 Aristotle proposes a solution that applies to definitions reached by the “method of division.” According to this method (see  Aristotle’s logic),  one begins with the broadest genus containing the species to be defined, and divides the genus into two sub-genera by means of some differentia. One then locates the definiendum in one of the sub-genera, and proceeds to divide this by another differentia, and so on, until one arrives at the definiendum species. This is a classic definition by genus and differentia. Aristotle’s proposal is that “the division should take the differentia of the differentia” (1038a9). For example, if one uses the differentia footed to divide the genus animal, one then uses a differentia such as cloven-footed for the next division. If one divides in this way, Aristotle claims, “it is evident that the ultimate (or completing, teleutaia) differentia will be the substance of the thing and its definition” (1038a19). For each “differentia of a differentia” entails its predecessor (being cloven-footed entails being footed), and so the long chain of differentiae can be replaced simply by the ultimate differentia, since it entails all of its predecessors. As Aristotle points out, it would be redundant to include any of the differentiae in the chain other than the ultimate one: “when we say footed two-footed animal … we shall be saying the same thing several times over” (1038a22–24).