And there are more important objections to the whole idea of a corresponding gradation in these two kinds of meaning. The idea of abstraction thus implied is altogether wrong. The meaning of a genus-name does not _omit_ the properties in which the species differ. If it did, it would omit nearly all properties. What happens is that the genus-idea represents the general plan on which the species are built, but provides for each of the parts that constitute the whole, varying in the specific cases within certain limits. Thus in the Ranunculaceae some species have no petals. But we do not omit the character “petals” from the genus-idea. We state the general plan so far as this element is concerned as “Petals five or more; rarely none.” This is read by a botanist to mean that in some groups the petals tend to be aborted, and sometimes are actually missing. In a symbolic representation of the genus-idea such a property may stand as A, and its various specific forms as A1, A2, A3, etc. There is nothing to prevent these specific phases approaching and sometimes reaching zero. No doubt if the classification is pursued in the direction of “universals” containing fewer and fewer properties, it is possible to arrive at concepts which appear to have a larger denotation and a smaller connotation than those “below” them. “Ranunculaceae,” “Dicotyledons,” “Plants,” “Organisms.” But this is only because we choose to form our system by that process of abstraction which consists in leaving out properties. _E.g._ comparing Frenchmen with men in general, {96} we assume that “Frenchman” indicates (_a_) all the qualities of humanity as such, and (_b_) the qualities of French humanity in addition to these. But is this so in fact? Humanity, considered as a wider, and therefore as a deeper, idea, may have more content, as well as more area, than Frenchmanity. We do not really, in thinking of humanity, omit from our schematic thought all references to qualities of Greek, Jew, English, and German, and their bearing and interaction upon one another. It is only that we have been drilled to assume a certain neatness in the pyramidal arrangement by which we vainly try to reduce the meaning of a great idea to something that has no system and no inter-relation of parts, but approaches as near as possible in fixity to the character of a definite image, though far removed from such a character in the impossibility of bringing it before the mind.