In the context of definition, the class whose membership is divided into…

Concept. Classical logic defines a term by locating it inside a hierarchy of classes. A wider class whose membership is divided into narrower subclasses is called the genus, and each narrower subclass carved out of it is called a species. The two names are relative rather than absolute: one and the same class is a genus with respect to the subclasses lying under it and a species with respect to the wider class lying above it. This pair is what makes the classical rule of definition work, namely definition per genus et differentiam: state the genus, then add the differentia that marks the defined term off from the other subclasses of that genus.

Application. The stem asks for the name of the class that undergoes the division, not for the name of what the division produces.

1. Separate the two roles named in the stem: one class is divided, and several narrower classes result from that division.

2. Match each role to its logical name: the class that is divided is the genus, and the narrower classes produced by the division are its species.

3. Test the match on an example: the class "polygon" divides into triangle, quadrilateral and pentagon, so "polygon" is the genus and "triangle" is one of its species.

Cross-check. The remaining terms either sit at the other end of the same pair or belong to a different vocabulary altogether:

• "Species" names what the division produces, so it lies one level below the class that is divided rather than being that class.

• "Set" is a term of modern mathematics for any well-defined collection of distinct objects; sets are related to one another by the subset relation, not by the ranked kinds that the classical logic of definition works with.

• "Group" in strict usage is an algebraic structure, a set closed under an associative operation with an identity and inverses, and in loose usage merely an informal collection; neither sense is the logical name for a dividing class.

Result. The class whose membership is divided into subclasses is the genus.