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 argu ment" of Zeno's book above mentioned ran as follows: "If exist ences are many, they must be both like and unlike (unlike, inas much 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. But this is impossible; for unlike things cannot be like, nor like things unlike. Therefore existences are not many." When in the second decade of the 4th century the pursuit of truth was resumed, it was plain that Zeno's paradox of predica tion must be disposed of before the discussion of the problems of knowledge and the problem of being could be resumed. Ac cordingly, in bk. 7 of the Republic, Plato directs the attention of studious youth primarily, if not exclusively, to the concurrence of inconsistent attributes; and in the Phaedo, 102 B—I03 A, taking as an instance the tallness and the shortness simultaneously discoverable in Simmias, he offers his own theory of the imma nent idea as the solution of the paradox. Simmias, he says, has in him the ideas of tall and short. Again, when it presently ap peared that the theory of the immanent idea was inconsistent with itself, and moreover inapplicable to explain predication except where the subject was a sensible thing, so that reconstruction be came necessary, the Zenonian difficulty continued to receive Plato's attention. Thus, in the Parmenides, with the paradox of
likeness and unlikeness for his text, he inquires how far the cur rent theories of being (his own included) are capable of provid ing, not only for knowledge, but also for predication, and in the concluding sentence he suggests that, as likeness and unlikeness, greatness and smallness, etc., 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 mutual Komoviarof eibri which are not alma icce airr6, is elaborately demonstrated.
In all probability Zeno did not observe that in his controversial defence of Eleaticism he was interpreting Parmenides's teaching anew. 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 plurality, becoming and opinion are one and all inconceivable. In a word, Parmen ides's tenet "The Ent is, the Non-ent is not," was with Zeno a declaration of the Non-ent's absolute nullity. Thus, just as Em pedocles developed Parmenides's theory of the Many to the ne glect 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 sev erance of its two members Eleaticism proper, the Eleaticism of Parmenides, ceased to exist.