The New International Encyclopædia/Division

DIVISION (OF. devision, division, Fr. division, from Lat. divisio, from dividere, to divide). In logic, the process of distributing all the objects included in the deuotation (q.v.) of a concept (q.v.) into mutually exclusive classes, each of which is marked off from the others by the possession of some distinctive attribute. Logical division must not be confounded with physical division. In the former the whole (called genus) can be predicated of the resultant parts (called species, see Predicables); in the latter such predication is not possible. Thus, when Cuvier divided his order of primates (q.v.) into homo, simia, lemur, and vespertilio, he performed a logical division because the whole thus divided, primate, is predicable of every one of the parts obtained; in other words, it can be said that man is a primate. But when a man is dissected into head, trunk, feet, etc., the division is not logical, but physical, because the whole cannot be predicated of the parts; we cannot say that the head is a man. Traditional logic generally gives the following rules for correct division: First, the division must be exhaustive; i.e. the sum of the denotations of the species must be exactly equal to the denotation of the genus. Second, the division must be exclusive: i.e. no object found in the denotation of any species must be found in the denotation of any other species. Third, in order to secure conformity to the above rules the division should be based on some one characteristic in regard to which the various objects in the denotation of the concept to be divided differ from each other. This characteristic used as the basis of division is called the fundamentum divisionis. Thus when plane triangles are divided into scalene, isosceles, and equilateral triangles, the fundamentum divisionis is the relative length of the sides of triangles.