Ordinarily our notion or concept of the common features signified by general names is vague and hazy. The business of Logic is to make them clear. It is to this end that the individual objects of the class are summoned before the mind. In ordinary thinking there is no definite array or muster of objects: when we think of "dog" or "cat," "accident," "book," "beggar," "ratepayer," we do not stop to call before the mind a host of representatives of the class, nor do we take precise account of their common attributes. The concept of "house" is what all houses have in common. To make this explicit would be no easy matter, and yet we are constantly referring objects to the class "house". We shall see presently that if we wish to make the connotation or concept clear we must run over the denotation or class, that is to say, the objects to which the general name is applied in common usage. Try, for example, to conceive clearly what is meant by house, tree, dog, walking-stick. You think of individual objects, so-called, and of what they have in common. A class may be constituted on one property or on many. There are several points common to all houses, enclosing walls, a roof, a means of exit and entrance. For the full concept of the natural kinds, _men_, _dogs_, _mice_, etc., we should have to go to the natural historian. DEGREES OF GENERALITY. One class is said to be of higher generality than another when it includes that other and more. Thus animal includes man, dog, horse, etc.; man includes Aryan, Semite, etc.; Aryan includes Hindoo, Teuton, Celt, etc. The technical names for higher and lower classes are GENUS and SPECIES. These terms are not fixed as in Natural History to certain grades, but are purely relative one to another, and movable up and down a scale of generality. A class may be a species relatively to one class, which is above it, and a genus relatively to one below it. Thus Aryan is a species of the genus man, Teuton a species of the genus Aryan. In the graded divisions of Natural History genus and species are fixed names for certain grades. Thus: Vertebrates form a "division"; the next subdivision, _e.g._, Mammals, Birds, Reptiles, etc., is called a "class"; the next, _e.g_., Rodents, Carnivora, Ruminants, an "order"; the next, _e.g._, Rats, Squirrels, Beavers, a "genus"; the next, _e.g._, Brown rats, Mice, a "species". Vertebrates (division). | Mammals, Birds, Reptiles, etc. (class). | Rodents, Ruminants, Carnivors, etc. (order). | Rats, Squirrels, Beavers, etc. (genus). | Brown rats, Mice, etc. (species). If we subdivide a large class into smaller classes, and, again, subdivide these subdivisions, we come at last to single objects.