Were Zeno's a Arguments Reply To Attacks upon Parmenides? N. B. BOOTH NE of the mysteries about Zeno of Elea's arguments is that, whereas learn from all the available that Zeno was we evidence particularly concerned to defend the One of Parmenides 1, yet we find him, in his arguments about plurality, doing all that he can to refute the "ones" of a plurality.2 This would be reasonable if we could be sure that his arguments were valid only against the "ones" of a plurality, not against Parmenides's One; but it is by no means certain that this is true, as we shall see in the course of my discussion. The difficulty was already felt by the ancient commentators 3, and perhaps by Plato as well 4 ; it may be a "pseudo-problem", but if so, it is a pseudo-problem of some antiquity. One suggested solution is to the effect that, before Zeno produced his 5 arguments, certain critics had attacked Parmenides's One with much the same arguments as Zeno later used to attack the "ones" of the pluralists. The two main sources of evidence 6 for this suggestion are a passage in Plato's Parmenides ( i 2 8 c), and Zeno's arguments themselves ' ; a third is possibly to be found in the arguments of Parmenides's other pupil, Melissus.8 There is, regrettably, no definite statement on the subject in any of our authorities. In the passage from the Parmenides ( i 2 8 c), Plato makes the character "Zeno" apologize for the shortcomings of his book about plurality: "It I is really an attempt to support Parmenides's argument against those who try to redicule his theory that 'One is', saying that, if 'One is', then many absurd and inconsistent conclusions follow. This book, then, argues against the pluralists, and repays them in their own coin, by trying to show that the assumption of plurality involves even more absurd consequences than the assumption that 'One is'. I wrote it when I was a young man, in a rather argumentative spirit; and somebody stole it when it was written, so that I was not even able to deliberate whether I should publish it or not". This has been taken to mean that Plato thought that Zeno's arguments were an answer to criticisms of Parmenides's One. Perhaps so; but we must not ignore the dramatic and philosophic purposes of Plato's Parmenides. "Parmenides" and "Zeno" are evidently idealized characters, and idealized thinkers, in the Parmenides; Plato constantly puts arguments into their mouths which are more advanced than any they actually 2 thought of themselves.i It is part and parcel of this somewhat ironical idealization of the Eleatics, that Plato makes "Zeno" apologize for his book, and explain it away as a work of his youth. We are certainly not compelled to believe, on this evidence at any rate, that Zeno's arguments were an answer to attacks that had been made upon Parmenides's s theory. Plato is perfectly capable of this much invention. So let us turn to the arguments themselves. Is there any evidence here that Zeno is answering attacks? No direct evidence, certainly; at no point does Zeno refer to any specific opponents. There might, however, be some indirect evidence. Suppose, for example, that we could see that some of Zeno's arguments against plural "ones" were valid against Parmenides's One also; would it not be fair to infer that hostile critics had already used these arguments against Parmenides, and that Zeno was throwing them back in the faces of these critics ? Now it is certainly true that, according to the ancient commentators, Zeno's arguments included attacks upon the "ones" of a plurality; and some of these attacks look as if they must have been valid against Parmenides's One. For instance, Zeno is said by Philoponus 3 to have had an "argument from the continuous", which ran as follows: "Suppose the continuous to be one. Then, since anything continuous is always 2 .