The nature and proper methods of logical division, διαίρεσις, are important concerns in at least four of Plato’s later dialogues, and reflections on the process may even have led Plato to a revised conception of the very nature of a Form. The place of division in Aristotle’s Topics - both in the organization of some of its materials and as the method for seeking definitions which many of the topoi are designed to regulate - suggests the importance διαίρεσις must have had in the Academy, as does the Epicrates fragment and Aristotle’s criticism of alternative views of the nature or purpose of division in Prior Analytics 1.31, Posterior Analytics II.5 and 11.13, and Parts of Animals 1.2-3. But, as David Balme has argued, Aristotle criticizes these alternative views not in order to reject division but to reform it. When he criticizes those who think the production of a definition by division constitutes a deduction, or even demonstration, of that definition, he reminds us that division is nonetheless useful, in the establishment of definitions, and appears to devote most of a long chapter (APo. 11.13) to the central role of division in "hunt[ng] out what is predicated in what a thing is"(96a22), which may be a reference to the definitions that feature as first principles in demonstrations. And when Aristotle rejects dichotomous division as a way of defining είδη in PA 1.2-3, he replaces it with division by multiple differentiae simultaneously, and argues that that procedure successfully avoids the criticisms dichotomous division falls prey to. Finally, in Metaphysics Z.12, he indicates how one of his reforms of division - the rule that one must divide "by the differentia of a differentia", e.g .footed by split footed and not by feathered - allows at least a partial resolution of the problem of the unity of definition. Balme has even argued - controversially but not entirely implausibly - that definitions by division are involved in the solution to be found in Metaph. H.6 of the unity problem for the object of definition. And Pierre Fellegrin has insisted that the very concepts of γένος, είδος and διαφορά which feature so centrally in the discussions of definitions and much else throughout the corpus, derive their precise logical relationships to each other from their place in the divisional process. These interpretative claims have been challenged, and alternative readings of some of the passages I’ve mentioned have been given, but these controversies, currently unresolved as they are, only underscore the fact that the topic of the place of division in Aristotle’s logic, metaphysics, and biology is an important one, and warrants more study.
Gotthelf, Allan, "Division and Explanation in Aristotle's Parts of Animals" (1991). The Society for Ancient Greek Philosophy Newsletter. 241.