Journal of the History of Philosophy

Plato's Parmenides: A Principle of Interpretation and Seven Arguments SANDRA PETERSON PART I. A PRINCIPLE OF INTERPRETATION 1. THE EVIDENT STRUCTURE OF THE PARMENIDES PLATO'S Parmenides falls naturally into halves. In the first half, which is a conversation between Socrates and Parmenides initiated by the young Socrates ' reaction to arguments of Zcno's, Socrates shows confusion as he tries to answer Parmenides' questions about forms. (Possibly Socrates represents a now self-criticized Plato. Or possibly hc represents a not fully reflective adherent of the theory of forms.) The second half consists of about 195 short, initially strange-looking, arguments given by Parmenides to a youngster, Aristotle , as respondent. In between the two halves, at 135d2- 3, Parmenides admires Socrates' "fine" and "divine" passion for arguments. But Parmenides has noticed, even in a conversation of Socrates with Aristotle previous to the setting of the Parmenides, that Socrates is trying to define (horizesthai) too soon. Parmenides then recommends to Socrates some exercise. The second half of the Parmenides illustrates it. What is the manner of exercise, Parmenides? he asked. The one you heard from Zeno, he replied. Except for this: I admired you also when you said to him that you would not allow inquiry to wander among the things we see, nor even in their domain, but rather in the field of those things which one would most especially grasp by reasoning and would take to be forms [e/de]. (a35d8-e4) 1 The text I use is that of John Burnet, vol. ~ of Platonis Opera (Oxford: Clarendon Press, 19ox). Unless I indicate otherwise, I follow the translation of R. E. Allen in Plato's "Parmenides" (Minneapolis: University of Minnesota Press, 1983), with an occasional alteration. [1671 168 JOURNAL OF THE HISTORY OF PHILOSOPHY 34:9 APRIL 1996 At 135e8-136al Parmenides further describes the exercise: "It is also necessary to do this in addition: to examine the consequences that follow from the hypothesis, not only if each thing is hypothesized to be, but also if that same thing is hypothesized not to be, if you wish to be more thoroughly exercised." To illustrate the exercise, Parmenides then considers, in the manner of Zeno, the consequences of a sample hypothesis and its negation: here the hypothesis is that the one is, and its negation is that the one is not. So the exercise itself has two parts: first, deductions from the hypothesis that the one is, and second, deductions from the hypothesis that the one is not. These two parts again each fall into two, according to the directions of Parmenides at 136bl-2. Socrates is to consider "what will follow from each hypothesis both for the very things hypothesized and for the others." So we have under each hypothesis, on the one hand, deductions concerning the one itself and, on the other hand, deductions concerning things other than the one, to make up now four clusters of deductions. Finally, there is a two-part plan to each of these four clusters. A striking superficial feature is that each of the four consists of a pair of subgroups which I will call "sections": one section reaches mostly negative results (either outright negations or subtler denials), while the other reaches more positive results. There is then a total of eight sections of deductions. In what follows I will abbreviate 'the hypothesis that the one is' by 'H'. I abbreviate 'the hypothesis that the one is not', by 'not-H'. I refer to both H and not-H as 'the hypotheses'. The apparent result of the deductions is that Plato generates contradictions from both H (in the first four sections) and from not-H (in the fifth through eighth sections). If he were to generate contradictions from H and also from not-H without the addition of anything else controversial," and if also the apparent contradictions generated were actual, and if further the arguments leading to the contradictions were valid--made by acceptable inferential moves--then both H and not-H would have been reduced to absurdity. A reduction to absurdity of H would allow us unconditionally to assert not-H. A reduction to absurdity of not-H would allow us...