Any given genus may be a species of some higher class. That is, “man,” which is a genus with reference to the kinds of men, is a species of the higher class “biped,” while “biped” is a species of “animal,” “animal” a species of “organized being,” “organized being” of “material being,” “material being” of “being.” But here we stop, as there is no higher grade to which “being” can be referred. This highest genus takes the name of _summum genus_. Similarly any given species may be a genus of some lower class. “White man,” for example, which is a species of “man,” is a genus of “American,” “Englishman,” “German,” “Frenchman,” etc. “American” is a genus of “New Yorker,” “Californian,” etc., while “New Yorker” is a genus of “Smith of Jamaica.” This last term is an individual and cannot be subdivided. It represents the lowest possible species and is referred to in logic as _infima species_. It is obvious that the highest genus cannot become a species, neither can the lowest species become a genus. PROXIMATE GENUS. The proximate genus is the next class above. To illustrate: “Animal” is a genus of “man,” but “biped” is the proximate genus of “man.” “Quadrilateral” is the genus of “square,” but “rectangle” is the proximate genus. The next class above “trigon” is _polygon_ not _figure_. Hence “polygon” is the proximate genus of “trigon.” GENUS AND SPECIES OF NATURAL HISTORY. In natural history the following terms are used to denote the various grades of kinship in any scheme of classification: (1) kingdom, (2) class, (3) order, (4) family, (5) genus, (6) species, (7) variety, (8) the individual thing. Here “genus” and “species” are absolute not relative and occupy a _fixed_ place in the scheme, while from a logical viewpoint any of the grades indicated between the lowest and highest would be the species of the next higher grade or a genus of the next lower; e. g., _order_ is a species of “class,” while it is the genus of “family.” GENUS, A DOUBLE MEANING. We recall that any class name or genus has a double use, extensional and intensional. When considered from the standpoint of its extension, a genus represents a group of objects or is _mathematical_ in its application, but when used in an intensional sense it represents a group of qualities or is _logical_ in its application. Considered extensionally the genus refers to a larger number of objects than the species. But when viewed intensionally the species refers to more qualities than the genus. This was made clear when discussing the law of variation in the extension and intension of terms. (3) _Differentia._ _The differentia of a term is that attribute which distinguishes a given species from all the other species of the genus._