But it is evident that rational signs admit of almost numberless degrees of complexity and elaboration; so that reason itself does not present a greater variety of manifestations in this respect than does the symbolism whereby it is expressed: an algebraical formula is included in the same category of sign-making as the simplest gesture whereby we intentionally communicate the simplest idea. Rational signs, therefore, may be made by gesture, by tone, by articulation, or by writing—using each of these words in its largest sense.[58] The following schema may serve to show this classification in a diagrammatic form—_i.e._ the classification which I have myself arrived at, and which follows closely the one given by Mr. Mivart. Indeed, there is no difference at all between the two, save that I have endeavoured to express the distinction between signs as intentional, unintentional, natural, conventional, emotional, and intellectual. The subdivision of the latter into denotative, connotative, denominative, and predicative, will be explained in Chapter VIII. [Illustration: LANGUAGE, OR SIGN-MAKING.] Or, neglecting the unintentional and merely initiative signs as not, properly speaking, signs at all, every kind of intentional sign may be represented diagrammatically as in the illustration opposite. Now, thus far we have been dealing with matters of fact concerning which I do not think there can be any question. That is to say, no one can deny any of the statements which this schema serves to express; a difference of opinion can only arise when it is asked whether the sundry faculties (or cases) presented by the schema are developmentally continuous with one another. To this topic, therefore, we shall now address ourselves. First let it be observed that there can be no dispute about one point, namely, that all the faculties or cases presented by the schema, with the single exception of the last (No. 7), are common to animals and men. Therefore we may begin by taking as beyond the reach of question the important fact that animals do present, in an unmistakable manner, a _germ_ of the sign-making faculty. But this fact is so important in its relation to our subject, that I shall here pause to consider the modes and degrees in which the faculty is exhibited by animals. * * * * *