Abstract
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.
Highlights
This paper attempts to articulate the three kinds of division that Plato and Aristotle acknowledge to be proper, valid methods of division, namely, diairesis, parallel division, and chiasmus
Vertical division refers to a single x-level division tree in which a genus is divided into the differentiae, and the differentiae are divided into the sub-differentiae, until an indivisible final differentia is arrived at
Among the two 2-level division trees, it is possible that either the same genus is divided in parallel into differentiae and parallel-differentiae or two non-subaltern genera are divided into their appropriate differentiae
Summary
This paper attempts to articulate the 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). The cross-division emerges from a parallel division, and the parallel division originates from ostensible diairesis (section 1). To prove the propriety and validity of the two conditions, I invoke the division of contrary in Categories 10 as an example. On this basis, I establish general schemes, thereby theoretically exploring how a parallel division emerges from ostensible diairesis, and how the parallel division causes a cross- division to occur (section 3). I conclude that there are three kinds of division, namely, diairesis, parallel division, and chiasmus – propriety and validity of which are admitted by both Plato and Aristotle. I add an appendix to answer the question of why chiasmus is familiar to philosophers and used by Plato, Aristotle, and Kant while being unknown to scholars for such a long time (Appendix)
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