§ 400. There is no better test, however, of the soundness of a division than to try whether the species overlap, that is to say, whether there are any individuals that would fall into two or more of the classes. When this is found to be the case, we may be sure that we have mixed two or more different fundamenta divisionis. If man, for instance, were to be divided into European, American, Aryan, and Semitic, the species would overlap; for both Europe and America contain inhabitants of Aryan and Semitic origin. We have here members of a division based on locality mixed up with members of another division, which is based on race as indicated by language. § 401. The classes which are arrived at by an act of division may themselves be divided into smaller classes. This further process is called Subdivision. § 402. Let it be noticed that Rule 1 applies only to a single act of division. The moment that we begin to subdivide we not only may, but must, adopt a new basis of division; since the old one has, 'ex hypothesi,' been exhausted. Thus, having divided men according to the colour of their skins, if we wish to subdivide any of the classes, we must look out for some fresh attribute wherein some men of the same complexion differ from others, e.g. we might divide black men into woolly-haired blacks, such as the Negroes, and straight-haired blacks, like the natives of Australia. § 403. We will now take an instance of division and subdivision, with a view to illustrating some of the technical terms which are used in connection with the process. Keeping closely to our proper subject, we will select as an instance a division of the products of thought, which it is the province of logic to investigate. Product of thought _______________|____________________________ | | | Term Proposition Inference ____|___ ______|_____ _____|______ | | | | | | Singular Common Universal Particular Immediate Mediate ___|___ ___|___ | | | | A E I O Here we have first a threefold division of the products of thought based on their comparative complexity. The first two of these, namely, the term and the proposition, are then subdivided on the basis of their respective quantities. In the case of inference the basis of the division is again the degree of complexity. The subdivision of the proposition is carried a step further than that of the others. Having exhausted our old basis of quantity, we take a new attribute, namely, quality, on which to found the next step of subdivision.