[1] See Jevons, p. 40.
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.
So we can only say, “the greater the denotation the less the connotation,” and “vice versâ”, in as far as we arrange ideas by progressive abstraction in the sense of progressive omission. But it is not the only way of regarding them. Things may develop new inter-relations as their number increases. Has the community, as Mr. Bradley asks, less meaning than the individual person? But we must not consider the community, would be the answer; we must simply consider the relation of an idea of one individual to any idea that applies to many individuals. This is simply to rule out those relations that arise within progressively larger wholes. We can do so, if we think the exclusion necessary in the interests of logical purity, but it is only by doing so that we can maintain the traditional view of connotation and denotation. It is worth while to think out the {97} matter for ourselves in relation to such familiar ideas as those of man and animal. It is plain that the idea of “animal” cannot omit all reference to intelligence, but must in some way allow for the different phases of this property which run throughout the animal kingdom, and only find a climax in man. And it is plain also, that even if intelligence were wholly omitted, this would not leave behind, as in a simple stratification, properties in which the whole animal kingdom was the same. Man’s animality is modified throughout in a way corresponding to his rationality, so that no general idea could be framed including him and other animals, simply by collecting properties which are the same and omitting those which are different. The idea of “man” really becomes richer when considered in the light of a comparison [1] with the rest of the animal world. Our great systems of natural classification, representing affinities graduated by descent, are what give the view which we have criticised a certain objective importance. But they do not establish it as an exclusive logical doctrine.
[1] If we insist on throwing the whole of this comparison, in explicit shape, into the complete idea of man, then the progress to the idea “animal” can add nothing; even so, however, it loses nothing, but simply becomes the same set of relations, looked at, so to speak, from the other end.
{98}
LECTURE VI PARTS OF THE JUDGMENT, AND ITS UNITY
Parts of the Judgment
1. The result of taking the Judgment as one with the Proposition has been to assume that its parts were the same as those of the Proposition; [1] and moreover the same as those of the Proposition in a very artificial form, viz. as analysed into three separable elements, “Subject,” “Predicate,” “Copula,” commonly represented in the examples of the text-books by Substantive, Adjective or Substantive, and the Verb “is.”
[1] This assumption involves (see Lecture V.) a confusion between the Proposition as thoroughly understood, and the Proposition as a series of partially significant sounds or signs. For obvious reasons, this confusion is very readily made.