7. It has sometimes been said that Connotation is in inverse ratio [1] to Denotation. Mill explains the fact upon which any such idea rests. [2] If we arrange things in classes, such that the one class includes the other--_e.g. Species_ “Buttercup,” _Genus_ “Ranunculus,” _Order_ “Ranunculaceae,”--of course the genus will contain many species besides the one mentioned, and the order many genera besides the one mentioned. The object of the arrangement is that they should do so, and thus bring out the graduated natural affinities which prevail in the world. Thus the denotation of the genus-name is larger than that [3] of the species, and the denotation of the order-name is larger than that of the genus-name. [1] See Venn, p. 174, for reference to Hamilton. Venn points out the fallacy. [2] _Logic_, Bk. I. ch. vii. § 5. [3] Or “than the species,” if we take the denotation as made up of species. But further, in such an arrangement the genus can contain only the attributes which are common to all the species, and the order can contain only the attributes which are common to all the genera; so the genus-name implies fewer attributes (less connotation) than any one species-name under it, and the order-name implies fewer attributes (less connotation) than any one genus-name under it. That is the fact which suggests the conception of Denotation and Connotation as varying inversely. But in any case it would not be right to speak thus mathematically of an inverse ratio, because there is no meaning in a numerical comparison of attributes and {95} individuals, and the addition of one attribute will exclude sometimes more and sometimes fewer individuals. [1] [1] See Jevons, p. 40.