Writings.
156. Diogenes speaks of Zeno’s “books,” and Souidas gives some titles which probably come from the Alexandrian librarians through Hesychios of Miletos.[[857]] In the Parmenides, Plato makes Zeno say that the work by which he is best known was written in his youth and published against his will.[[858]] As he is supposed to be forty years old at the time of the dialogue, this must mean that the book was written before 460 B.C. ([§ 84]), and it is very possible that he wrote others after it. The most remarkable title which has come down to us is that of the Interpretation of Empedokles. It is not to be supposed, of course, that Zeno wrote a commentary on the Poem of Empedokles; but, as Diels has pointed out,[[859]] it is quite credible that he should have written an attack on it, which was afterwards called by that name. If he wrote a work against the “philosophers,” that must mean the Pythagoreans, who, as we have seen, made use of the term in a sense of their own.[[860]] The Disputations and the Treatise on Nature may, or may not, be the same as the book described in Plato’s Parmenides.
It is not likely that Zeno wrote dialogues, though certain references in Aristotle have been supposed to imply this. In the Physics[[861]] we hear of an argument of Zeno’s, that any part of a heap of millet makes a sound, and Simplicius illustrates this by quoting a passage from a dialogue between Zeno and Protagoras.[[862]] If our chronology is right, there is nothing impossible in the idea that the two men may have met; but it is most unlikely that Zeno should have made himself a personage in a dialogue of his own. That was a later fashion. In another place Aristotle refers to a passage where “the answerer and Zeno the questioner” occurred,[[863]] a reference which is most easily to be understood in the same way. Alkidamas seems to have written a dialogue in which Gorgias figured,[[864]] and the exposition of Zeno’s arguments in dialogue form must always have been a tempting exercise. It appears also that Aristotle made Alexamenos the first writer of dialogues.[[865]]
Plato gives us a clear idea of what Zeno’s youthful work was like. It contained more than one “discourse,” and these discourses were subdivided into sections, each dealing with some one presupposition of his adversaries.[[866]] We owe the preservation of Zeno’s arguments on the one and many to Simplicius.[[867]] Those relating to motion have been preserved by Aristotle himself;[[868]] but, as usual, he has restated them in his own language.
Dialectic.
157. Aristotle in his Sophist[[869]] called Zeno the inventor of dialectic, and this, no doubt, is substantially true, though the beginnings at least of that method of arguing were contemporary with the foundation of the Eleatic school. Plato[[870]] gives us a spirited account of the style and purpose of Zeno’s book, which he puts into his own mouth:—
In reality, this writing is a sort of reinforcement for the argument of Parmenides against those who try to turn it into ridicule on the ground that, if reality is one, the argument becomes involved in many absurdities and contradictions. This writing argues against those who uphold a Many, and gives them back as good and better than they gave; its aim is to show that their assumption of multiplicity will be involved in still more absurdities than the assumption of unity, if it is sufficiently worked out.
The method of Zeno was, in fact, to take one of his adversaries’ fundamental postulates and deduce from it two contradictory conclusions.[[871]] This is what Aristotle meant by calling him the inventor of dialectic, which is just the art of arguing, not from true premisses, but from premisses admitted by the other side. The theory of Parmenides had led to conclusions which contradicted the evidence of the senses, and Zeno’s object was not to bring fresh proofs of the theory itself, but simply to show that his opponents’ view led to contradictions of a precisely similar nature.
Zeno and Pythagoreanism.
158. That Zeno’s dialectic was mainly directed against the Pythagoreans is certainly suggested by Plato’s statement, that it was addressed to the adversaries of Parmenides, who held that things were “a many.”[[872]] Zeller holds, indeed, that it was merely the popular form of the belief that things are many that Zeno set himself to confute;[[873]] but it is surely not true that ordinary people believe things to be “a many” in the sense required. Plato tells us that the premisses of Zeno’s arguments were the beliefs of the adversaries of Parmenides, and the postulate from which all his contradictions are derived is the view that space, and therefore body, is made up of a number of discrete units, which is just the Pythagorean doctrine. Nor is it at all probable that Anaxagoras is aimed at.[[874]] We know from Plato that Zeno’s book was the work of his youth.[[875]] Suppose even that it was written when he was thirty, that is to say, about 459 B.C., Anaxagoras had just taken up his abode at Athens at that time,[[876]] and it is very unlikely that Zeno had ever heard of him. There is, on the other hand, a great deal to be said for the view that Anaxagoras had read the work of Zeno, and that his emphatic adhesion to the doctrine of infinite divisibility was due to the criticism of his younger contemporary.[[877]]