These remarks lead us to the nature of definition, which is one of the important designations growing out of the operation of generalizing. To define, is to limit, settle, and specify the exact compass of the properties common to a class. Usually tills is done by means of language; but in reality it is, and must be done, by a reference, direct or remote, to the particulars themselves. This reference frequently has the appearance of being dispensed with. The reason is that many general notions are compounded of others, and we can understand the composite notion from its components, without going further; that is, without producing particulars. Thus, a circle in the abstract might be made intelligible by pointing to a number of concrete circles, such as are drawn in Euclid; we should then have to impress on our minds a sufficient number of these to pre vent its from ever associating with the general idea any one size, or any one color of the outline (which must be drawn in black, red, blue, or some other color). No one circle is really the general notion; this must be nothing less than a multitude of actual circles, which the mind apprehends by turns, so as to be sure of never affirming any attribute as common that is in fact peculiar to one or a few. But the concept, circle, can be got at in another way. If we determine first what is called a "point" in space, and a "line" proceeding from that point, and made to revolve around it, the other extremity of the revolving line will mark a course which is a circle. Here, if we possess ourselves of the simple notions or concepts, point, line, revolution, we may attain to the notion, circle, without examining actual circles in the concrete. So we may define an oval, or ellipse, and many other figures. This practice of referring to a simpler order of concepts for
the constituents of a given one, is the main function of the definition, which applies, therefore, to complex notions, and not to such as are ultimate, or simple in the extreme degree. To define in the last resort, we must come to quoting the,partieulars. We can not define a line by anything more elementary. To say, with Euclid, that it is length without breadth, is no assistance, as we Must still go to our experience for examples of length; and length is not a more simple idea than line, being, in fact, but another word for the same thing. Nevertheless, it has been often supposed that there are general notions independent of all experience, or reference to particulars; the form commonly given to the foundations of the science of mathematics having favored this view.
The name "genus" is also connected with the present subject. It is co-relative with another word, "species," which, however, is itself to some extent a generalization; for every species is considered to have individuals under it. Thus, in zoology, fells is a genus of animals, and the lion, tiger, cat, etc., are among its species; but each of those species is the generalization of an innumerable number of 'individual lions,- tigers, etc., differing considerably from one another, so that to express the species we are still obliged to have recourse to the operations of comparison, abstraction, and definition. Genus and species, therefore, introduce to us the existence of successive generalizations, more and more extensive in their range of application, and possessing, in consequence, a smaller amount.of. similarity or community of feature (see .E'rEasiSION).