On Diairesis, Parallel Division, and Chiasmus: Plato’s and Aristotle’s Methods of Division

In this paper, I articulate three kinds of division that Plato and Aristotle acknowledge to be proper, valid methods of division, namely, diairesis (vertical division), parallel division, and chiasmus (cross-division). 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 (as it appears to be) 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.