Liu Xin

In this paper, I aim to explore the structure of the exercise in the second part of the Parmenides. In analyzing the transitional section, I claim that in addition to diairesis, there is another method of division, namely, cross-division, which Porphyry terms chiasmus. On this basis, I explain how Plato uses chiasmus to divide the exercise into eight hypotheses, in which the subjects of the paired hypotheses (I–VI, II–V, III–VII, and IV–VIII) are the same and those of the nonpaired hypotheses differ. In closing, I reconstruct the universal scheme of the exercise on the basis of Plato’s use of chiasmus.

In this paper, I articulate three kinds of division that Plato and Aristotle acknowledge to be proper, valid methods of division, namely, diairesis, parallel division, and chiasmus. I attempt to explain the relationship among the three kinds of division, namely, how they transform from one to another. Starting with Plato’s division of constitution in the Statesman, I illuminate that from ostensible diairesis emerges a parallel division, and the parallel division causes a cross-division to occur. Thus, the sixfold division of constitution is not a diairesis but rather is a 3 x 2 cross-division. Inheriting the three kinds of division from Plato, Aristotle advances the form by providing a theoretical explanation to the transformation of the three kinds of division. In Topics Z6, Aristotle prescribes two conditions under which a parallel division can originate from or construct ostensible diairesis and how the parallel division further causes a cross-division to occur.