Abstract

In lieu of an abstract, here is a brief excerpt of the content:The Interpretation of Plato's Parmenides: Zeno s Paradox and the Theory of Forms R. E. ALLEN PLATO'S Parmenides is divided into three main parts, of uneven length, and distinguished from each other both by their subject matter and their speakers. In the first and briefest part (127d-130a), Socrates offers the Theory of Forms in solution of a problem raised by Zeno. In the second (130a-135d), Parmenides levels a series of objections against Socrates' theory, objections putatively meant as refutation. Then, after an interlude to explain an unfamiliar method of dialectic (135d-137c), that method is applied in the third part by Parmenides, with the help of the young Aristoteles (137c-166c). This final part forms more than two-thirds of the whole. I propose here to examine the first part of the dialogue, the interchange between Zeno and Socrates, and to examine it with special attention to the bearing which questions of dialectical structure and dramatic characterization may have upon its interpretation. It is perhaps here proper to indicate the general view of the dialogue which this discussion will help serve to recommend. Briefly, it is this. The Parmenides is a sustained examination of Plato's Theory of Forms, and the manner of examination is Socratic: the student is presented, not with a body of conclusions, but with a series of arguments whose implications he is left to think through for himself. When he has done so, he will realize that the Theory of Forms is proof against the objections here brought against it: the Parmenides provides no direct support for the thesis, currently popular, that Plato in later life ceased to believe that Forms exist. But though sound as far as it goes, the Theory of Forms does not go far enough: the Parmenides demonstrates that there is a range of problems, bound up with the application of unrestricted predicates, which Forms do not solve but are prey to. A broader theory is required, though a theory which may well contain the Theory of Forms as a part. The Parmenides, whose purpose is critical, leaves unanswered the question of what that theory may be. Zeno's Paradox and the Theoryof Forms (127d-130a) It is Zeno who begins the dialectic of the Parmenides,and fittingly, he begins it with a paradox. If there are many things, the same things must be both [143] 144 HISTORY OF PHILOSOPHY like and unlike. But this is impossible: unlike things cannot be like, nor like things unlike. Therefore, there cannot be many things (127e). Socrates' reply begins with a solution, and ends with a challenge. There exists, alone by itself, a Form of Likeness, and also a Form of its opposite, Unlikeness. The things we call 'many' are both like and unlike; but in this they differ from the Forms in which they partake. For things which are just alike (abr& r& 6uoLa)1 cannot be unlike, nor things just unlike alike. But it is no more surprising that the same things should partake both in Likeness and Unlikeness than it is that a thing should be both one and many by partaking in both Unity and Plurality. Still, Unity itself is not many, nor Plurality one. And so with other Forms: Socrates would be filled with wonder if someone could show that Likeness and Unlikeness, Unity and Plurality, Rest and Motion, and the other Forms, can be combined with (~v'rK~p&vvwOaO and separated from (SLaKotp~0a,) each other. Forms cannot be qualified by their opposite. 2 Socrates' denial is a conjunction. Several translators, including Cornford and Taylor, have rendered ~v3,~p&vvvaOa~ ~as &aKps as though it were a disjunction, 'combined or separated'. The reason for this was no doubt stylistic; but the Greek means, not 'or' but 'and', and logically, the difference is important. Zeno and Parmenides are challenged to prove, not one of two alternatives, but both together. This conclusion rests on more than a Kas In the Sophist, knowing how to separate (&a~ps 253e 3) according to kinds is equivalent to distinguishing (&a~m~a0a~ 253d 1) according to kinds, and both are equivalent to not believing that the same Form is different or a different Form the same (253d 1...