In the Sophist, Plato introduces a procedure of “Division” as a method for discovering definitions.
To find a definition of X, first locate the largest kind of thing under which X falls; then, divide that kind into two parts, and decide which of the two X falls into.
Repeat this method with the part until X has been fully located.
This method is part of Aristotle’s Platonic legacy.
His attitude towards it, however, is complex.
He adopts a view of the proper structure of definitions that is closely allied to it:
a correct definition of X should give the genus (genos: kind or family) of X, which tells what kind of thing X is, and the differentia (diaphora: difference) which uniquely identifies X within that genus. [NB]
Something defined in this way is a species (eidos: the term is one of Plato’s terms for “Form”), and the differentia is thus the “difference that makes a species” (eidopoios diaphora, “specific difference”).
In Posterior Analytics II.13, he gives his own account of the use of Division in finding definitions.
However, Aristotle is strongly critical of the Platonic view of Division as a method for establishing definitions.
In Prior Analytics I.31, he contrasts Division with the syllogistic method he has just presented, arguing that Division cannot actually prove anything but rather assumes the very thing it is supposed to be proving.
He also charges that the partisans of Division failed to understand what their own method was capable of proving.