching anew. But so it was. For, while Parmenides had recognized, together with the One, which is, and is the object of knowledge, a Many, which is not, and therefore is not known, but nevertheless becomes, and is the object of opinion, Zeno plainly affirmed that plur ality, becoming, and opinion are one and all inconceivable. In a word, the fundamental dogma, " The Ent is, the Non- ent is not," which with Parmenides had been an assertion of the necessity of distinguishing between the Ent, which is, and the Non-ent, which is not, but becomes, was with Zeno a declaration of the Non-ent s absolute nullity. Thus, just as Empedocles developed Parmenides s theory of the Many to the neglect of his theory of the One, so Zeno developed the theory of the One to the neglect of the theory of the Many. With the severance of its two mem bers Eleaticism proper, the Eleaticism of Parmenides, ceased to exist. The first effect of Zeno s teaching was to complete the discomfiture of philosophy. For the parodox of predica tion, which he had used to disprove the existence of plurality, was virtually a denial of all speech and all thought, and thus led to a more comprehensive scepticism than that which sprang from the contemporary theories of sensation. Nevertheless, he left an enduring mark upon Greek speculation, inasmuch as he not only recognized the need of a logic, and grappled, however unsuccessfully, with one of the most obvious of logical problems, but also by the invention of dialectic provided a new and powerful instrument against the time when the One and the Many should be reunited in the philosophy of Plato. Bibliography. F. W. A. Mullach, Fragmenta Philosophonim Gnvcornm, Paris, 1860, i. 266 sq. ; Zelh-r, Die Philosophic d. Gricchen, Leipsic, 1876, i. 534-552 ; P. Tannery, Pour V Histoirc de In Science Hellene, Paris, 1887, pp. 247- 2(il. Ignoring the philosophical aspect of Zeno s teaching, Tannery supposes him to have main tained in opposition to the Pythagoreans that body is not a sum of points, time not a sum of moments, and motion not a sum of passages from point to point. For histories of philosophy and other works upon Eleaticism, see PAKMEMDKS. (H. JA.)
ZEXOBIA. See PALMYRA, vol. xviii. p. 201 */.